Quantum Mechanics: All Exams

8.22. One of the properties of a valid wave function is that in order to __ the wave function, the function must approach __ as x approaches __. a. normalize; infinity; infinity b. equalize; zero; zero c. normalize; zero; infinity d. equalize; zero; infinity e. none of the above

c. One of the properties of a valid wave function is that in order to normalize the wave function, the function must approach zero as x approaches infinity.

11.24. Quantum mechanics allows L to be quantized along __ in space. a. all directions b. two directions c. only one direction d. three directions e. none of the above

c. Quantum mechanics allows L to be quantized along only one direction in space.

7.29. Three foundational concepts are combined to form a logical interpretation of the physical meaning of quantum theory. The three concepts are (a) Heisenberg's __ principle, (b) Bohr's __ principle, and (c) Born's __ interpretation based on __ determined by the wave function. a. complementarity; statistical; probabilities; uncertainty b. uncertainty; complementarity; statistical; probabilities c. statistical; probabilities; uncertainty; complementarity d. uncertainty; statistical; probabilities; complementarity e. none of the above

b. Three foundational concepts are combined to form a logical interpretation of the physical meaning of quantum theory. The three concepts are (a) Heisenberg's uncertainty principle, (b) Bohr's complimentarity principle, and (c) Born's statistical interpretation based on probabilities determined by the wave function.

13.17. Transition metals have __-shell electrons with unpaired spins. a. s b. d c. p d. f e. none of the above

b. Transition metals have d-shell electrons with unpaired spins.

12.3. When there are 2 electrons in an atom's electron shells, the 2 electrons __. a. attract each other b. repel each other c. exert no force on each other d. merge with the nucleus e. none of the above

b. When there are 2 electrons in an atom's electron shells, the 2 electrons repel each other.

12.16. The second rule that determines the structure of the periodic-table of the elements is that __ can be in a state with a given (complete) set of __ (Pauli exclusion principle). a. only one proton; quantum numbers b. only two protons; nuclear levels c. only one electron; quantum numbers d. only two electrons; nuclear levels e. none of the above

c. The second rule that determines the structure of the periodic-table of the elements is that only one electron can be in a state with a given (complete) set of quantum numbers (Pauli exclusion principle).

13.27. The spin angular momentum is denoted by __. a. SAM b. A c. S d. M e. none of the above

c. The spin angular momentum is denoted by S.

13.24. The total angular momentum (for an atom) = __ angular momentum + __ angular momentum. a. linear; rotational b. orbital; linear c. orbital; spin d. parabolic; exponential e. none of the above

c. The total angular momentum (for an atom) = orbital angular momentum + spin angular momentum.

13.30. The total angular momentum of an electron in an atom is __. a. angularized b. continuous c. quantized d. analog e. none of the above

c. The total angular momentum of an electron in an atom is quantized.

8.8. The wave function of the particle is given by Psi(x,t) = __. a. A*[cos(kx-wt) * i*sin(kx-wt)] b. A*[cos(kx-wt) / i*sin(kx-wt)] c. A*[cos(kx-wt) + i*sin(kx-wt)] d. A+[cos(kx-wt) - i*sin(kx-wt)] e. none of the above

c. The wave function of the particle is given by Psi(x,t) = A*[cos(kx-wt) + i*sin(kx-wt)].

10.1 For a particle in a square-well potential, the particle is viewed as being trapped in a 3-D box __ walls that the particle __. a. without; is not limited by b. with soft; can penetrate c. with infinitely hard; cannot penetrate d. with intermediate; cannot penetrate e. none of the above

c. For a particle in a square-well potential, the particle is viewed as being trapped in a 3-D box with infinitely hard walls that the particle cannot penetrate.

13.12. Halogens need __ to fill the outermost subshell. a. two more electrons b. three more electrons c. one more electron d. four more electrons e. none of the above

c. Halogens need one more electron to fill the outermost subshell.

4.26. In Rutherford scattering, when the impact parameter b is small, the incoming particle can be __. a. repelled forward b. attracted forward c. repelled backward d. attracted backward e. none of the above

c. In Rutherford scattering, when the impact parameter b is small, the incoming particle can be repelled backward.

10.18. In the Schrodinger Wave Equation for a two-body problem, i*cross*del psi / del t = __. a. - (hcross^2/2m) / del^2 psi/ del x^X * V psi b. - (hcross^2/2m) * del^2 psi/ del x^X + V psi c. - (hcross^2/2m) + del^2 psi/ del x^X + V psi d. - (hcross^2/2m)- del^2 psi/ del x^X * V psi e. none of the above

b. In the Schrodinger Wave Equation for a two-body problem, i*cross*del psi / del t = - (hcross^2/2m) * del^2 psi/ del x^X + V psi.

10.27. Solving the Schrodinger equation for an atom, with appropriate __, leads to the quantum number __ and __. a. boundary equations; 1; 2 b. boundary conditions; l; ml c. internal constants; n; s d. external variables; n; l e. none of the above

b. Solving the Schrodinger equation for an atom, with appropriate boundary conditions, leads to the quantum number l and _ml.

10.8. The 3-D differential equations for a square-well potential can be separated out into three __ __ equations. a. connected; algebraic b. separated ordinary; differential c. separated; exponential d. connected ordinary; integral e. none of the above

b. The 3-D differential equations for a square-well potential can be separated out into three separated ordinary differential equations.

13.23. The actinides are all __. a. compounds b. radioactive c. not radioactive d. mixtures e. none of the above

b. The actinides are all radioactive.

7.15. The phase constant phi shifts the wave along the __. The corresponding wave equation is psi(x,t) = __. a. x axis; A/sin(kx+wt-phi) b. x axis; A*sin(kx-wt+phi) c. y axis; A/sin(kx+wt+phi) d. y axis; A*sin(kx-wt-phi) e. none of the above

b. The phase constant phi shifts the wave along the x-axis_. The corresponding wave equation is psi(x,t) =A*sin(kx-wt+phi).

12.29. The principal quantum number designates the __ shell, __ shell etc. a. s;p b. K; L c. m1; m2 d. +1/2; -1/2 e. none of the above

b. The principal quantum number designates the K shell, L shell etc.

13.29. The spin angular momentum (of an electron in an atom) is __. a. continuous b. quantized c. zero d. infinite e. none of the above

b. The spin angular momentum (of an electron in an atom) is quantized.

7.27. The __ Rule or law states that the __ probability of finding the electron is __. Forcing this condition on the wave function is called __. a. Planck; partial; 0.5; halfization b. Heisenberg; total; 1; unitarization c. Einstein; partial; 0.5; halfization d. Born; total; 1; normalization e. none of the above

d. The Born Rule or law states that the total probability of finding the electron is 1. Forcing this condition on the wave function is called normalization.

9.3. The Expectation value is the __ result of the __ of many measurements of a given quantity. The expectation value of x is denoted by __. a. normalized; sum; [x] b. expected; average; <x] c. normalized; intergral; [x> d. expected; average; <x> e. none of the above

d. The Expectation value is the expected result of the average of many measurements of a given quantity. The expectation value of x is denoted by <x>.

8.17. The Probability of the particle being between x1 and x2 is given by P = integral from x1 to x2 of __. a. Psi' - Psi dx b. Psi' + Psi dx c. Psi' / Psi dx d. Psi' * Psi dx e. none of the above

d. The Probability of the particle being between x1 and x2 is given by P = integral from x1 to x2 of Psi' * Psi dx.

9.7. The Time derivative of the free-particle wave function is del Psi/ del t = __, where a. -i*w+e^(i*(kx+wt) b. -i*w-e^(i*(kx/wt) c. -i*w/e^(i*(kx*wt) d. -i*w*e^(i*(kx-wt) e. none of the above

d. The Time derivative of the free-particle wave function is del Psi/ del t = -i*w*e^(i*(kx-wt), where

13.8. The electrical conductivity of alkali elements is __. a. infinite b. zero c. very low d. relatively good e. none of the above

d. The electrical conductivity of alkali elements is relatively good.

4.30. In Rutherford scattering, particles with __ impact parameters approach the nucleus __ and scatter to the __ angles. a. large; most closely; smallest b. small; most distantly; smallest c. large; most distantly; largest d. small; most closely; largest e. none of the above

d. In Rutherford scattering, particles with small impact parameters approach the nucleus most closely and scatter to the largest angles.

5.6. In Rutherford scattering, the number of scattered particles (per unit area) is __ proportional __ sin(theta/2), where theta is the scattering angle. a. directly; to b. directly; to the fourth power of c. inversely; to d. inversely; to the fourth power of e. none of the above

d. In Rutherford scattering, the number of scattered particles (per unit area) is inversely proportional to the fourth power of sin(theta/2), where theta is the scattering angle.

9.27. In a classical simple harmonic oscillator operating in a __ potential well, the lowest energy level is __, this __ the uncertainty principle. a. parabolic; one; is consistent with b. square; infinity; violates c. square; two; is consistent with d. parabolic; zero; violates e. none of the above

d. In a classical simple harmonic oscillator operating in a parabolic potential well, the lowest energy level is zero, this violates the uncertainty principle.

9.19. In the case of an infinite-potential square well, the energy for n = 1 is called the __ energy. a. first state b. unitary c. finite state d. ground state e. none of the above

d. In the case of an infinite-potential square well, the energy for n = 1 is called the ground state energy.

9.17. In the case of an infinite-potential square well, the quantized wave number becomes kn = __. a. n*pi*L * sqrt(2*m*En/hcross^2) b. n*pi/L + sqrt(2*m*En/hcross^2) c. n*pi*L - sqrt(2*m*En/hcross^2) d. n*pi/L = sqrt(2*m*En/hcross^2) e. none of the above

d. In the case of an infinite-potential square well, the quantized wave number becomes kn = n*pi/L = sqrt(2*m*En/hcross^2).

1.10. In the particle theory of light travels in ____. a. spirals b. straight lines c. elliptical orbits d. curved lines e. none of the above

(b) In the particle theory of light travels in straight lines.

3.25 In field emission, a strong ____ _____ field pulls the _____ out of the material. a. internal; electric; photon b. external; magnetic; photon c. external; electric; electron d. internal; magnetic; electron e. none of the above

(c) In field emission, a strong external electric field pulls the electron out of the material.

The normalized spherical harmonic Y(theta, phi) for the quantum numbers l = o and ml = o is __. a. 2*sqrt(pi) b. 2*pi c. 1/(2*pi) d. 1/(2*sqrt(pi)) e. none of the above

(d.) The normalized spherical harmonic Y(theta, phi) for the quantum numbers l = o and ml = o is 1/(2*sqrt(pi)).

13.11. Alkaline Earth elements have __ electrical conductivity. a. high b. low c. zero d. infinite e. none of the above

a. Alkaline Earth elements have high electrical conductivity.

3.6 When matter is headed, it emits ____. a. radiation b. alpha-rays c. X-rays d. gamma rays e. none of the above

(a) When matter is heated, it emits radiation.

2.9. X-rays penetrated materials ___ cathode rays. a. more than b. less than c. to the same extent as d. all of the above e. none of the above

(a) X-rays penetrated materials more than cathode rays.

The three quantum numbers are __, __, and __. a. s; p; d b. n; l; ml c. n; k; m d. k; l; m e. none of the above

(b.) The three quantum numbers are n, l, and ml.

10.20. In the Schrodinger Wave Equation for a two-body problem, the Eigen Value Operator is __. a. E b. V c. H d. hcross e. none of the above

c. In the Schrodinger Wave Equation for a two-body problem, the Eigen Value Operator is H.

12.28. The electronic designation for the electrons in a helium atom is __. a. 1s1 b. 2p2 c. 1s2 d. 2s2 e. none of the above

c. The electronic designation for the electrons in a helium atom is 1s2.

7.11. The period of a matter wave is given by T= __. a. lambda+v = 1+f b. lambda*v = 1*f c. lambda/v = 1/f d. lambda-v = 1-f e. none of the above

c. The period of a matter wave is given by T= lambda/v = 1/f.

12.7. Wolfgang Pauli proposed an exclusion principle to help explain __ data for __ frequencies. a. molecular; supersonic b. atomic; subsonic c. atomic spectroscopic; optical d. nuclear; optical e. none of the above

c. Wolfgang Pauli proposed an exclusion principle to help explain atomic spectroscopic data for optical frequencies.

9.25. A Quantum state is __ when there is more than one wave function for a given energy. This is a result of __. __ results from particular properties of the potential energy function that describes the system. A __ of the potential energy can remove the __. a. discrete; symmetry; Discrete; continuity; discrete state b. degenerate; antisymmetry; Discrete; perturbation; discrete state c. discrete; antisymmetry; Degeneracy; continuity; degeneracy d. degenerate; symmetry; Degeneracy; perturbation; degeneracy e. none of the above

d. A Quantum state is degenerate when there is more than one wave function for a given energy. This is a result of symmetry. Degeneracy results from particular properties of the potential energy function that describes the system. A perturbation of the potential energy can remove the degeneracy.

3.8 Black body radiation is theoretically interesting because the radiation properties of the black body are ____ the particular ___ of the body. a. dependent on; material b. dependent on; shape c. independent of; material d. independent of; shape e. none of the above

(c) Blackbody radiation is theoretically interesting because the radiation properties of the blackbody are independent of the particular material of the body.

1.6. Particles transfer energy via ____ interactions. a. relativistic b. quantum mechanical c. point mass d. wave mass e. none of the above

(c) Particles transfer energy via point mass interactions.

3.2. The charge of an electron is __ coulombs. a. 1.602E-1.9 b. 1.602E-190 c. 1.602E-19 d. 1.602E-1900 e. none of the above

(c) The charge of an electron is 1.602E-19.

The principal quantum number can take the values n = __. a. 0, 1, 2, 3, ... b. +1/2; -1/2 c. 1, 2, 3, 4, ... d. 0; +1/2; -1/2 e. none of the above

(c.) The principal quantum number can take the values n = 1, 2, 3, 4, ....

2.12. ___ were discovered by J.J. Thomson. a. protons b. neutrons c. atoms d. electrons e. none of the above

(d) Electrons were discovered by J.J. Thomson.

2.15. ___ rays are generated when two plates are held in a vacuum with a large ___ potential between them. a. anode; electric b. cathode; electric c. X-; magnetic d. cathode; magnetic e. none of the above

15. Cathode rays are generated when two plates are held in a vacuum with a large electric potential.

1.17. Avogadro proposed that all gases at the same ____, ____ and ____ contain the same ____. a. pressure; volume; temperature; number of molecules or atoms b. density; volume; temperature; mass c. pressure; mass; temperature; number of molecules or atoms d. pressure; volume; wavelength; density e. none of the above

(a) Avogadro proposed that all gases at the same pressure, volume, and temperature contain the same number of molecules or atoms.

1.11. Newton promoted the ____ theory of light. a. particle b. wave c. complementarity d. statistical e. none of the above

(a) Newton promoted the particle theory of light.

The maximum __ energy of photoelectrons depends on the value of the light __ and not on the __ of the light that stimulated the photoemission. a. kinetic; frequency; intensity b. kinetic; intensity; frequency c. potential; frequency; intensity d. potential; intensity; frequency e. none of the above

(a) The maximum kinetic energy of photoelectrons depends on the value of light frequency and not on the intensity of the light that stimulated the photoemission.

10.13. A solution to the Schrödinger equation for a particle in an infinite square-well potential is psi(x,y,z) = __. a. A* sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) b. A* sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) / sin(nx*pi*x/Lx) c. A/ sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) / sin(nx*pi*x/Lx) d. A/ sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) e. none of the above

a. A solution to the Schrödinger equation for a particle in an infinite square-well potential is psi(x,y,z) = A* sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx) * sin(nx*pi*x/Lx).

11.15. An atomic energy level or state with n = 3 and l = 2 is called a __ state. a. 3d b. 3s c. 3p d. 3m e. none of the above

a. An atomic energy level or state with n = 3 and l = 2 is called a 3d state.

11.27. An electron orbiting an atom results in a current loop with a magnetic moment mu = __ and a period T = __. a. I*A; 2*pi*4/v b. I*A; pi*4/v c. I*A^2; pi*4/v d. I^2*A; 2*pi*4/v e. none of the above

a. An electron orbiting an atom results in a current loop with a magnetic moment mu = l*A and a period T = 2*pi*4/v.

9.4. Any measurable quantity for which we can calculate the expectation value is called a __. The expectation values of __ (for example, position, linear momentum, angular momentum, and energy) must be _, because the experimental results of measurements are __. a. physical observable; physical observables; real; real b. metaphysical observable; metaphysical observables; real; meta-real c. physical non-observable; physical non-observables; unreal; unreal d. metaphysical non-observable; metaphysical observables; meta-real; real e. none of the above

a. Any measurable quantity for which we can calculate the expectation value is called a physical observable. The expectation values of physical observables (for example, position, linear momentum, angular momentum, and energy) must be real, because the experimental results of measurements are real_.

11.25. Based on Quantum Mechanics, the average of the angular momentum squared is given by <L^2> = __. a. l*(l+1)*hcross^2 b. l*(l+1)/hcross^2 c. l*(l+1)*hcross d. l*(l+1)/hcross e. none of the above

a. Based on Quantum Mechanics, the average of the angular momentum squared is given by <L^2> = l*(l+1)*hcross^2.

7.1. Crystals act as three-dimensional __, scattering __ waves and producing observable __ effects. a. gratings; X-ray; interference b. continuum; atomic; reflection c. gratings; light; interference d. continuum; X-ray; diffraction e. none of the above

a. Crystals act as three-dimensional gratings, scattering X-ray waves and producing observable interference effects.

7.26. For a Gaussian wave packet, delta k * delta x = __. a. (delta p /hcross) * delta x = 1/2 b. (delta p /hcross) / delta x = 2 c. (delta p /hcross) + delta x = 1/2 d. (delta p /hcross) - delta x = 2 e. none of the above

a. For a Gaussian wave packet, delta k * delta x = (delta p /hcross) * delta x = 1/2.

10.4. For a particle in a 3-D square-well potential box, at the walls of the box, V(x,y,z) = __. a. infinity b. 100 c. 0 d. 1000 e. none of the above

a. For a particle in a 3-D square-well potential box, at the walls of the box, V(x,y,z) = infinity.

10.6. For a particle in a 3-D square-well, when the functions are independent of coordinate axes, we can set psi(x,y,z) = __. a. X(x)*Y(y)*Z(z) b. X(x)+Y(y)+Z(z) c. X(x)-Y(y)-Z(z) d. X(x)/Y(y)/Z(z) e. none of the above

a. For a particle in a 3-D square-well, when the functions are independent of coordinate axes, we can set psi(x,y,z) = X(x)*Y(y)*Z(z).

6.8. For non-relativistic particles, Total energy = __, where KE is the kinetic energy and PE is the potential energy. a. KE + PE b. KE - PE c. KE * PE d. KE / PE e. none of the above

a. For non-relativistic particles, Total energy = KE + PE, where KE is the kinetic energy and PE is the potential energy.

13.14. Halogens have __ atomic configurations as the p subshell is filled. a. more stable b. less stable c. more complex d. less complex e. none of the above

a. Halogens have more stable atomic configurations as the p subshell is filled.

12.17. Hydrogen: has the following quantum numbers (n, l, ml, ms) = __, __, __, __ in the ground state. a. 1; 0; 0; +/- 1/2 b. 0; 0; 0; 0 c. 0; 0; 0; 1 d. 1; 0; 0; +/- 1 e. none of the above

a. Hydrogen: has the following quantum numbers (n, l, ml, ms) = 1, 0, 0, +/- 1/2 in the ground state.

13.21. In Lanthanides, large orbital __ contributes to large __ effects. a. angular momentum; ferromagnetic b. spin energy; electric c. angular momentum; electric d. spin energy; ferromagnetic e. none of the above

a. In Lanthanides, large orbital angular momentum contributes to large ferromagnetic effects.

5.1. In Rutherford scattering, the scattering cross-section is related to the __ of a particle being __ by a nucleus. a. probability; scattered b. probability; absorbed c. deterministic certainty; absorbed d. deterministic certainty; emitted e. none of the above

a. In Rutherford scattering, the scattering cross-section is related to the probability of a particle being scattered by a nucleus.

4.29. In Rutherford scattering, when the kinetic energy of the incoming atom increases, the impact parameter b __. a. decreases b. increases c. stays the same d. increases and then decreases e. none of the abovedecreases and then increases (Proofread your shit pls)

a. In Rutherford scattering, when the kinetic energy of the incoming atom increases, the impact parameter b decreases.

12.21. In a Helium atom, electrons have __ spins and are __. a. antialigned; paired b. aligned; paired c. antialigned; unpaired d. aligned; unpaired e. none of the above

a. In a Helium atom, electrons have anti-aligned spins and are paired.

5.27. Mosely's empirical results showed that the K-series X-ray is produced from a __ to __ transition. His research clarified the importance of __ for all elements, not just for __. a. n=2; n=1; electron shells; hydrogen b. n=1; n=2; atomic nucleii; helium c. n=1; n=2; electron shells; hydrogen d. n=2; n=1; atomic nucleii; helium e. none of the above

a. Mosely's empirical results showed that the K-series X-ray is produced from a n=1 to n=2 transition. His research clarified the importance of shells for all elements, not just for hydrogen.

9.1. __ can be derived from __, so the __ is the more fundamental. a. Newton's second law; the Schrodinger wave equation; latter b. Newton's second law; the Schrodinger wave equation; former c. The Schrodinger wave equation; Newton's second law; latter d. The Schrodinger wave equation; Newton's second law; former e. none of the above

a. Newton's second law can be derived from the Schrodinger wave equation, so the latter is the more fundamental.

4.21. One of the assumptions of Rutherford Scattering is that the incident particle and target scatterer are __ that they may be treated as __ and __. a. so small; point masses; charges b. so small; extended masses; waves c. so large; extended masses; charges d. so large; point masses; waves e. none of the above

a. One of the assumptions of Rutherford Scattering is that the incident particle and target scatterer are so small that they may be treated as point masses and charges.

11.4. Solving the Schrodinger equation for an atom gives us a quantized energy (for the atom energy levels) of En=___. a. -(mu/2)*[(e^2/(4*pi*epsilonZero*hcross)]^2 * (1/n^2) b. -(mu/2)/[(e^2/(4*pi*epsilonZero*hcross)]^2 * (1/n^2) c. -(mu/2)*[(e^2/(4*pi*epsilonZero*hcross)]^2 / (1/n^2) d. -(mu/2)/[(e^2/(4*pi*epsilonZero*hcross)]^2 / (1/n^2) e. none of the above

a. Solving the Schrodinger equation for an atom gives us a quantized energy (for the atom energy levels) of En= -(mu/2)*[(e^2/(4*pi*epsilonZero*hcross)]^2 * (1/n^2).

11.23. Space quantization is the phenomenon where only certain __ of __ are permitted. a. orientations; L b. values; n c. values; s d. orientations; m e. none of the above

a. Space quantization is the phenomenon where only certain orientations of L are permitted.

6.23. The Electron Double-Slit Experiment demonstrated that precisely the same behavior occurs for both __ (__) and __ (__). a. light; waves; electrons; particles b. electrons; waves; light; particles c. light; electrons; electrons; light d. light; waves; electrons; waves e. none of the above

a. The Electron Double-Slit Experiment demonstrated that precisely the same behavior occurs for both light (waves) and electrons (particles).

7.21. The Electron Double-Slit Experiment, shows double-slit __ effects for electrons by using __ slits and relatively __ between the slits and the observation screen. a. interference; very narrow; large distances b. interference; very wide; small distances c. diffraction; very narrow; small distances d. reflection; very wide; large distances e. none of the above

a. The Electron Double-Slit Experiment, shows double-slit interference effects for electrons by using very narrow slits and relatively large distances between the slits and the observation screen.

6.28. The Heisenberg uncertainty principle states that __ >= hcross/2. a. delta px * delta x b. delta px / delta x c. delta px + delta x d. delta px - delta x e. none of the above

a. The Heisenberg uncertainty principle states that delta px * delta x >= hcross/2.

7.19. The group velocity of the deBroglie wave is given by Ugr = __. a. dE/dp = p*c^2/E b. dE/dp = p/c^2/E c. dE*dp = p*c^2*E d. dE*dp = p/c^2*E e. none of the above

a. The group velocity of the deBroglie wave is given by Ugr = dE/dp = p*c^2/E.

6.5. The lambda of a matter wave is called the __ wavelength. a. de Broglie b. matter c. Planck d. material e. none of the above

a. The lambda of a matter wave is called the de Broglie wavelength.

11.19. The magnetic quantum number is denoted by __. a. ml b. mq c. m d. n e. none of the above

a. The magnetic quantum number is denoted by ml.

12.30. The nl quantum numbers designate the subshells __, __, __ etc. a. 1s; 2p; 3d b. K;L;M c. a;b;c d. 1K;2L;3M e. none of the above

a. The nl quantum numbers designate the subshells 1s, 2p, 3d, etc.

11.7. The orbital angular momentum quantum number l is related to the orbital angular momentum of the electron L by the expression L = __. a. sqrt[l*(l+1)*hcross] b. sqrt[l*(l+1)/hcross] c. [l*(l+1)*hcross] d. [l*(l+1/*hcross] e. none of the above

a. The orbital angular momentum quantum number l is related to the orbital angular momentum of the electron L by the expression L = sqrt[l*(l+1)*hcross].

4.2 The phenomenon of ___ is that certain elements can combine ___ with some elements, but not with others. a. valence; chemically b. reactivity; chemically c. valence; physically d. reactivity; chemically e. none of the above

a. The phenomenon of valence is that certain elements can combine chemically with some elements, but not with others.

12.23. The principal quantum number can take the following numerical values __. a. 1,2,3,4 . . . b. 0,1,2,3,4 . . . c. -4,-3,-2,-1,1,2,3,4 . . . d. -4,-3,-2,-1,0,1,2,3,4 . . . e. none of the above

a. The principal quantum number can take the following numerical values 1,2,3,4....

6.16. The principle of superposition states that two or more waves traverse the same region __ each other. a. act independently of b. act in concert with c. change the frequency of d. change the phase of e. none of the above

a. The principle of superposition states that two or more waves traverse the same region act independently of each other.

12.10. The quantum numbers (for electrons in an atom) are denoted by __, __, __, and __. a. n; l; ml; ms b. s; p; d; f c. k; l; m; n d. primary; secondary; tertiary; quarternary e. none of the above

a. The quantum numbers (for electrons in an atom) are denoted by n, l, ml, and ms.

8.6. The solution of the Schrodinger __ equation describes __ moving in the __ direction. a. wave; a wave; x b. particle; a particle; y c. energy; energy; x d. momentum; a particle; y e. none of the above

a. The solution of the Schrodinger wave equation describes a wave moving in the x direction.

8.9. The __ function __ restricted to being real. a. wave; is not b. wave; is c. particle; is not d. particle; is e. none of the above

a. The wave function is not restricted to being real.

7.25. The wave number k may be rewritten as k = __. a. 2*pi/lambda = 2*pi/(h/p) = p/hcross b. 2*pi*lambda = 2*pi*(h/p) = p*hcross c. pi/lambda = 2*pi/(h/p) = p/hcross d. pi*lambda = 2*pi*(h/p) = p*hcross e. none of the above

a. The wave number k may be rewritten as k = 2*pi/lambda = 2*pi/(h/p) = p/hcross.

4.11 When an alpha particle hits an electron, the maximum momentum change of the alpha particle is given by DPmax = __, where Me is the mass of the electron and Valpha is the incoming velocity of the alpha particle. a. 2*Me*Valpha b. Me*Valpha c. 2*Me/Valpha d. Me/Valpha e. none of the above

a. When an alpha particle hits an electron, the maximum momentum change of the alpha particle is given by DPmax = 2*Me*Valpha, where Me is the mass of the electron and Valpha is the incoming velocity of the alpha particle.

12.2. When there is 1 electron in a hydrogen atom's electron shell, the nucleus of the atom has __ that __ the electron. a. 1 proton; attracts b. 2 protons; attract c. 1 proton; repel d. 2 protons; repel e. none of the above

a. When there is 1 electron in a hydrogen atom's electron shell, the nucleus of the atom has 1 proton that attracts the electron.

6.22. Young's double-slit diffraction experiment demonstrates the __ property of light. However, dimming the light results in single flashes on the screen representative of __. a. wave; particles b. particle; particles c. wave; waves d. particle; waves e. none of the above

a. Young's double-slit diffraction experiment demonstrates the wave property of light. However, dimming the light results in single flashes on the screen representative of particles.

8.23. A wave solution that __ the properties of __ wave function does not generally correspond to physically realizable circumstances. a. does not satisfy; a valid b. does not satisfy; an infinite c. satisfies; a valid d. satisfies; normalized e. none of the above

b. A wave solution that does not satisfy the properties of an infinite wave function does not generally correspond to physically realizable circumstances.

13.5. Alkali elements have __ outside an inner core. a. a single p electron b. a single s electron c. two s electrons d. two p electrons e. none of the above

b. Alkali elements have a single s electron outside an inner core.

7.28. Bohr's and Heisenberg.'s interpretation of the wave function consisted of three principles, (a) Heisenberg's __ principle, (b) Bohr's __ principle, and (c) Born's __ interpretation based on __ determined by the wave function. a. complementarity; statistical; probabilities; uncertainty b. uncertainty; complementarity; statistical; probabilities c. statistical; probabilities; uncertainty; complementarity d. uncertainty; statistical; probabilities; complementarity e. none of the above

b. Bohr's and Heisenberg.'s interpretation of the wave function consisted of three principles, (a) Heisenberg's uncertainty principle, (b) Bohr's complimentarity principle, and (c) Born's statistical interpretation based on probabilities determined by the wave function.

5.17. Classical laws of physics __ to transitions between __ states in the Bohr model of the atom. a. apply; stationary b. do not apply; stationary c. do not apply; dynamic d. apply; dynamic e. none of the above

b. Classical laws of physics do not apply to transitions between stationary states in the Bohr model of the atom.

9.29. Considering Quantum mechanical barriers and tunneling. When a particle of energy E approaches a __ barrier of height V0 and the potential everywhere else is __, the resulting wave function will consist of an incident wave, a reflected wave, and a transmitted wave. a. kinetic; infinity b. potential; zero c. kinetic; zero d. potential; infinity e. none of the above

b. Considering Quantum mechanical barriers and tunneling. When a particle of energy E approaches a potential barrier of height V0 and the potential everywhere else is zero, the resulting wave function will consist of an incident wave, a reflected wave, and a transmitted wave.

7.5. De Broglie postulated that mass particles have __ properties similar to __. a. particle; atoms b. wave; electromagnetic radiation c. wave; atoms d. particle; electromagnetic radiation e. none of the above

b. De Broglie postulated that mass particles have wave properties similar to electromagnetic radiation.

10.22. For a hydrogen atom, the Schrodinger equation gives us (E+V) psi = __. a. -(hcross^2 + (2*m)) Del^2 psi b. -(hcross^2 / (2*m)) Del^2 psi c. -(hcross^2 * (2*m)) Del^2 psi d. -(hcross^2 - (2*m)) Del^2 psi e. none of the above

b. For a hydrogen atom, the Schrodinger equation gives us (E+V) psi = -(hcross^2 / (2*m)) Del^2 psi.

10.2. For a particle in a 3-D square-well potential, i*hcross*del psi/ del t = __ a. -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + V*psi(x,y,z,t) b. -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + V*psi(x,y,z,t) c. -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + V*psi(x,y,z,t) d. -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + V*psi(x,y,z,t) e. none of the above

b. For a particle in a 3-D square-well potential, i*hcross*del psi/ del t = -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + V*psi(x,y,z,t).

13.13. Halogens form __ __ bonds with alkali elements. a. weak; ionic b. strong; ionic c. strong; covalent d. weak; covalent e. none of the above

b. Halogens form strong ionic bonds with alkali elements.

6.4. A Bragg __ scatters X-rays from several crystals. The intensity of the __ beam is determined as a function of __ by rotating the crystal and the __. a. spectroscope; diffracted; interference angle; sample b. crystallometer; reflected; scattering angle; detector c. reflectrometer; refracted; interference angle; sample d. spectrometer; diffracted; scattering angle; detector e. none of the above

d. 4. A Bragg spectrometer scatters X-rays from several crystals. The intensity of the diffracted beam is determined as a function of scattering angle by rotating the crystal and the detector.

11.9. A given energy level is __ with respect to the orbital angular momentum quantum number l when the energy is __ l. a. generate; dependent on b. generate; independent of c. degenerate; dependent on d. degenerate; independent of e. none of the above

d. A given energy level is degenerate with respect to the orbital angular momentum quantum number l when the energy is independent of l.

3.3. Charges of particles are quantized in units of + or - the ______. a. Planck charge b. electron charge c. atomic charge d. nuclear charge e. none of the above

(b) Charges of particles are quantized in units of + or - electron charge.

1.5. Energy can be transported by ____ or ____. a. particles; wave equations b. particles; waves c. particle equations; waves d. particle complementarity; wave uncertainty e. none of the above

(b) Energy can be transported by particles or waves.

3.20 To derive Planck's Radiation Law, the first modification that Planck made to classical electromagnetic theory was that _____ of electromagnetic origin can only have certain _____ determined by En=_____, where n is an integer, f is the frequency, and h is the Planck's constant. a. photons; discrete; energies; n*h*f b. photons; analog; energies; n*h*f c. electrons; discrete; wavelengths; n*h/f d. electrons; analog; wavelengths; n*h*f e. none of the above

(a) 3.20 To derive Planck's Radiation Law, the first modification that Planck made to classical electromagnetic theory was that photons of electromagnetic origin can only have certain discrete energies determined by En= n*h*f, where n is an integer, f is the frequency, and h is the Planck's constant.

1.16. Based on chemical reactions, Boyle and Proust proposed the law of ____. a. definite proportions b. indefinite proportions c. definite reactions d. indefinite reactions e. none of the above

(a) Based on chemical reactions, Boyle and Proust proposed the law of definite proportions.

2.16. Cathode rays ___ penetrate ___. a. can; matter b. cannot; matter c. cannot; electric fields d. cannot; magnetic fields e. none of the above

(a) Cathode rays can penetrate matter.

1.19. Einstein explained the random motion of pollen grains in water using ____. a. atomic theory b. relativity c. quantum mechanical tunneling d. grain theory e. none of the above

(a) Einstein explained the random motion of pollen grains in water using atomic theory.

1.25. Einstein used the hypothesis of the existence of molecules to explain____. a. Brownian motion b. relativity c. black holes d. continuum mechanics e. none of the above

(a) Einstein used the hypothesis of the existence of molecules to explain Brownian motion.

1.8. Energy transfer at localized points in space are characteristic of ____. a. particles b. waves c. both waves and particles d. neither waves nor particles e. none of the above

(a) Energy transfer at localized points in space are characteristic of particles.

3.17 For Planck's Radiation Law, Planck assumed that the radiation in a blackbody cavity is emitted and absorbed by ____ that are contained in the ____ of the cavity. a. oscillators; walls b. static sources; walls c. static sources; body d. oscillators; body e. none of the above

(a) For Planck's Radiation Law, Planck assumed that the radiation in a blackbody cavity is emitted and absorbed by oscillators that are contained in the walls of the cavity.

3.24 In secondary emission, an electron gains enough energy by ____ from another ____ that strikes the ____ from outside. a. transfer; high-speed particle; material b. emission; high-speed photon; electron c. emission; high- speed particle; electron d. transfer; high-speed photon; material e. none of the above

(a) In secondary emission, an electron gains enough energy by transfer from another high-speed particle that strikes the material from outside.

2.3. In the 1890s, scientists surmised that cathode rays had something to do with ___. a. atoms b. X-rays c. protons d. Zeeman-rays e. none of the above

(a) In the 1890s, scientists surmised that cathode rays had something to do with atoms.

2.27. In the Thomson experiment to calculate the charge/mass of the electron, the magnetic field is adjusted until the net force on the electron (resulting from the ___ and ___ fields) is ___. a. magnetic; electric; zero b. magnetic; electric; one c. gravitational; electric; zero d. magnetic; gravitational; one e. none of the above

(a) In the Thomson experiment to calculate the charge/mass of the electron, the magnetic field is adjusted until the net force on the electron (resulting from the magnetic and electric fields) is zero..

2.25. In the Thomson experiment to calculate the ___ of the electron, the magnetic field is used to deflect the electron against the ___ force. a. charge/mass; electric field b. charge/mass; magnetic c. energy/momentum; electric field d. energy/momentum; magnetic e. none of the above

(a) In the Thomson experiment to calculate the charge/mass of the electron, the magnetic field is used to deflect the electron against the electric field force.

3.28 In the photoelectric effect, the photoelectric current ____ ____ with the light _____, for a ____ frequency of light. a. increases; linearly; intensity; fixed b. increases; inversely; wavelength; fixed c. decreases; linearly; intensity; varying d. decreases; inversely; wavelength; varying e. none of the above

(a) In the photoelectric effect, the photoelectric current increases linearly with the light intensity for a fixed frequency of light.

2.14. J. J. Thomson showed that cathode rays were ___ charged particles, by deflecting them in ___ and ___ fields. a. negatively; electric; magnetic b. negatively; liquids; magnetic c. positively; electric; magnetic d. positively; solids; electric e. none of the above

(a) J. J. Thomson showed that cathode rays were negatively charged particles, by deflecting them in electric and magnetic fields.

1.23. Max Planck used the hypothesis of submicroscopic quanta to explain ____. a. blackbody radiation b. movement of pollen grains c. movement of bacteria d. continuous spectral lines e. none of the above

(a) Max Planck used the hypothesis of submicroscopic quanta to explain blackbody radiation.

1.2. Mechanics, electromagnetism and thermodynamics all include ____ laws. a. complementary b. uncertainty c. conservation d. non-conservation e. none of the above

(a) Mechanics, electromagnetism and thermodynamics all include complementary laws.

2.2. Some of the key phenomena that provided the experimental basis for quantum physics include the discovery and explanation of _____, _____, _____ and _____ production and annihilation. (a) the photoelectric effect; Z ray production; the Compton effect; pair (b) the Zeeman effect; alpha ray production; the Compton effect; electron (c) the quantum effect; beta ray production; the anti Compton effect; positron (d) the relativity effect; gamma ray production; the anti Compton effect; proton

(a) Some of the key phenomena that provided the experimental basis for quantum physics include the discovery and explanation of the photoelectric effect, Z Ray production, the Compton effect, and pair production and annihilation.

1.9. In diffraction, light waves can ____ around ____ and ____. a. reflect; slits; windows b. bend; corners; edges c. refract; slits; windows d. reflect; corners; edges e. none of the above

(b) In diffraction, light waves can bend around corners and edges.

2.1. Some of the key phenomena that provided the experimental basis for quantum physics include the discovery of _____ and _____, the determination of _____, and _____ to help explain _____. (a) X - rays; electrons; electron charge; quantization; black-body radiation (b) Zeeman rays; electrons; proton charge; energy continuum; black hole radiation (c) X - rays; protons; electron chterm-30arge; quantization; black hole radiation (d) Zeeman rays; protons; proton charge; energy continuum; black body radiation

(a) Some of the key phenomena that provided the experimental basis for quantum physics include the discovery of X-rays and electrons, the determination of electron charge, and quantization to help explain blackbody radiation.

2.29. The Millikan oil-drop experiment uses ___ and ___ to suspend a charged oil drop, and uses these to determine the magnitude of the ___ the oil drop. a. an electric field; gravity; charge on b. a magnetic field; an electric field; charge on c. an electric field; gravity; mass of d. a magnetic field; gravity; energy of e. none of the above

(a) The Millikan oil-drop experiment uses an electric field and gravity to suspend a charged oil drop, and uses these to determine the magnitude of the charge on the oil drop.

3.14 The emissivity of a real object is always ____ 1. a. less than b. greater than c. equal to d. infinity greater than e. none of the above

(a) The emissivity of a real object is always less than 1.

1.1 The major steps that led to the birth of modern physics include ____ of the 1890s, ____ and ____, the ____ theory of matter, and ____ of 1895. a. classical physics; waves; particles; atomic; unresolved questions b. quantum physics; uncertainty principle; particles; atomic; unknown questions c. relativistic physics; waves; uncertainty principle; atomic; unresolved questions d. classical physics; waves; particles; complementary; known questions e. none of the above

(a) The major steps that led to the birth of modern physics include classical physics of the 1890s, waves and particles, the Atomic theory of matter, and unresolved questions of 1895.

1.14. The speed of light in a vacuum is given by c = ____, where u0 is the permeability of free space and e0 is the permittivity of free space. a. 1/sqrt(u0*e0) b. 1/(u0*e0) c. u0*e0 d. sqrt(u0*e0) e. none of the above

(a) The speed of light in a vacuum is given by c= 1/sqrt(u0*e0), where u0 is the permeability of free space and e0 is the permittivity of free space.

3.9 Wein's Displacement Law states that the maximum of the blackbody distribution shifts to _____ wavelengths as the ____ of the blackbody increases. a. shorter; temperature b. longer; temperature c. infinite; luminosity d. shorter; luminosity e. none of the above

(a) Wein's Displacement Law states that the maximum of the blackbody distribution shifts to shorter wavelengths as the temperature of the blackbody increase

In quantum mechanics, __ effects (for a particle in a potential well) can lead to almost pure __ for certain wavelengths. a. cancellation; transmission b. cancellation; reflection c. reflection; transmission d. transmission; transmission e. none of the above

(a.) In quantum mechanics, cancellation effects (for a particle in a potential well) can lead to almost pure transmission for certain wavelengths.

In quantum tunneling, the penetration of the barrier (which __ allowed in classical physics) __ allowed by quantum mechanics and __. a. is not; is; the uncertainty principle b. is; is; the Planck principle c. is not; is not; the uncertainty principle d. is; is not; the Planck principle e. none of the above

(a.) In quantum tunneling, the penetration of the barrier (which is not allowed in classical physics) is allowed by quantum mechanics and the uncertainty principle.

The __ quantum number is ml. a. magnetic b. principal c. primary d. orbital angular momentum e. none of the above

(a.) The magnetic quantum number is ml.

The normalized spherical harmonic Y(theta, phi) for the quantum numbers l = 1 and ml = o is __. a. (1/2)*sqrt(3/pi)*cos(theta) b. 2*sqrt(3/pi)*cos(theta) c. (1/2)*sqrt(3*pi)*cos(theta) d. 2*sqrt(3(pi)*cos(theta) e. none of the above

(a.) The normalized spherical harmonic Y(theta, phi) for the quantum numbers l = 1 and ml = o is (1/2)*sqrt(3/pi)*cos(theta).

When solving the Schrodinger equation for an atom, the __ and the __ determine the probability density for the various quantum states. a. radial wave function; spherical harmonics b. wave function; particle equations c. radial function; azimuthal equations d. Uncertainty Principle, Complementary Principle e. none of the above

(a.) When solving the Schrodinger equation for an atom, the radial wave function and the spherical harmonics determine the probability density for the various quantum states.

3.7. A black body is a _____ a material that only ____ thermal radiation. Incoming radiation is _____ the ______. a. body of; absorbs; absorbed by; body b. cavity in; emits; absorbed in; cavity c. body of; absorbs; reflected by; body d. cavity in; absorbs, emitted by; cavity e. none of the above

(b) A black body is a cavity in a material that only emits thermal radiation. Incoming radiation is absorbed in the cavity.

2.23. An electron moving through an electric field is accelerated by a force F = ___, where q is the charge of the electron, and E is the strength of the electric field. a. q/E b. q*E c. E/q d. 0.5*q*E^2 e. none of the above

(b) An electron moving through an electric field is accelerated by a force F = q*E, where q is the charge of the electron, and E is the strength of the electric field.

2.26. An electron that is traveling through an electric field and a magnetic field, the force of the electron is given by F = ___, where q is the charge of the electron, E is the electric field vector; v is the vector velocity of the electron, B is the Magnetic Field vector, and X is the vector cross-product. a. (q*E) * (q*v X B) b. (q*E) + (q*v X B) c. (q*E) / (q*v X B) d. (q*E) - (q*v X B) e. none of the above

(b) An electron that is traveling through an electric field and a magnetic field, the force of the electron is given by F = (q*E) + (q*v X B), where q is the charge of the electron, E is the electric field vector; v is the vector velocity of the electron, B is the Magnetic Field vector, and X is the vector cross-product.

1.21. Blackbody radiation is typically plotted in terms of ____ verses ____. a. brightness per unit frequency; wavelength b. intensity per unit wavelength; wavelength c. intensity per unit frequency; wavelength d. brightness per unit wavelength; frequency e. none of the above

(b) Blackbody radiation is typically plotted in terms of intensity per unit wavelength verses wavelength.

2.30. In the Millikan oil-drop experiment, the mass of the droplet is determined using Stoke's relationship of the ___ of the drop to its ___ and___. a. terminal velocity; mass; energy b. terminal velocity; radius; density c. acceleration; mass; density d. terminal acceleration; radius; energy e. none of the above

(b) In the Millikan oil-drop experiment, the mass of the droplet is determined using Stoke's relationship of the terminal velocity of the drop to its radius and density.

2.28. In the Thomson experiment to calculate the charge/mass of the electron, the electron charge/mass = ___, where E is the electric field, theta is the electron deflection angle, B is the magnetic field strength, L is the path-length of the electron in the fields. a. (E*tan(theta))*(B^2*L) b. (E*tan(theta))/(B^2*L) c. (E*tan(theta))+(B^2*L) d. (E*tan(theta))-(B^2*L) e. none of the above

(b) In the Thomson experiment to calculate the charge/mass of the electron, the electron charge/mass = (E*tan(theta))/(B^2*L), where E is the electric field, theta is the electron deflection angle, B is the magnetic field strength, L is the path-length of the electron in the fields.

3.26 In the photoelectric effect, ___ that ____ incident on the ____ transfer (or transfers) ____ to the electrons, allowing them to ____. a. protons; are; electrons; momentum; emit b. light; is; material; energy; escape c. light; is; electrons; frequency; emit d. photons; are; material; frequency; escape e. none of the above

(b) In the photoelectric effect, light that is incident on the material transfer (or transfers) energy to the electrons, allowing them to escape.

3.30 In the photoelectric effect, the maximum kinetic energy of the photoelectrons depends only on the ____ of the ____. a. intensity; light b. frequency; light c. intensity; electrons d. frequency; electrons e. none of the above

(b) In the photoelectric effect, the maximum kinetic energy of the photoelectrons depends only on the frequency the light.

1.18. Maxwell derived the ____ of atoms in a gas. a. masses b. speed distribution c. volumes d. pressure distribution e. none of the above

(b) Maxwell derived the speed distribution of atoms in a gas.

3.5 Measured atomic weights have values that are close to _____ of a unit mass. a. fractional multiples b. integral multiples c. the same as that d. less than that e. none of the above

(b) Measured atomic weights have values that are close to integral multiples of a unit mass.

3.19 Planck used ____ statistical methods to arrive at the formula that fits blackbody ____ data. a. Planck; radiation b. Boltzmann; radiation c. relativistic; power d. quantum; wavelength e. none of the above

(b) Planck used Boltzmann statistical methods to arrive at the formula that fits blackbody radiation data.

2.11. Rontgen used X-rays to image the ___ of a hand on a ___. a. tissues; sheet of photographic paper b. bones; phosphorescent screen c. bones; CCD camera d. bones; sheet of photographic paper e. none of the above

(b) Rontgen used X-rays to image the bones of a hand on a phosphorescent screen.

3.10 The Stefan-Boltzmann Law states the total ____ that is radiated by a blackbody increases with the ____ of the blackbody. a. frequency; temperature b. power; temperature c. energy; luminosity d. wavelength; luminosity e. none of the above

(b) The Stefan-Boltzmann Law states the total power that is radiated by a blackbody increases with the temperature of the blackbody.

3.12 The emissivity of an idealized blackbody is _____. a. 0 b. 1 c. 10 d. infinity e. none of the above

(b) The emissivity of an idealized blackbody is 1.

2.22. Thomson measured the ratio of the electron's ___ to ___ by looking at its behavior when it passed through a region containing ___ field ___ to ___ field. a. speed; momentum; a magnetic; parallel; an electric b. charge; mass; a magnetic; perpendicular; an electric c. energy; momentum; an electroweak; perpendicular; a magnetic d. charge; mass; an electroweak; parallel; a magnetic e. none of the above

(b) Thomson measured the ratio of the electron's charge to mass by looking at its behavior when it passed through a region containing a magnetic field perpendicular to an electric field.

3.1. Thousands of Milliken oil-drop experiments showed that there is a certain minimum ____ electron ______. a. continuous; mass b. quantized; charge c. continuous; momentum d. quantized; energy e. none of the above

(b) Thousands of Miliken oil-drop experiments showed that there is a certain minimum quantized electron charge.

1.13. Visible light is ____ of the total ____ spectrum. a. 100%; electromagnetic b. a very small part; electromagnetic c. 1%; electromagnetic d. a very small part; visible e. none of the above

(b) Visible light is a very small part of the total electromagnetic spectrum.

1.22. When the temperature of an object is increased, the peak-wavelength of the black-body radiation that it emits ____. a. increases b. decreases c. stays the same d. increases then decreases e. none of the above

(b) When the temperature of an object is increased, the peak-wavelength of the black-body radiation that it emits decreases.

2.6. ___ were discovered by Wilhelm Rontgen in 1895. a. alpha rays b. X-rays c. beta rays d. gamma rays e. none of the above

(b) X-Rays were discovered by Wilhelm Rontgen in 1895.

2.18. Rontgen called the rays that were generated when cathode rays passed through a material ___. a. alpha-rays b. X-rays c. beta-rays d. gamma-rays e. none of the above

(b)Rontgen called the rays that were generated when cathode rays passed through a material X-rays.

Based on the Schrodinger equation for an atom, the total wave function depends on __, __, and __. a. s; p; d b. n; l; ml c. wave; particle; properties d. uncertainty; probability; certainty e. none of the above

(b.) Based on the Schrodinger equation for an atom, the total wave function depends on n, l, and ml.

2.10. Rontgen constructed an X-ray tube by allowing ___ to impact the ___ of the tube and generate ___. a. X-rays; glass wall; Cathode-rays b. Cathode-rays; metal wall; X-rays c. Cathode-rays; vacuum; Anode-rays d. Cathode-rays; glass wall; X-rays e. none of the above

(d) Rontgen constructed an X-ray tube by allowing Cathode-rays to impact the glass wall of the tube and generate X-rays.

Consider a particle or wave in a potential well. When the width of the potential well is precisely equal to __ units of the wavelength (of the particle or equivalent wave), the waves reflected (at the boundary of the potential well) may be __ with the original wave, and cancellations may occur. a. integral; out of phase b. half-integral; out of phase c. quarter-integral; in phase d. half-integral, in phase e. none of the above

(b.) Consider a particle or wave in a potential well. When the width of the potential well is precisely equal to half-integral units of the wavelength (of the particle or equivalent wave), the waves reflected (at the boundary of the potential well) may be out of phase with the original wave, and cancellations may occur.

Quantum tunneling: Consider the situation where classically the particle does not have enough energy to surmount the potential barrier, E<Vo. The quantum mechanical result, however, is one of the most remarkable features of modern physics, and there is ample experimental proof of its existence. There is a __, probability that the particle __ penetrate the barrier and __ emerge on the other side. a. zero; can; so cannot b. small but finite; can; can even c. large; can; can even d. small but finite; cannot; cannot

(b.) Quantum tunneling: Consider the situation where classically the particle does not have enough energy to surmount the potential barrier, E<Vo. The quantum mechanical result, however, is one of the most remarkable features of modern physics, and there is ample experimental proof of its existence. There is a small but finite, probability that the particle can penetrate the barrier and can even emerge on the other side.

2.24. An electron moving through an electric field that is perpendicular to its direction of motion, is deflected through an angle that is given by tan(theta) = ___ where q is the electron charge, E is the strength of the electric field, L is the path length of the electron, m is the mass of the electron and v is the initial velocity of the electron. a. (q*E/L)/(m*v^2) b. (q*E/L)/(m*v) c. (q*E*L)/(m*v^2) d. (q*E*L)/(m*v) e. none of the above

(c) An electron moving through an electric field that is perpendicular to its direction of motion, is deflected through an angle that is given by tan(theta) = (q*E*L)/(m*v^2) where q is the electron charge, E is the strength of the electric field, L is the path length of the electron, m is the mass of the electron and v is the initial velocity of the electron.

3.27 In an experimental setup to investigate the photoelectric effect, ___ potentials are the opposing potentials needed to ____ the _____ electrons. a. accelerating; stop; most energetic b. accelerating; stop; most energetic c. retarding; stop; most energetic d. retarding; speed up; least energetic e. none of the above

(c) In an experimental setup to investigate the photoelectric effect, retarding potentials are the opposing potentials needed to stop the most energetic electrons.

1.12. In the wave theory of light, light propagates as a ____ of ____ from the point of origin. a. ray; straight lines b. wave; straight lines c. wave; concentric circles d. ray; concentric spirals e. none of the above

(c) In the wave theory of light, light propagates as a wave of concentric circles from the point of origin.

3.4 Measured atomic weights ______ continuous. The only have _____ values. a. are; continuous b. are not; continous c. are not; discrete d. are; discrete e. none of the above

(c) Measured atomic weights are not continuous. The only have discrete values.

1.26. One of the unresolved Physics questions of 1895 included the question of whether ____ really exist. a. black-holes b. particles c. atoms d. waves e. none of the above

(c) One of the unresolved Physics questions of 1895 included the question of whether atoms really exist.

1.27. One of the unresolved Physics questions of 1895 included what the structure of ____ really is. a. relativistic particles b. quanta c. matter d. waves e. none of the above

(c) One of the unresolved Physics questions of 1895 included what the structure of matter really is.

1.7. Particles interact in the form of ____. a. wave equations b. wave masses c. point masses d. point equations e. none of the above

(c) Particles interact in the form of point masses.

3.18 Planck's Radiation law states that the intensity of radiation = _____, where pi is 3.145, c is the speed of light, h is Planck's constant, lambda is the wavelength of the radiation, k is the Boltzmann's constant, and T is the absolute temperature of the blackbody in Kelvin. a. 2*pi*c^2*h/lambda^2 * (1/(e^(h*c/(lambda*k*T)) - 1)) b. 2*pi*c^2*h/lambda^4 / (1/(e^(h*c/(lambda*k*T)) - 1)) c. 2*pi*c^2*h/lambda^5 * (1/(e^(h*c/(lambda*k*T)) - 1)) d. 2*pi*c^2*h/lambda^2 / (1/(e^(h*c/(lambda*k*T)) - 1)) e. none of the above

(c) Planck's Radiation law states that the intensity of radiation = 2*pi*c^2*h/lambda^5 * (1/(e^(h*c/(lambda*k*T)) - 1)), where pi is 3.145, c is the speed of light, h is Planck's constant, lambda is the wavelength of the radiation, k is the Boltzmann's constant, and T is the absolute temperature of the blackbody in Kelvin.

3.11 The Stefan-Boltzmann Law states that the total ___ that is radiated by a blackbody increases _____ the _______. a. frequency; inversely with; fourth power of the temperature b. power; inversely with; fourth power of the temperature c. power; with; fourth power of the temperature d. wavelength; with; second power of the temperature e. none of the above

(c) The Stefan-Boltzmann Law states that the total power that is radiated by a blackbody increases with the power of the temperature.

3.13 The emissivity is the ratio of the emissive power of an object to that of _____. a. its inverse b. its absorptive power c. an ideal blackbody d. the material of the object e. none of the above

(c) The emissivity is the ratio of the emissive power of an object to that of an ideal blackbody.

1.15. The energy of a photon is given by E = ____, where h is Planck's constant, Lambda is the wavelength of the the light wave, and f is the frequency of the light wave. a. h * f* Lambda b. h / f/ Lambda c. h * f = h*c/ Lambda d. h / f* Lambda e. none of the above

(c) The energy of a photon is given by E = h * f = h*c/ Lambda, where h is Planck's constant, Lambda is the wavelength of the the light wave, and f is the frequency of the light wave.

2.20. Rontgen deduced that X-rays were produced by ___ bombarding the ___ of his vacuum tube. a. X-rays; glass walls b. atoms; glass walls c. cathode rays; electric fields d. cathode rays; glass walls e. none of the above

(d) Rontgen deduced that X-rays were produced by cathode rays bombarding the glass walls of his vacuum tube.

3.21 To derive Plank's Radiation Law, the second modification that Planck made to classical electromagnetic theory was that _____ of electromagnetic origin can only absorb or emit ___ in ___ multiples of the fundamental ____ of energy given by: DeltaE = ______, where h is Plank's constant and f is the frequency. a. oscillators; energy; analog; quantum; h*f b. static sources; wavelengths; discrete; quantum; h/f c. oscillators; energies; discrete; quantum; h*f d. static sources; wavelengths; analog; quantum; h/f e. none of the above

(c) To derive Plank's Radiation Law, the second modification that Planck made to classical electromagnetic theory was that oscillators of electromagnetic origin can only absorb or emit energies in discrete multiples of the fundamental quantum of energy given by: DeltaE = h*f, where h is Plank's constant and f is the frequency.

2.17. Wilhelm Rontgen noticed that a ___ glowed when it was near ___ rays that were passing through various materials. a. photographic film; cathode b. phosphorescent screen; anode c. phosphorescent screen; cathode d. photographic film; anode e. none of the above

(c) Wilhelm Rontgen noticed that a Phosphorescent screen glowed when it was near cathode rays that were passing through various materials.

2.5. Wilhelm Rontgen studied the effects of cathode rays passing through various ___. He noticed that a ___ near the cathode-ray tube ___ during some of his experiments. a. materials; metal plate; conducted electricity b. X-ray fields; metal plate; conducted electricity c. materials; phosphorescent screen; glowed d. electric fields; magnet; became charged e. none of the above

(c) Wilhelm Rontgen studied the effects of cathode rays passing through various materials. He noticed that a phosphorescent screen near the cathode-ray tube glowed during some of his experiments.

2.7. William Rontgen observed___ that were emitted by ___ hitting glass. a. anode rays; cathode rays b. cathode rays; X-rays c. X-rays; cathode rays d. cathode rays; anode rays e. none of the above

(c) William Rontgen observed X-Rays that were emitted by cathode rays hitting glass.

In the case of an infinite-potential square well, the normalized wave function becomes psi(x) = __, where L is the length of the well, pi is 3.1415, and x is the x-position along the well. a. sqrt(2*L) + sin(n*pi*x/L) b. sqrt(2*L) - sin(n*pi*x/L) c. sqrt(2/L) * sin(n*pi*x/L) d. sqrt(2/L) / sin(n*pi*x/L) e. none of the above

(c.) In the case of an infinite-potential square well, the normalized wave function becomes psi(x) = sqrt(2/L) * sin(n*pi*x/L), where L is the length of the well, pi is 3.1415, and x is the x-position along the well.

The __ quantum number is n. a. primary b. orbital angular momentum c. principal d. magnetic e. none of the above

(c.) The principal quantum number is n.

When solving the Schrodinger equation for an atom, the wave function becomes psi(r,theta,phi) = __, were R is a function of the quantum numbers n and l and Y is a function of l and ml. a. R(theta)* Y(theta,phi) b. R(r,theta)/ Y(phi) c. R(r)* Y(theta,phi) d. R(r,phi)/ Y(theta,phi e. none of the above

(c.) When solving the Schrodinger equation for an atom, the wave function becomes psi(r,theta,phi) = R(r)* Y(theta,phi), were R is a function of the quantum numbers n and l and Y is a function of l and ml.

1.28. A fundamental problem of classical physics (in 1895) was the observed differences in the ____ and ____ between stationary and moving reference systems. a. electric particles; magnetic particles b. magnetic fields; electric fields c. electric particles; magnetic fields d. electric fields; magnetic fields e. none of the above

(d) A fundamental problem of classical physics (in 1895) was the observed differences in the electric particles and magnetic particles between stationary and moving reference systems.

1.29. Additional discoveries that did not quite match classical physics, and so set the stage for modern physics, include the discoveries of ____, ____, ____ and ____. a. Zeeman-rays; relativity; neutrons; X effect b. X-rays; relativity; electrons; Zeeman effect c. Zeeman-rays; radioactivity; protons; Zeeman effect d. X-rays; radioactivity; electrons; Zeeman effect e. none of the above

(d) Additional discoveries that did not quite match classical physics, and so set the stage for modern physics, include the discoveries of X-rays, radioactivity, electrons, and Zeeman effect.

1.20. Ernst mach opposed Atomic theory on the basis of ____. a. quantum mechanics b. rational positivism c. rationality theory d. logical positivism e. none of the above

(d) Ernst mach opposed Atomic theory on the basis of logical positivism.

1.24. Evidence for the existence of atoms include the behavior of ____, ____, ____ and ____. a. black-hole radiation; statistical mechanics; Brownian motion; Newton's predictions being matched experimentally. b. blackbody radiation; continuum mechanics; Brownian particles; Einstein's predictions being matched experimentally. c. black-hole radiation; continuum mechanics; Brownian particles; Newton's predictions being matched experimentally. d. blackbody radiation; statistical mechanics; Brownian motion; Einstein's predictions being matched experimentally. e. none of the above

(d) Evidence for the existence of atoms include the behavior of blackbody radiation, statistical mechanics, Brownian motion, and Einstein's predictions being matched experimentally.

2.4. In the 1890s, it was known that cathode rays could penetrate ___. a. electrons b. X-rays c. protons d. matter e. none of the above

(d) In the 1890s, it was known that cathode rays could penetrate matter.

3.29 In the photoelectric effect, the kinetic energy of the photoelectrons is ____ the light ____. a. independent of; wavelength b. independent of; frequency c. dependent on; intensity d. independent of; intensity e. none of the above

(d) In the photoelectric effect, the kinetic energy of the photoelectrons is independent of the light intensity

3.23 In thermionic emission, the application o f___ allows electrons to gain enough ___ to _____. a. ionic energy; energy; escape b. heat; momentum; emit c. ionic energy; momentum; absorb d. heat; energy; escape e. none of the above

(d) In thermionic emission, the application of heat allows electrons to gain enough energy to escape.

2.13. J.J. Thomson observed that cathode rays were ___. a. electrically neutral particles b. charged photons c. uncharged photons d. charged particles e. none of the above

(d) J.J. Thomson observed that cathode rays were charged particles.

3.22 The four major methods of electron emission are ___, ____, ____, and ____ emission. a. thermoelectric; secondary; particle; photomagnetic b. thermoionic; primary; particle; photoelectric c. thermoelectric; primary; field; photomagnetic d. thermionic; secondary; field; photoelectric e. none of the above

(d) The four major methods of electron emission are thermionic, secondary, field, and photoelectric emission.

1.4. The law of conservation of ____ states that in the absence of net ____, ____ is conserved in all of its interactions. a. angular momentum; external forces; linear momentum b. linear momentum; internal torque; angular momentum c. angular momentum; internal forces; angular momentum d. angular momentum; external torque; angular momentum e. none of the above

(d) The law of conservation of angular momentum states that in the absence of net external torque, angular momentum is conserved in all of its interactions.

1.30. The theory of ____ and ____ became the starting point of the new revision of classical physics, now called Modern Physics. a. atoms; chemistry b. statistical mechancis; relativistic mechanics c. statistical dynamics; quantum mechanics d. relativity; quantum mechanics e. none of the above

(d) The theory of relativity and quantum mechanics became the starting point of the new revision of classical physics, now called Modern Physics.

2.19. X-rays are ___ by magnetic fields, and penetrate materials ___ cathode rays. a. affected; more than b. unaffected; less than c. affected; less than d. unaffected; more than e. none of the above

(d) X-rays are unaffected by magnetic fields, and penetrate materials more than cathode rays.

2.8. X-rays were affected by interaction with ___. a. electric fields b. magnetic fields c. gravitational fields d. matter e. none of the above

(d) X-rays were affected by interaction with matter.

1.3. The law of conservation of ____ states that the total sum of ____ in all its forms is ____ in ____ interactions. a. momentum; momentum; conserved b. energy; energy; conserved; some c. energy; energy; not conserved; all d. energy; energy; conserved; all e. none of the above

(d)The law of conservation of energy states that the total sum of energy in all its forms is conserved in all interactions

Consider a particle or wave in a potential well. When the width of the potential well is precisely equal to __ of the wavelength (of the particle or equivalent wave), the waves reflected (at the boundary of the potential well) may be __ with the original wave, and resonances occur. a. integral; out of phase b. half-integral; out of phase c. quarter-integral; in phase d. integral, in phase e. none of the above

(d.) Consider a particle or wave in a potential well. When the width of the potential well is precisely equal to integral of the wavelength (of the particle or equivalent wave), the waves reflected (at the boundary of the potential well) may be in phase with the original wave, and resonances occur.

In quantum mechanics, __ effects (for a particle in a potential well) can lead to almost pure __ for certain wavelengths. a. cancellation; reflection b. transmission; reflection c. cancellation; reflection d. reflection; reflection e. none of the above

(d.) In quantum mechanics, reflection effects (for a particle in a potential well) can lead to almost pure reflection for certain wavelengths.

In quantum mechanics, when a particle is reflected or transmitted at a boundary, there is a situation in which the transmission probability is __ (or h) when k = n*pi, at x=0 (or x=L), and the path difference is __, causing the incident and reflected wave functions to be __ phase and therefore, to __ each other. a. zero; L; in; cancel b. zero; 2L; in; reinforce c. one; L; out of; reinforce d. one; 2L; out of; cancel e. none of the above

(d.) In quantum mechanics, when a particle is reflected or transmitted at a boundary, there is a situation in which the transmission probability is one (or h) when k = n*pi, at x=0 (or x=L), and the path difference is 2L, causing the incident and reflected wave functions to be out of phase and therefore, to cancel each other.

The __ quantum number is l (lower case L). a. principal b. magnetic c. primary d. orbital angular momentum e. none of the above

(d.) The orbital angular momentum quantum number is l (lower case L).

When a particle is reflected or transmitted at a boundary, the probability of reflection + the probability of transmission = __%. a. 0 b. 1 c. 10 d. 100 e. none of the above

(d.) When a particle is reflected or transmitted at a boundary, the probability of reflection + the probability of transmission = 100%

2.21. ___ can be used to image the bones of a hand on a ___ screen. a. cosmic-rays; photographic b. cosmic-rays; phosphorescent c. X-rays; metal d. X-rays; phosphorescent e. none of the above

21. X-rays can be used to image the bones of a hand on a phosphorescent screen.

3.16 The Rayleigh formula (for the intensity of blackbody spectral radiation as a function of wavelength) is close to experimental data at ____ wavelengths, but deviates badly at _____ wavelengths. This issue is called the _____ catastrophe and indicates that classical physics is insufficient to explain the radiation wavelength- distribution of black-bodies. a. longer; shorter; ultraviolet b. shorter; longer; ultraviolet c. longer; shorter; infrared d. shorter; longer; infrared e. none of the above

The Rayleigh formula (for the intensity of blackbody spectral radiation as a function of wavelength) is close to experimental data at longer wavelengths, but deviates badly at shorter wavelengths. This issue is called the ultraviolet catastrophe and indicates that classical physics is insufficient to explain the radiation wavelength- distribution of black-bodies.

10.14. A solution to the Schrodinger equation for a particle in an infinite square-well potential corresponds to E = [hcross^2*pi^2/2m] * __. a. [ (nx/Lx)^2 + (ny/Ly)^2 + (nz/Lz)^2 ] b. [ (nx/Lx)^2 - (ny/Ly)^2 + (nz/Lz)^2 ] c. [ (nx/Lx)^2 * (ny/Ly)^2 * (nz/Lz)^2 ] d. [ (nx/Lx)^2 + (ny/Ly)^2 / (nz/Lz)^2 ] e. none of the above

a. A solution to the Schrodinger equation for a particle in an infinite square-well potential corresponds to E = [hcross^2*pi^2/2m] * a. [ (nx/Lx)^2 + (ny/Ly)^2 + (nz/Lz)^2 ].

4.18. Based on the results of alpha-particles scattering off of gold-foil, Rutherford proposed that the atom has a __ charged __, surrounded by __ charged __. a. positively; core; negatively; electrons b. negatively; core; negatively; electrons c. positively; core; positively; protons d. negatively; core; negatively; protons e. none of the above

a. Based on the results of alpha-particles scattering off of gold-foil, Rutherford proposed that the atom has a positively charged core, surrounded by negatively charged electrons.

6.26. Bohr's principle of complementarity states that it __ possible to describe physical observables simultaneously in terms of both __ and __. a. is not; particles; waves b. is not; energy; time c. is; particles; waves d. is; energy; time e. none of the above

a. Bohr's principle of complementarity states that it is not possible to describe physical observables simultaneously in terms of both particles and waves.

6.12. Electron diffraction in transmission experiments show spot patterns from __ crystals and __ patterns from randomly oriented __ samples. a. single; ring; polycrystalline b. single; ring; single-crystal c. poly; block; polycrystalline d. poly; block; single-crystal e. none of the above

a. Electron diffraction in transmission experiments show spot patterns from single crystals and ring patterns from randomly oriented polycrystalline samples.

11.12. Energy levels and states in atoms are referred to by their __ and __. a. principal quantum number; angular orbital quantum number b. primary quantum number; secondary quantum number c. principal wave state; angular orbital wave state.d. primary wave state; secondary wave state e. none of the above

a. Energy levels and states in atoms are referred to by their principal quantum number and angular orbital quantum number.

13.20. For Lanthanides, the electrons in the __ subshell have __ electrons that align themselves (across atoms). a. 4f; unpaired b. 4s; unpaired c. 4p; paired d. 4d; paired e. none of the above

a. For Lanthanides, the electrons in the 4f subshell have unpaired electrons that align themselves (across atoms).

7.7. For a non-relativistic particle, Group velocity = v =__ .a. lambda*f = dw/dk b. lambda/f = dw/dk c. lambda+f = dw*dk d. lambda-f = dw*dk e. none of the above

a. For a non-relativistic particle, Group velocity = v = lambda*f = dw/dk.

4.24. In Rutherford scattering, when the impact parameter b is small, the Coulomb force __. a. becomes large but finite b. becomes small c. disappears d. becomes infinite e. none of the above

a. In Rutherford scattering, when the impact parameter b is small, the Coulomb force becomes large but finite.

12.19. In a Helium atom, the first electron has the following values for its four quantum numbers __, __, __, and __. a. 1; 0; 0; 1/2 b. 1; 0; 0; 1 c. 1; 0; 0; -1 d. 1; 0; 0; -1/2 e. none of the above

a. In a Helium atom, the first electron has the following values for its four quantum numbers 1, 0, 0, and 1/2.

10.23. In a hydrogen atom, the potential (central force) V(r) (for the Schrodinger equation) depends on the distance r between the _ and the __. a. electron; proton b. first shell; second shell c. proton; second shell d. proton; neutron e. none of the above

a. In a hydrogen atom, the potential (central force) V(r) (for the Schrodinger equation) depends on the distance r between the electron and the proton.

5.16. In the Bohr model of the atom, the frequency of radiation emitted by an atom is __ proportional to the __ of the two stationary states. a. directly; difference in energy b. directly; sum of energy c. inversely; difference in momentum d. inversely; sum of momentum e. none of the above

a. In the Bohr model of the atom, the frequency of radiation emitted by an atom is directly proportional to the difference in energy of the two stationary states.

5.21. In the Bohr model, the electron's orbital velocity in the ground state, is a bit less than __ of the speed of light. a. 1 % b. 10 % c. 100 % d. 200 % e. none of the above

a. In the Bohr model, the electron's orbital velocity in the ground state, is a bit less than 1% of the speed of light.

10.19. In the Schrodinger Wave Equation for a two-body problem, the Eigen value is __. a. E b. V c. H d. hcross e. none of the above

a. In the Schrodinger Wave Equation for a two-body problem, the Eigen value is E.

9.23. In the case of a Finite potential square-well, the penetration distance is proportional to __ and __ classical physics. a. Planck's constant; violates b. the speed of light; violates c. Heisenberg's constant; is consistent with d. the quantum constant; is consistent with e. none of the above

a. In the case of a Finite potential square-well, the penetration distance is proportional to Planck's constant and violates classical physics.

9.21. In the case of a Finite potential square-well, there __ wave amplitude outside the square well. This __ the rules of classical physics. a. is a non-zero; violates b. is a non-zero; matches c. is no; violates d. is no; matches e. none of the above

a. In the case of a Finite potential square-well, there is a non-zero wave amplitude outside the square well. This violates the rules of classical physics.

9.14. In the case of an infinite-potential square well, the boundary conditions of the potential dictate that the wave function must be __ at x = 0 and x = L. This yields valid solutions for __ values of n such that kL = __. a. zero; integer; n*pi b. infinity; fractional; n/pi c. plus one; integer; n*pi^2 d. minus one; fractional; n+pi e. none of the above

a. In the case of an infinite-potential square well, the boundary conditions of the potential dictate that the wave function must be zero at x = 0 and x = L. This yields valid solutions for integer values of n such that kL = n*pi_.

9.16. In the case of an infinite-potential square well, the normalized wave function becomes identical to that for __ with __. a. a vibrating string; fixed ends b. a vibrating string; one fixed end c. a resonating pipe; open ends d. a resonating pipe; a closed end and an open end e. none of the above

a. In the case of an infinite-potential square well, the normalized wave function becomes identical to that for a vibrating string with fixed ends.

5.8. In the classical atomic model, the atom consists of a __, __, __ charged nucleus surrounded by __ charges. a. small; massive; positively; moving b. small; massless; positively; stationary c. large; massless; negatively; moving d. large; massive; negatively; stationary e. none of the above

a. In the classical atomic model, the atom consists of a small, massive, positively charged nucleus surrounded by moving charges.

8.25. In the time-independent Schrodinger Wave Equation, the dependence on __ and __ can be separated from each other. a. time; position b. time; energy c. momentum; position d. energy; position e. none of the above

a. In the time-independent Schrodinger Wave Equation, the dependence on time and position can be separated from each other.

13.18. In transition metals, as the __ subshell is filled, the __ and the tendency for neighboring atoms to __ are reduced. a. d; magnetic moments; align spins b. d; dielectric moments; randomize spins c. p; magnetic moments; randomize spins d. p; dielectric moments; align spins e. none of the above

a. In transition metals, as the d subshell is filled, the magnetic moments and the tendency for neighboring atoms to align spins are reduced

13.2. Inert gases (other than __) have __ p subshell. a. helium; a closed b. helium; an open c. hydrogen; a closed d. hydrogen; an open e. none of the above

a. Inert gases (other than helium) have a closed p subshell.

6.1. Laue suggested that if X-rays were a form of electromagnetic radiation, __ effects should be observed. a. interference b. refraction c. reflection d. relativistic e. none of the above

a. Laue suggested that if X-rays were a form of electromagnetic radiation, interference effects should be observed.

8.19. One of the properties of a valid wave function is that in order to avoid __ probabilities, the wave function must be __ everywhere. a. infinite; finite b. zero; infinite c. infinite; normalized d. normalized; finite e. none of the above

a. One of the properties of a valid wave function is that in order to avoid infinite probabilities, the wave function must be finite everywhere.

5.13. Planck proposed the hypothesis of __ behavior of radiation. a. quantum b. spectrum c. Planck d. continuum e. none of the above

a. Planck proposed the hypothesis of quantum behavior of radiation.

4.8. Rutherford, Geiger and Marsden invented a technique for investigating the __ by scattering __ from __. a. structure of matter; alpha particles; atoms b. structure of electrons; alpha particles; electrons c. structure of protons; proton particles; protons d. structure of photons; photonic particles; atoms e. none of the above

a. Rutherford, Geiger and Marsden invented a technique for investigating the structure of matter by scattering alpha particles from atoms.

10.28. Solving the Schrodinger equation for an atom gives us Eo = __. a. hcross^2 / (2*mu*ao^2) b. hcross^2 + (2*mu*ao^2) c. hcross^2 * (2*mu*ao^2) d. hcross^2 - (2*mu*ao^2) e. none of the above

a. Solving the Schrodinger equation for an atom gives us Eo = hcross^2 / (2*mu*ao^2).

9.8. The Quantum mechanical Energy operator is E hat = __. a. i*hcross* del/ del t b. i*hcross+ del/ del t c. i*hcross- del/ del t d. i*hcross/ del/ del t e. none of the above

a. The Quantum mechanical Energy operator is E hat = i*hcross* del/ del t.

10.10. The differential equation for a square-well potential, along the y axis is __ = -ky^2 a. (1/Y)*(d^2Y/dy^2) b. (1/Y)/(d^2Y/dy^2) c. (1/Y)+(d^2Y/dy^2) d. (1/Y)-(d^2Y/dy^2) e. none of the above

a. The differential equation for a square-well potential, along the y axis is (1/Y)*(d^2Y/dy^2) = -ky^2

12.26. The electrons for H and He atoms are in the __ shell. a. K b. L c. s d. p e. none of the above

a. The electrons for H and He atoms are in the K shell.

12.9. The energy levels for electrons in an atom are subject to __ quantum numbers. a. four b. three c. two d. five e. none of the above

a. The energy levels for electrons in an atom are subject to four quantum numbers.

8.4. The general form of the solution of the Schrodinger wave equation is given by Psi(x,t) = __. a. A*e^(i*(kx-wt)) b. A/e^(i/(kx-wt)) c. A+e^(i+(kx-wt)) d. A-e^(i-(kx-wt)) e. none of the above

a. The general form of the solution of the Schrodinger wave equation is given by Psi(x,t) = A*e^(i*(kx-wt)).

6.20. The group velocity of a deBroglie wave __ the phase velocity. a. may be greater or less than b. can only be less than c. can only be greater than d. must be equal to e. none of the above

a. The group velocity of a deBroglie wave may be greater or less than the phase velocity.

11.21. The relationship between the magnetic quantum number ml and the z component of the orbital angular momentum L is given by Lz = __. a. ml*hcross b. ml/hcross c. ml+hcross d. ml-hcross e. none of the above

a. The relationship between the magnetic quantum number ml and the z component of the orbital angular momentum L is given by Lz = ml*hcross.

7.2. The second condition for constructive interference of scattered x-rays is that the Difference in path lengths must be __. a. an integral number of wavelengths b. a fractional number of wavelengths c. an integral number of frequencies d. a fractional number of frequencies e. none of the above

a. The second condition for constructive interference of scattered x-rays is that the Difference in path lengths must be an integral number of wavelengths.

8.10. The __ term of the wave equation has __ number. a. sine; an imaginary b. sine; a real c. cosine; an imaginary d. all of the above e. none of the above

a. The sine term of the wave equation has an imaginary number.

5.19. The smallest diameter of the hydrogen atom is about __. a. 1 Angstrom b. 1 micron c. 1 mm d. 1 cm e. none of the above

a. The smallest diameter of the hydrogen atom is about 1 Angstrom.

12.14. The structure of the periodic table of elements can be understood based on __ rules. a. two b. three c. four d. five e. none of the above

a. The structure of the periodic table of elements can be understood based on two rules.

8.24. The time-independent Schrodinger Wave Equation can be used when the __ does not depend explicitly on __. a. potential; time b. kinetics; energy c. kinetics; duality d. potential; energy e. none of the above

a. The time-independent Schrodinger Wave Equation can be used when the potential does not depend explicitly on time.

8.27. The __ __ Equation is a fundamental equation in quantum mechanics. a. time-independent; Schrodinger Wave b. time-dependent; Schrodinger Wave c. energy-independent; Planck Uncertainty d. energy-dependent; Einstein Relativity e. none of the above

a. The time-independent Schrodinger Wave Equation is a fundamental equation in quantum mechanics.

13.25. The total angular momentum is denoted by __. a. J b. L c. S d. T e. none of the above

a. The total angular momentum is denoted by J.

5.10. The total energy of an electron orbiting a nucleus is the sum of the __ energy and __ energy. a. kinetic; potential b. kinetic; dynamic c. static; dynamic d. electric; potential e. none of the above

a. The total energy of an electron orbiting a nucleus is the sum of the kinetic energy and potential energy.

7.12. The wave number of a matter wave is k = __. a. 2*pi/lambda b. 2*pi*lambda c. pi*lambda d. pi/lambda e. none of the above

a. The wave number of a matter wave is k = 2*pi/lambda.

10.25. To solve the Schrodinger equation for a hydrogen atom, we separate it into __ ordinary __ differential equations, each containing __. a. three; second-order; one variable b. two; second-order; two variables c. three; first-order; three variable d. two; first-order; one variable e. none of the above

a. To solve the Schrodinger equation for a hydrogen atom, we separate it into three ordinary second-order differential equations, each containing one variable.

8.18. Wave function must also be __ so that the probability of the particle being somewhere on the x axis is __. a. normalized; 1 b. normalized; -1 c. fractionalized; 0.5 d. binarized; 2 e. none of the above

a. Wave function must also be normalized so that the probability of the particle being somewhere on the x axis is 1.

10.30. When solving the Schrodinger equation for a Hydrogen atom, the solutions to the resulting __ and __ equations are linked because both have __ in them. a. angular; azimuthal; ml b. wave; particle; n c. wave; particle; k d. wave; angular; ml e. none of the above

a. When solving the Schrodinger equation for a Hydrogen atom, the solutions to the resulting angular and azimuthal equations are linked because both have ml in them.

12.1. When there are 2 electrons in an atom's electron shells, the nucleus of an un-ionized atom has __ protons that __ the electrons. a. 2; attract b. 4; attract c. 2; repel d. 4; repel e. none of the above

a. When there are 2 electrons in an atom's electron shells, the nucleus of an un-ionized atom has 2 protons that attract the electrons.

5.26. A transition of an electron from a L shell to a K shell results in the emission of a __. a. L alpha X-ray b. K alpha X-ray c. K alpha electron d. K beta electron e. none of the above

b. A transition of an electron from a L shell to a K shell results in the emission of a K alpha X-ray.

13.9. Alkaline Earth elements have __ in an outer subshell. a. one s electron b. two s electrons c. two p electrons d. one p electron e. none of the above

b. Alkaline Earth elements have two s electrons in an outer subshell.

11.16. An atomic energy level or state with n = 1 and l = 0 is called a __ state. a. 1p b. 1s c. 1k d. 1n e. none of the above

b. An atomic energy level or state with n = 1 and l = 0 is called a 1s state.

11.1. Based on solving the Schrodinger equation for an atom, the quantized energy is En = __, where n is the principal quantum number, and Eo is the energy of the lowest energy state. a. -Eo/n b. -Eo/n^2 c. -Eo*n^2 d. -Eo*n e. none of the above

b. Based on solving the Schrodinger equation for an atom, the quantized energy is En = -Eo/n^2, where n is the principal quantum number, and Eo is the energy of the lowest energy state.

7.8. Bohr's Quantization Condition: Bohr's assumption of the hydrogen atom model was that the __ of the electron-nucleus system in a stationary state is an integral multiple of __. a. angular momentum; h*(2*pi) b. angular momentum; h/(2*pi) c. kinetic energy; h*(2/pi) d. potential energy; h/(2*pi) e. none of the above

b. Bohr's Quantization Condition: Bohr's assumption of the hydrogen atom model was that the __ of the electron-nucleus system in a stationary state is an integral multiple of angular momentum; h/(2*pi).

6.2. Bragg's Law interpreted x-ray __ as the __ of the incident x-ray beam from a unique set of __ of atoms. a. scattering; reflection; types b. scattering; reflection; planes c. reflection; scattering; directions d. reflection; scattering; volumes e. none of the above

b. Bragg's Law interpreted x-ray scattering as the reflection of the incident x-ray beam from a unique set of planes of atoms.

10.7. For a given solution of the differential equation for a square-well potential, the term E is __. a. variable b. a constant c. exponential d. cyclic e. none of the above

b. For a given solution of the differential equation for a square-well potential, the term E is a constant.

7.6. For a photon, E = __ = pc, where h is Planck's constant, f is the frequency, p is the momentum, lambda is the wavelength, f is the frequency, c is the speed of light. a. hf = (p/lambda)f b. hf = (p*lambda)f c. h/f = (p+lambda)/f d. h/f = (p-lambda)f e. none of the above

b. For a photon, E = hf = (p*lambda)f = pc, where h is Planck's constant, f is the frequency, p is the momentum, lambda is the wavelength, f is the frequency, c is the speed of light.

4.16. If an alpha particle is scattered by all 79 electrons in an atom of gold, the alpha particle would be scattered (or deflected) by about __ degrees. a. 68 b. 6.8 c. 0.68 d. 680 e. none of the above

b. If an alpha particle is scattered by all 79 electrons in an atom of gold, the alpha particle would be scattered (or deflected) by about 6.8 degrees.

5.12. In Classical electromagnetic theory, an electron orbiting a nucleus must __ electromagnetic radiation, which means that the electron __, and so the radius of the electron's orbit must __, until the electron __ the nucleus. However, it does not. And this was a problem for __ electromagnetic theory. a. radiate; gains energy; increase; escapes from; modern b. radiate; loses energy; decrease; crashes into; classical c. absorb; gains energy; increase; crashes into; classical d. absorb; loses energy; decrease; escapes from; modern e. none of the above

b. In Classical electromagnetic theory, an electron orbiting a nucleus must radiate electromagnetic radiation, which means that the electron loses energy, and so the radius of the electron's orbit must decrease, until the electron crashes into the nucleus. However, it does not. And this was a problem for classical electromagnetic theory.

4.25. In Rutherford scattering, when the impact parameter b is small, the scattering angle theta can be __ compared to when the impact parameter b is large. a. small b. large c. the same d. infinity e. none of the above

b. In Rutherford scattering, when the impact parameter b is small, the scattering angle theta can be large compared to when the impact parameter b is large.

12.18. In a Hydrogen atom, in the absence of a magnetic field, the state ms = 1/2 is __ the ms = -1/2 state. a. congruent to b. degenerate with c. generate with d. circumstantial with e. none of the above

b. In a Hydrogen atom, in the absence of a magnetic field, the state ms = 1/2 is degenerate with the ms = -1/2 state.

9.24. In a Three-Dimensional Infinite-Potential Well, the three dimensional Schrodinger wave equation is __, where the first term represents the kinetic energy, the second term V represents the potential, and the E is the total energy. a. -(hcross^2*2m)*Del^2 Psi / V*Psi + E*Psi b. -(hcross^2/2m)*Del^2 Psi + V*Psi = E*Psi c. -(hcross^2*2m)*Del^2 Psi - V*Psi * E*Psi d. -(hcross^2/2m)*Del^2 Psi / V*Psi / E*Psi e. none of the above

b. In a Three-Dimensional Infinite-Potential Well, the three dimensional Schrodinger wave equation is -(hcross^2/2m)*Del^2 Psi + V*Psi = E*Psi, where the first term represents the kinetic energy, the second term V represents the potential, and the E is the total energy.

5.3. In an actual Rutherford scattering experiment, a detector is positioned between __ and __ that corresponds to incident particles between __ and __. a. b; b plus delta b; theta; theta plus delta theta; b. theta; theta plus delta theta; b; b plus delta b c. alpha; beta; b; b plus delta b d. theta; theta plus delta theta; alpha; beta e. none of the above

b. In an actual Rutherford scattering experiment, a detector is positioned between theta and theta plus delta theta that corresponds to incident particles between b and b plus delta b

9.11. In an infinite square-well potential, the Wave function must be __ where the potential is __. a. zero; finite b. zero; infinite c. one; zero d. infinity; infinite e. none of the above

b. In an infinite square-well potential, the Wave function must be zero where the potential is infinite.

9.26. __ describe many physical situations: springs, diatomic molecules and atomic lattices a. Complex harmonic oscillators b. Simple harmonic oscillators c. Simple anharmonic actuators d. Complex harmonic actuators e. none of the above

b. Simple harmonic oscillators describe many physical situations: springs, diatomic molecules and atomic lattices

5.28. In modern Rutherford Backscattering Spectrometry, a beam of particles is directed at a sample with a current of __, and a __ particle detector is used to detect the scattered particles. a. 100 mA; semiconductor field b. 100 nA; semiconductor surface-barrier c. 100 Amps; metal surface-barrier d. 100 mA; insulator field e. none of the above

b. In modern Rutherford Backscattering Spectrometry, a beam of particles is directed at a sample with a current of 100 nA, and a semiconductor surface-barrier particle detector is used to detect the scattered particles.

9.6. In quantum mechanics, the momentum operator is p^ (p hat) = __. a. -i+hcross+del/delx b. -i*hcross*del/delx c. -i-hcross-del/delx d. -i*hcross/del*delx e. none of the above

b. In quantum mechanics, the momentum operator is p^ (p hat) = -i*hcross*del/delx.

5.15. In the Bohr model of the atom, __ or __ of electromagnetic __ can only occur in conjunction with a __ two stationary states. a. emission; absorption; radiation; cancelling of b. emission; absorption; radiation; transition between c. creation; destruction; energy; cancelling of d. creation; destruction; energy; transition between e. none of the above

b. In the Bohr model of the atom, emission or absorption of electromagnetic radiation can only occur in conjunction with a transition between two stationary states.

6.11. In the Bohr model, the standing wave condition for the electron is given by 2*pi*r = __. a. n/lambda = n*h/p b. n*lambda = n*h/p c. n*lambda = n/h*p d. n/lambda = n*h*p e. none of the above

b. In the Bohr model, the standing wave condition for the electron is given by 2*pi*r = n*lambda = n*h/p.

11.8. In the case of Bohr's semi-classical planetary model of electrons orbiting a nucleus, the orbital angular momentum L = __. a. n/hcross b. n*hcross c. n+hcross d. n-hcross e. none of the above

b. In the case of Bohr's semi-classical planetary model of electrons orbiting a nucleus, the orbital angular momentum L = n*hcross.

9.20. In the case of an infinite-potential square well, there __ wave amplitude outside the square-well. In the case of a Finite potential square-well, there __ wave amplitude outside the square well. a. is no; is no b. is no; is a non-zero a. is no; is no c. is a non-zero; is a non-zero d. is a non-zero; is no e. none of the above

b. In the case of an infinite-potential square well, there is no wave amplitude outside the square-well. In the case of a Finite potential square-well, there is non-zero wave amplitude outside the square well.

11.26. In the normal Zeeman effect, an atomic spectral line is __. a. merged into one b. split into three lines c. both merged and split d. split into two lines e. none of the above

b. In the normal Zeeman effect, an atomic spectral line is split into three lines .

4.6. In the plum-pudding model, the atom has __ charges spread __ throughout a sphere the size of the atom, with __ embedded in the __ background. a. positive; discretely; positive protons; discrete b. positive; uniformly; negative electrons; uniform c. negative; discretely; negative electrons; discrete d. negative; uniformly; positive protons; uniform e. none of the above

b. In the plum-pudding model, the atom has positive charges spread uniformly throughout a sphere the size of the atom, with negative electrons embedded in the uniform background.

4.7. In the plum-pudding model, when the atom is __, __ can vibrate about their equilibrium positions, and thereby produce __. a. heated; protons; ionic radiation b. heated; electrons; electromagnetic radiation c. cooled; electrons; ionic radiation d. cooled; protons; electromagnetic radiation e. none of the above

b. In the plum-pudding model, when the atom is heated, electrons can vibrate about their equilibrium positions, and thereby produce electromagnetic radiation.

10.17. In the solution to the Schrodinger equation for a particle in an infinite square-well, the ground state has E = __. a. (3*h^2*pi^2) * (2*m*L^2) b. (3*h^2*pi^2) / (2*m*L^2) c. (3*h^2*pi^2) + (2*m*L^2) d. (3*h^2*pi^2) - (2*m*L^2) e. none of the above

b. In the solution to the Schrodinger equation for a particle in an infinite square-well, the ground state has E = (3*h^2*pi^2) / (2*m*L^2).

8.11. In the solutions to the Schrodinger wave equation, __ quantities are __. a. both physically measurable and not-measurable; real b. only the physically measurable; real c. both physically measurable and not-measurable; imaginary d. only the physically not-measurable; real e. none of the above

b. In the solutions to the Schrodinger wave equation, only the physically measurable quantities are real.

8.12. In the solutions to the Schrodinger wave equation, the probability, momentum and energy are __ quantities. a. physically not-measurable b. physically measurable c. imaginary d. indeterminate e. none of the above

b. In the solutions to the Schrodinger wave equation, the probability, momentum and energy are physically measurable quantities.

13.3. Inert gases have __ net spin and __ ionization energy. a. 1/2; large b. zero; large c. -1/2; small d. zero; small e. none of the above

b. Inert gases have zero net spin and large ionization energy.

6.27. It is __ to measure simultaneously, with no uncertainty, the __ values of __ and x for the same particle. a. possible; precise; k b. impossible; precise; k c. impossible; discrete; time d. possible; analog; E e. none of the above

b. It is impossible to measure simultaneously, with no uncertainty, the precise values of k and x for the same particle.

13.19. Lanthanides have their outside __ subshell filled with electrons. a. 2s2 b. 6s2 c. 3p6 d. 5d10 e. none of the above

b. Lanthanides have their outside 6s2 subshell filled with electrons.

4.1 One of the pieces of evidence that scientists had in 1900 to indicate that the atom was not a fundamental unit includes the fact that there ___ of ___, for any given chemical element. a. is only one kind; atom b. are many kinds; atoms c. are many kinds; electrons d. is only one kind; electron e. none of the above

b. One of the pieces of evidence that scientists had in 1900 to indicate that the atom was not a fundamental unit includes the fact that there are many kinds of atoms, for any given chemical element.

12.13. Particles in the nucleus of an atom are __. a. bosons b. fermions c. leptons d. hadrons e. none of the above

b. Particles in the nucleus of an atom are fermions.

12.12. Particles of half-integer spin are called __. a. bosons b. fermions c. leptons d. hadrons . none of the above

b. Particles of half-integer spin are called fermions.

10.26. Solving the Schrodinger equation for an atom, with appropriate __, leads to the quantum number l (lowercase L) where l = __. a. boundary equations; 1,2,3... b. boundary conditions; 0,1,2,3... c. internal constants; 0,1,2,3... d. external variables; 1,2,3... e. none of the above

b. Solving the Schrodinger equation for an atom, with appropriate boundary conditions, leads to the quantum number l (lowercase L) where l = 0,1,2,3....

5.24. The Bohr model was an important step in Quantum Theory, but had its limitations. It can only work with __ atoms. It could not account for __ or __ of __ lines. And it could not explain binding of __ into __. a. multiple electron; intensities; large-structure; spectral; atoms; molecules b. single electron; intensities; fine-structure; spectral; atoms; molecules c. multiple electron; energies; global-structure; atomic; electrons; atoms d. single electron; energies; universal-structure; nuclear; protons; nucleii e. none of the above

b. The Bohr model was an important step in Quantum Theory, but had its limitations. It can only work with single electron atoms. It could not account for intensities or fine-structure of spectral lines. And it could not explain binding of atoms into molecules.

7.17. The Gaussian wave packet describes the __ of a pulse wave, with a group velocity Ugr = __. a. envelope; dw*dk b. envelope; dw/dk c. wavelength; dw*dk d. frequency; dw/dk e. none of the above

b. The Gaussian wave packet describes the envelope of a pulse wave, with a group velocity Ugr = dw/dk.

11.5. The Orbital Angular Mometum Quantum Number 1 (lower-case L) is associated with the ___ and ___ parts of the wave function. a. wave; particle b. R(r); f(theta) c. R(theta); f(theta) d. R(r); theta(f) e. none of the above

b. The Orbital Angular Mometum Quantum Number 1 (lower-case L) is associated with the R(r) and f(theta) parts of the wave function.

12.8. The Pauli exclusion principle states that no two electrons in an atom may have the same set of __. a. charges b. quantum numbers c. nuclear identities d. fermion identities e. none of the above

b. The Pauli exclusion principle states that no two electrons in an atom may have the same set of quantum numbers.

11.3. The Principal Quantum Number n results from the solution of ___. a. Y(Theta) b. R(r) c. psi(theta) d. psi(r) e. none of the above.

b. The Principal Quantum Number n results from the solution of R(r).

8.1. The Schrodinger wave equation in its time-dependent form for a particle of energy E moving in a potential V in one dimension is i*hcross*delPsi(x,t)/del(t) = __. a. - (hcross^2/2*m)*(del^2Psi(x,t)/delx^2) * V*Psi(x,t) b. - (hcross^2/2*m)*(del^2Psi(x,t)/delx^2) + V*Psi(x,t) c. - (hcross^2/2*m)/(del^2Psi(x,t)/delx^2) + V*Psi(x,t) d. - (hcross^2/2*m)+(del^2Psi(x,t)/delx^2) + V*Psi(x,t) e. none of the above

b. The Schrodinger wave equation in its time-dependent form for a particle of energy E moving in a potential V in one dimension is i*hcross*delPsi(x,t)/del(t) = - (hcross^2/2*m)*(del^2Psi(x,t)/delx^2) + V*Psi(x,t).

6.6. The de Broglie relationship holds for __ and __ (fast moving) and __ (slow moving) particles, provided that the appropriate expression (i.e., value) of __ is used. a. photons; non-relativistic; relativistic; energy b. photons; relativistic; non-relativistic; momentum c. protons; non-relativistic; relativistic; energy d. electrons; relativistic; non-relativistic; momentum e. none of the above

b. The de Broglie relationship holds for photons and relativistic (fast moving) and non-relativistic (slow moving) particles, provided that the appropriate expression (i.e., value) of momentum is used.

10.11. The differential equation for a square-well potential, along the z axis is __ = -kz^2 a. (1/Z)+(d^2Z/dz^2) b. (1/Z)*(d^2Z/dz^2) c. (1/Z)-(d^2Z/dz^2) d. (1/Z)/(d^2Z/dz^2) e. none of the above

b. The differential equation for a square-well potential, along the z axis is (1/Z)*(d^2Z/dz^2) = -kz^2

12.27. The electronic designation for the electron in a hydrogen atom is __. a. 2s1 b. 1s1 c. 1s0 d. 2s0 e. none of the above

b. The electronic designation for the electron in a hydrogen atom is 1s1.

12.15. The first rule that determines the structure of the periodic-table of the elements is that __ in an atom tend to occupy the __ __ available to them. a. electrons; highest; momentum levels b. electrons; lowest; energy levels c. protons; highest; energy levels d. protons; lowest; momentum levels e. none of the above

b. The first rule that determines the structure of the periodic-table of the elements is that electrons in an atom tend to occupy the lowest energy levels available to them.

11.10. The following letter names __,__,__,__ are used to refer to the __ quantum number values l = 0,1,2,3. a. s,p,d,f; principal b. s,p,d,f; orbital angular momentum c. k,l,m,n; principal d. k,l,m,n; orbital angular momentum e. none of the above

b. The following letter names s, p, d, f are used to refer to the orbital angular momentum quantum number values l = 0,1,2,3.

9.13. The general solution to Schrodinger's equation for an infinite square-well potential is psi(x) = __. a. A sin(k/x) * B cos(k/x b. A sin(kx) + B cos(kx) c. A sin(kx) / B cos(kx) d. A sin(k/x) + B cos(k/x) e. none of the above

b. The general solution to Schrodinger's equation for an infinite square-well potential is psi(x) = A sin(kx) + B cos(kx).

13.28. The orbital angular momentum (of an electron in an atom) is __. a. continuous b. quantized c. zero d. infinite e. none of the above

b. The orbital angular momentum (of an electron in an atom) is quantized.

13.26. The orbital angular momentum is denoted by __. a. O b. L c. A d. M e. none of the above

b. The orbital angular momentum is denoted by L.

6.15. The phase velocity is the velocity of a __ on the wave that has a given __ (for example, the crest) and is given by Vph = __, where lambda is the wavelength, T is the period, w is the angular velocity, k is the wave vector. a. point; phase; lambda*T = w*k b. point; phase; lambda/ T = w/k c. frequency; wavelength; lambda*T = w*k d. wave number; frequency; lambda/ T = w/k e. none of the above

b. The phase velocity is the velocity of a point on the wave that has a given phase (for example, the crest) and is given by Vph = lambda/ T = w/k, where lambda is the wavelength, T is the period, w is the angular velocity, k is the wave vector.

7.18. The physical nature of a particle is not clearly described by the __. Unlike a classical wave, the __ of the particle wave is not thought of as being __ the extent of the wave, but rather, is regarded as being __ the particle. a. mass; energy; spread over; localized within b. de Broglie wave; energy; spread over; localized within c. mass; momentum; localized within; spread over d. de Broglie wave; momentum; localized within; spread over e. none of the above

b. The physical nature of a particle is not clearly described by the de Broglie wave. Unlike a classical wave, the energy of the particle wave is not thought of as being spread over the extent of the wave, but rather, is regarded as being localized within the particle.

12.24. The principal quantum number can take the following letter values __. a. s,p,d,f b. K,L,M,N . . . c. n,m,p,q d. 1,2,3,4 e. none of the above

b. The principal quantum number can take the following letter values K, L, M, N.

12.25. The principal quantum number value of 3 matches the principal quantum number letter value of __. a. K b. M c. L d. d e. none of the above

b. The principal quantum number value of 3 matches the principal quantum number letter value of M.

8.16. The probability P(x) dx of a particle being between x and X + dx is given by P(x)dx = __ where Psi' denotes the complex conjugate of Psi. a. Psi'(x,t) / Psi(x,t) dx b. Psi'(x,t) * Psi(x,t) dx c. Psi'(x,t) + Psi(x,t) dx d. Psi'(x,t) - Psi(x,t) dx e. none of the above

b. The probability P(x) dx of a particle being between x and X + dx is given by P(x)dx = Psi'(x,t) * Psi(x,t) dx where Psi' denotes the complex conjugate of Psi.

11.22. The z-component of the orbital angular momentum, Lz is __, and as a result, only certain __ of L are permitted. This is called __. a. continuous; values; space continuity b. quantized; orientations; space quantization c. quantized; values; particle quantization d. continuous; orientations; particle continuity e. none of the above

b. The z-component of the orbital angular momentum, Lz is quantized, and as a result, only certain orientations of L are permitted. This is called space quantization.

7.22. To determine which slit the electron went through, we set up a __ the double slit and use a powerful microscope to look at the region. After the electron passes through one of the slits, __ bounces off the electron; we observe the reflected __, and so we know which slit the electron came through. a. light shining on; an electron; electron b. light shining on; light; light c. electron source shining on; an electron; electron d. electron source shining on; light; electron e. none of the above

b. To determine which slit the electron went through, we set up a light shining on the double slit and use a powerful microscope to look at the region. After the electron passes through one of the slits, light bounces off the electron; we observe the reflected light, and so we know which slit the electron came through.

13.15. Transition metals are in the three rows of elements (in the periodic table) in which the __, __, and __ shells are being filled with electrons. a. 1s; 2s; 2p b. 3d; 4d; 5d c. 2s; 2p; sd d. 3d; 3f; 3g e. none of the above

b. Transition metals are in the three rows of elements (in the periodic table) in which the 3d, 4d, and 5d shells are being filled with electrons.

12.4. When there are 3 electrons in an atom's electron shells, the the 3 electrons __. a. attract each other b. repel each other c. exert no force on each other d. merge with the nucleus e. none of the above

b. When there are 3 electrons in an atom's electron shells, the the 3 electrons repel each other.

7.16. When two waves are combined, the combined wave oscillates within __ that denotes the __ of the combined waves. a. an envelope; average frequency b. an envelope; maximum displacement c. a box; average frequency d. a box; maximum wavelength e. none of the above

b. When two waves are combined, the combined wave oscillates within an envelope that denotes the maximum displacement of the combined waves.

6.18. When waves are combined, the range of wave numbers and angular frequencies that produce a wave packet have the following relations, __ = 2*pi, and __ = 2*pi. a. delta k /delta x; delta omega /deta t b. delta k * delta x; delta omega * deta t c. delta k * delta x; delta omega + deta t d. delta k + delta x; delta omega * deta t e. none of the above

b. When waves are combined, the range of wave numbers and angular frequencies that produce a wave packet have the following relations, delta k * delta x= 2*pi, and delta omega * deta t = 2*pi.

11.30. A magnetic dipole that is placed in a magnetic field has a potential energy V = __, where mu and B are vectors. a. - mu x V b. - mu / V c. - mu dot V d. - mu cross V

c. A magnetic dipole that is placed in a magnetic field has a potential energy V = -mu dot V, where mu and B are vectors.

6.21. A medium is called __ when the phase velocity is the same for all frequencies and is equal to the group velocity. a. particulate b. dispersive c. nondispersive d. wave-like e. none of the above

c. A medium is called nondispersive when the phase velocity is the same for all frequencies and is equal to the group velocity.

13.6. Alkali atoms easily form __ ions with a charge of __. a. negative; -1e b. negative; -2e c. positive; +1e d. positive; +2e e. none of the above

c. Alkali atoms easily form positive ions with a charge of +1e.

13.7. Alkali atoms have __ ionization energies. a. zero b. the highest c. the lowest d. infinite e. none of the above

c. Alkali atoms have the lowest ionization energies.

13.10. Alkaline Earth metals have __ atomic radius in a given period (within the periodic table of the elements). a. the largest b. zero c. the smallest d. infinite e. none of the above

c. Alkaline Earth metals have the smallest atomic radius in a given period (within the periodic table of the elements).

4.13. An alpha particle is the nucleus of __. a. an electron b. a hydrogen atom c. a helium atom d. a gamma particle e. none of the above

c. An alpha particle is the nucleus of a helium atom.

11.17. An atomic energy level or state with n = 4 and l = 3 is called a __ state. a. 4s b. 4p c. 4f d. 4k e. none of the above

c. An atomic energy level or state with n = 4 and l = 3 is called a 4f state.

5.23. An improvement on the Bohr model replaces the electron mass with its __. a. momentum b. energy c. reduced mass d. frequency e. none of the above

c. An improvement on the Bohr model replaces the electron mass with its reduced mass.

9.28. Analysis of a parabolic potential well, in Quantum Mechanics, shows that the largest probability for the lowest energy state is for the particle to be at the __. In contrast, in the classical case, the largest probability is at the __ of the motion and lowest for the particle to be at the __. a. ends; center; ends b. center; center; center c. center; ends; center d. ends; ends; ends e. none of the above

c. Analysis of a parabolic potential well, in Quantum Mechanics, shows that the largest probability for the lowest energy state is for the particle to be at the center. In contrast, in the classical case, the largest probability is at the ends of the motion and lowest for the particle to be at the center.

9.30. At a Quantum mechanical Barrier, an Incident Particle experiences __ the barrier. a. only transmission across b. only reflection at c. reflection at and transmission across d. neither reflection at nor transmission across e. none of the above

c. At a Quantum mechanical Barrier, an Incident Particle experiences reflection at and transmission across the barrier.

9.9. Based on the solution to the Scrodinger equation, the expectation value of the energ is <E> = __. a. i*hcross + integral from -infinity to +infinity of Psi'(x,t) del Psi(x,t)/del t + dx b. i*hcross - integral from -infinity to +infinity of Psi'(x,t) del Psi(x,t)/del t - dx c. i*hcross * integral from -infinity to +infinity of Psi'(x,t) del Psi(x,t)/del t * dx d. i*hcross / integral from -infinity to +infinity of Psi'(x,t) del Psi(x,t)/del t / dx e. none of the above

c. Based on the solution to the Scrodinger equation, the expectation value of the energ is <E> = i*hcross * integral from -infinity to +infinity of Psi'(x,t) del Psi(x,t)/del t * dx.

9.2. Classical mechanics only appears to be more precise because it deals with __ phenomena. The underlying __ in __ measurements are just too __ to be significant. a. macroscopic; certainties; macroscopic; large b. microscopic; certainties; microscopic; small c. macroscopic; uncertainties; macroscopic; small d. microscopic; uncertainties; microscopic; large e. none of the above

c. Classical mechanics only appears to be more precise because it deals with macroscopic phenomena. The underlying uncertainties in macroscopic measurements are just too small to be significant.

8.30. Comparing classical and quantum mechanics, we see that Newton's second law and Schrodinger's wave equation are both __ equations. a. energy b. kinetic c. differential d. parabolic e. none of the above

c. Comparing classical and quantum mechanics, we see that Newton's second law and Schrodinger's wave equation are both differential equations.

11.13. Energy levels and states in atoms are referred to by their __ and __ values. a. n; k b. s; p c. n; l d. P; S e. none of the above

c. Energy levels and states in atoms are referred to by their n and l values.

10.3. For a particle in a 3-D square-well potential box, inside the box, V(x,y,z) = __. a. infinity b. 100 c. 0 d. 1000 e. none of the above

c. For a particle in a 3-D square-well potential box, inside the box, V(x,y,z) = 0.

6.7. For a photon, the phase velocity of the wave becomes u = __, where lambda is the wavelength, f is the frequency, and c is the speed of light. a. lambda*f * c b. lambda*f/ c c. lambda*f = c d. lambda/f = c e. none of the above

c. For a photon, the phase velocity of the wave becomes u = lambda*f = c, where lambda is the wavelength, f is the frequency, and c is the speed of light.

4.15. For a thick gold foil that is 0.6 microns thick, the alpha particle is scattered by about __ degrees. a. 8 b. 80 c. 0.8 d. 800 e. none of the above

c. For a thick gold foil that is 0.6 microns thick, the alpha particle is scattered by about 0.8 degrees.

4.9. Geiger showed that many __ were scattered from thin gold-leaf targets at backward angles __ 90 degrees. a. beta particles; greater than b. gamma particles; less than c. alpha particles; greater than d. photonic particles; less than e. none of the above

c. Geiger showed that many alpha particles were scattered from thin gold-leaf targets at backward angles greater than 90 degrees.

13.22. In Actinides, inner subshells are being filled while the __ subshell is complete. a. 5s2 b. 6s2 c. 7s2 d. 4s2 e. none of the above

c. In Actinides, inner subshells are being filled while the 7s2 subshell is complete.

5.11. In Classical electromagnetic theory, __ electric charge __ energy, which means that the total energy of the particle must __. a. a stationary; radiates; decrease b. a moving; radiates; increase c. an accelerated; radiates; decrease d. an accelerated; does not radiate; stay constant e. none of the above

c. In Classical electromagnetic theory, an accelerated electric charge radiates energy, which means that the total energy of the particle must decrease.

5.2. In Rutherford scattering, the fraction of incident particles that is scattered is given by f = __, where Te is the target area exposed by scatterers, and Tt is the total target area. a. Te*Tt b. Te^Tt c. Te/Tt d. Te+Tt e. none of the above

c. In Rutherford scattering, the fraction of incident particles that is scattered is given by f = Te/Tt, where Te is the target area exposed by scatterers, and Tt is the total target area.

5.5. In Rutherford scattering, the number of scattered particles is __ proportional to the __ of __ of the incident particle. a. directly; the square; kinetic energy b. directly; the; potential energy c. inversely; the square; kinetic energy d. inversely; the; potential energy e. none of the above

c. In Rutherford scattering, the number of scattered particles is inversely proportional to the the square of kinetic energy of the incident particle.

4.28. In Rutherford scattering, when the atomic number of the scattering atom (Z2) increases, the impact parameter b __. a. decreases b. increases c. stays the same d. increases and then decreases e. none of the abovedecreases and then increases (This is horrible)

c. In Rutherford scattering, when the atomic number of the scattering atom (Z2) increases, the impact parameter b increases.

4.10 In a Rutherford experiment, the maximum scattering angle corresponds to the __ change. a. minimum frequency b. maximum frequency c. maximum momentum d. minimum momentum e. none of the above

c. In a Rutherford experiment, the maximum scattering angle corresponds to the maximum momentum change.

9.12. In an infinite square-well potential, the potential is __ inside the box. a. infinity b. minus one c. zero d. plus one e. none of the above

c. In an infinite square-well potential, the potential is zero inside the box.

11.6. In classical physics, the orbital angular momentum is L = ___. a. m/Vorbital*r b. m+Vorbital*r c. m*Vorbital*r d. m-Vorbital*r e. none of the above

c. In classical physics, the orbital angular momentum is L = m*Vorbital*r.

5.20. In the Bohr model, n = 1 gives us the __ energy state, also called the __ state. a. lowest; Bohr b. highest; ground c. lowest; ground d. highest; Bohr e. none of the above

c. In the Bohr model, n = 1 gives us the lowest energy state, also called the ground state.

7.9. In the Bohr model, the __ of the electron (in orbit around the proton) is given by L = __. a. energy; r*p^2 = n*h*(2*pi) = n*hcross b. inertia; r^2*p = n*h/(2*pi) = n/hcross c. angular momentum; r*p = n*h/(2*pi) = n*hcross d. angular momentum; r^2*p = n*h*(2*pi) = n/hcross e. none of the above

c. In the Bohr model, the __ of the electron (in orbit around the proton) is given by L = angular momentum; r*p = n*h/(2*pi) = n*hcross.

11.29. In the absence of a strong external magnetic field, the magnetic moments of indvidual atoms point __. a. all in the same direction b. half upward and half downward c. in random directions d. a quarter each upward, downward, rightward, leftward e. none of the above

c. In the absence of a strong external magnetic field, the magnetic moments of individual atoms point in random directions.

9.22. In the case of __ potential square-well, the __ depth is the distance outside the potential well where the probability is non-zero but decreases quickly to a small value. a. an infinite; potential b. an infinite; outside c. a finite; penetration d. a finite; skin e. none of the above

c. In the case of a finite potential square-well, the penetration depth is the distance outside the potential well where the probability is non-zero but decreases quickly to a small value.

9.18. In the case of an infinite-potential square well, solving for the energy gives us En = n^2*pi^2*hcross^2/(2*m*L^2), where n = 1,2,3... This tell us that the energy is __ and __. a. continuous; nonzero b. continuous; nonzero c. quantized; nonzero d. quantized; zero e. none of the above

c. In the case of an infinite-potential square well, solving for the energy gives us En = n^2*pi^2*hcross^2/(2*m*L^2), where n = 1,2,3... This tell us that the energy is quantized and nonzero.

9.15. In the case of an infinite-potential square well, the normalized wave function becomes psi(x) = __, where L is the length of the well, pi is 3.1415, x is the x-position along the well. a. sqrt(2*L) + sin(n*pi*x/L), b. sqrt(2*L) - sin(n*pi*x/L), c. sqrt(2/L) * sin(n*pi*x/L), d. sqrt(2/L) / sin(n*pi*x/L), e. none of the above

c. In the case of an infinite-potential square well, the normalized wave function becomes psi(x) = sqrt(2/L) * sin(n*pi*x/L), where L is the length of the well, pi is 3.1415, x is the x-position along the well.

10.15. In the solution to the __ equation for a particle in __ square-well potential, the integers nx, ny, and nz are __ and are used to specify the quantum states of the system a. Heisenberg; a finite; Planck numbers b. Schrodinger; a finite; quantum numbers c. Schrödinger; an infinite; quantum numbers d. Heisenberg; an infinite; quantum numbers e. none of the above

c. In the solution to the Schrödinger equation for a particle in an infinite square-well potential, the integers nx, ny, and nz are quantum numbers and are used to specify the quantum states of the system.

7.23. In the which-slit double-slit electron experiment, the momentum of a photon is __. In comparison, the momentum of the electrons is __. a. Pph = h/d; Pel > h/d b. Pph < h*d; Pel = h/d c. Pph > h/d; Pel ~h/d d. Pph = h*d; Pel < h*d e. none of the above

c. In the which-slit double-slit electron experiment, the momentum of a photon is Pph > h/d. In comparison, the momentum of the electrons is Pel ~h/d.

6.13. In wave motion, the displacement of matter waves is given as psi(x,t) = __, where A is the amplitude, pi is 3.1415, lambda is the wavelength, x is the position along the x-axis, v is the velocity of the wave, and t is the time-position along the time-axis. a. A/sin((2*pi/lambda)*(x-v*t)) b. A*sin((2/pi/lambda)/(x-v*t)) c. A*sin((2*pi/lambda)*(x-v*t)) d. A*sin((2*pi*lambda)/(x-v*t)) e. none of the above

c. In wave motion, the displacement of matter waves is given as psi(x,t) = A*sin((2*pi/lambda)*(x-v*t)), where A is the amplitude, pi is 3.1415, lambda is the wavelength, x is the position along the x-axis, v is the velocity of the wave, and t is the time-position along the time-axis.

4.22. One of the assumptions of Rutherford Scattering is that only __ forces are active. a. Rutherford b. magnetic c. Coulombic d. nuclear strong e. none of the above

c. One of the assumptions of Rutherford Scattering is that only Coulombic forces are active.

4.20. One of the assumptions of Rutherford Scattering is that the target is so __ that __ scattering __. a. thin; many; events occur. b. thick; many; events occur c. thin; only a single; event occurs. d. thick; only a single; event occurs. e. none of the above

c. One of the assumptions of Rutherford Scattering is that the target is so thin that only a single scattering event occurs.

2.21. One of the properties of a valid wave function is that for __ potentials, the wave function and its derivative must be __. This is required because the second-order derivative term in the wave equation must be __ valued. a. finite; discrete; multi b. infinite; continuous; multi c. finite; continuous; single d. infinite; discrete; single e. none of the above

c. One of the properties of a valid wave function is that for finite potentials, the wave function and its derivative must be continuous. This is required because the second-order derivative term in the wave equation must be single valued.

3.15 Rayleigh used classical theories of electromagnetism and thermodynamics to show that blackbody spectral distribution should be Intensity = ___, where pi=3.1415, c=speed of light, l= Boltzmann's constant, T= temperature in kelvin, Lambda= wavelength. a. 2*pi*c*T/(lambda^2) b. 2*pi*c*k*T/(lambda^2) c. 2*pi*c*k*T/(lambda^4) d. 2*pi*k*T/(lambda^4) e. none of the above

c. Rayleigh used classical theories of electromagnetism and thermodynamics to show that blackbody spectral distribution should be Intensity = 2*pi*c*k*T/(lambda^4), where pi=3.1415, c=speed of light, l= Boltzmann's constant, T= temperature in kelvin, Lambda= wavelength.

5.30. Rutherford Backscattering Spectrometry acts as a quantitative depth microscope, where the energy loss of the scattered ions gives us the __, the yield of scattered ions gives us the __ in the sample. The technique is __, requiring about __ per sample, and provides direct __ analysis. a. atoms/cm^2; depth scale; fast; 15 min; energy b. atoms/cm^2; depth scale; slow; 1.5 hours; depth c. depth scale; atoms/cm^2; fast; 15 min; depth d. depth scale; atoms/cm^2; slow; 1.5 hours; energy e. none of the above

c. Rutherford Backscattering Spectrometry acts as a quantitative depth microscope, where the energy loss of the scattered ions gives us the depth scale, the yield of scattered ions gives us the atoms/cm^2 in the sample. The technique is fast, requiring about 15 min per sample, and provides direct depth analysis.

10.29. Solving the Schrodinger equation for a Hydrogen atom gives us different hydrogen atom __ for different values of the quantum numbers __ and __. a. tangential wave functions; n; k b. linear particle equations; s; p c. radial wave functions; n; l d. radial wave functions; s; p e. none of the above

c. Solving the Schrodinger equation for a Hydrogen atom gives us different hydrogen atom radial wave functions for different values of the quantum numbers n and l.

5.18. The Bohr radius is about __. a. 0.5 mm b. 0.5 cm c. 0.5 Angstroms d. 0.5 meters e. none of the above

c. The Bohr radius is about 0.5 Angstroms.

6.29. The Heisenberg energy-time uncertainty principle states that __ >= hcross/2. a. delta E / delta t b. delta E + delta t c. delta E * delta t d. delta E - delta t e. none of the above

c. The Heisenberg energy-time uncertainty principle states that delta E * delta t >= hcross/2.

8.7. The amplitude of the solution to the Schrodinger wave equation __. a. must be real b. must be complex c. can be complex d. must be integral e. none of the above

c. The amplitude of the solution to the Schrodinger wave equation can be complex.

12.22. The __ of the two electrons in a Helium atom are a consequence of __ principle. a. aligned spins; the Heisenberg b. anti-aligned spins; the Heisenberg c. anti-aligned spins; the Pauli exclusion d. aligned spins; the Pauli exclusion e. none of the above

c. The anti-aligned spins of the two electrons in a Helium atom are a consequence of the Pauli exclusion principle.

13.4. The atoms of inert gases __ with each other. a. do not interact b. interact strongly c. interact weakly d. coalesce strongly e. none of the above

c. The atoms of inert gases interact weakly with each other.

5.9. The centrifugal force acting on an electron that is orbiting a nucleus is given by __, where m is the mass of the electron, v is the velocity of the electron, and r is the radius of the orbit of the electron. a. m*v/r b. m*v^2*r c. m*v^2/r d. m*v*r e. none of the above

c. The centrifugal force acting on an electron that is orbiting a nucleus is given by m*v^2/r, where m is the mass of the electron, v is the velocity of the electron, and r is the radius of the orbit of the electron.

10.9. The differential equation for a square-well potential, along the x axis is __ = -kx^2 a. (1/X)/(d^2X/dx^2) b. (1/X)+(d^2X/dx^2) c. (1/X)*(d^2X/dx^2) d. (1/X)-(d^2X/dx^2) e. none of the above

c. The differential equation for a square-well potential, along the x axis is (1/X)*(d^2X/dx^2) = -kx^2

8.14. The energy of the wave (solution to Schrodinger equation) is given by E = __, where hcross is Planck's constant divided by 2*pi, and equivalent w is the angular rotational speed for the wave. a. hcross/w b. hcross+w c. hcross*w d. hcross-w e. none of the above

c. The energy of the wave (solution to Schrodinger equation) is given by E = hcross*w, where hcross is Planck's constant divided by 2*pi, and equivalent w is the angular rotational speed for the wave.

8.2. The extension to three dimensions of the Schrodinger wave equation is i*hcross*delPsi(x,y,z,t)/del(t) = __. a. - (hcross^2/2*m)+(del^2Psi/delx^2 + del^2Psi/dely^2 + del^2Psi/delz^2) + V*Psi(x,y,z,t) b. - (hcross^2/2*m) - (del^2Psi/delx^2 + del^2Psi/dely^2 + del^2Psi/delz^2) + V*Psi(x,y,z,t) c. - (hcross^2/2*m)*(del^2Psi/delx^2 + del^2Psi/dely^2 + del^2Psi/delz^2) + V*Psi(x,y,z,t) d. - (hcross^2/2*m)/(del^2Psi/delx^2 + del^2Psi/dely^2 + del^2Psi/delz^2) + V*Psi(x,y,z,t) e. none of the above

c. The extension to three dimensions of the Schrodinger wave equation is i*hcross*delPsi(x,y,z,t)/del(t) = - (hcross^2/2*m)*(del^2Psi/delx^2 + del^2Psi/dely^2 + del^2Psi/delz^2) + V*Psi(x,y,z,t)

4.3 The fact that certain elements can combine with some elements, but not with others, indicates that atoms have an __ __ structure. a. internal; nuclear b. external; atomic c. internal; atomic d. external; nuclear e. none of the above

c. The fact that certain elements can combine with some elements, but not with others, indicates that atoms have an internal atomic structure.

6.3. The first conditions for __ interference of the scattered x-rays is that the Angle of __ must equal the angle of __ of the outgoing wave. a. destructive; scattering; reflection b. destructive; incidence; scattering c. constructive; incidence; reflection d. constructive; scattering; reflection e. none of the above

c. The first conditions for constructive interference of the scattered x-rays is that the Angle of incidence must equal the angle of reflection of the outgoing wave.

11.11. The following letter names __,__ are used to refer to the __ quantum number values l = 4,5. a. s,p; orbital angular momentum b. k, l; principal c. g, h; orbital angular momentum d. d, f; magnetic e. none of the above

c. The following letter names g, h are used to refer to the orbital angular momentum quantum number values l = 4,5.

8.5. The general form of the solution of the Schrodinger wave equation is given by Psi(x,t) = __. a. A*[cos(kx-wt) * i*sin(kx-wt)] b. A*[cos(kx-wt) - i*sin(kx-wt)] c. A*[cos(kx-wt) + i*sin(kx-wt)] d. A*[cos(kx-wt) / i*sin(kx-wt)] e. none of the above

c. The general form of the solution of the Schrodinger wave equation is given by Psi(x,t) = A*[cos(kx-wt) + i*sin(kx-wt)].

13.16. The properties of transition metals are determined by the __ electrons, rather than by the __ subshell being filled a. s; p b. p; s c. s; d d. d; s e. none of the above

c. The properties of transition metals are determined by the s electrons, rather than by the d subshell being filled

7.20. The relationship between the phase velocity of a deBroglie wave and its group velocity is Ugr = __. a. vph * k-dv/dk b. vph / k*dv/dk c. vph + k*dv/dk d. vph - k+dv/dk e. none of the above

c. The relationship between the phase velocity of a deBroglie wave and its group velocity is Ugr = vph + k*dv/dk.

11.20. The solution to the Schrodinger equation specifies that ml is __ and is related to the z component of __, the __. a. zero; L; angular momentum b. a fraction; S; spin c. an integer; L; angular momentum d. an integer; m; magnetism e. none of the above

c. The solution to the Schrodinger equation specifies that ml is an integer and is related to the z component of L, the angular momentum.

8.28. The solution to the time-independent Schrodinger Wave Equation results in a __ that is __ in __. a. probability distribution; constant; energy b. wave distribution; variable; space c. probability distribution; constant; time d. particle distribution; variable; momentum e. none of the above

c. The solution to the time-independent Schrodinger Wave Equation results in a probability distribution that is constant in time.

6.25. The solution to the wave-particle __ of an event is given by Bohr's principle of __. a. complementarity; duality b. singularity; complementarity c. duality; complementarity d. duality; relativity e. none of the above

c. The solution to the wave-particle duality of an event is given by Bohr's principle of complementarity.

10.24. To help solve the Schrödinger equation for a hydrogen atom, we transform the problem to __ coordinates because of __ symmetry. a. x-y; linear b. cartesian; x-y c. spherical polar; radial d. spherical cartesian; tangential e. none of the above

c. To help solve the Schrödinger equation for a hydrogen atom, we transform the problem to spherical polar coordinates because of radial symmetry.

7.4. When a beam of x rays passes through a powdered crystal, the diffraction __ (that correspond to a single crystal) become a series of __. a. rings; dots b. triangles; squares c. dots; rings d. squares; triangles e. none of the above

c. When a beam of x rays passes through a powdered crystal, the diffraction dots (that correspond to a single crystal) become a series of rings.

12.5. When a helium atom has two electrons in its electronic shells, the Schrodinger equation __ be used to solve the electron-electron and electron-proton interaction problems to obtain exact solutions. This is because of __. a. can; the simple potential interactions b. can; the simple kinetic interactions c. cannot; the complex potential interactions d. cannot; the complex kinetic interactions e. none of the above

c. When a helium atom has two electrons in its electronic shells, the Schrodinger equation cannot be used to solve the electron-electron and electron-proton interaction problems to obtain exact solutions. This is because of the complex potential interactions.

6.17. When combining many waves with __ amplitudes and frequencies, a pulse, or __, is formed which moves at a __ velocity, where Ugr = __, where w is the angular frequency and k is the wave vector. a. the same; wave particle; pulse; Deltaw*deltak b. the same; wave phase; wave; Deltaw/deltak c. different; wave packet; group; Deltaw/deltak d. different; wave group; packet; Deltaw*deltak e. none of the above

c. When combining many waves with different amplitudes and frequencies, a pulse, or wave packet, is formed which moves at a group velocity, where Ugr =Deltaw/deltak, where w is the angular frequency and k is the wave vector.

9.10. A particle is trapped in a box with infinitely hard walls that the particle cannot penetrate. This potential is called __ well. a. a hard walled b. a finite wall c. a finite square d. an infinite square e. none of the above

d. A particle is trapped in a box with infinitely hard walls that the particle cannot penetrate. This potential is called an infinite square well.

7.30. According to the Copenhagen interpretation, physics depends on the outcomes of __. a. gedanken experiments b. wave probabilities c. wave equations d. measurement e. none of the above

d. According to the Copenhagen interpretation, physics depends on the outcomes of measurement.

5.25. An atom is __ in its __ state. If there is a vacancy at a __ shell, an electron from a __ shell will drop down to fill the __ vacancy. If this is a radiative transition, __ is immediately emitted. a. least stable; ground; lower; lower; inner-shell; a photon b. metastable; vacuum; higher; lower; outer-shell; an electron c. most stable; vacuum; lower; higher; outer-shell; an electron d. most stable; ground; lower; higher; inner-shell; a photon e. none of the above

d. An atom is most stable in its ground state. If there is a vacancy at a lower shell, an electron from a higher shell will drop down to fill the inner-shell vacancy. If this is a radiative transition, a photon is immediately emitted.

11.14. An atomic energy level or state with n = 2 and l = 1 is called a __ state. a. 2s b. 2d c. 1p d. 2p e. none of the above

d. An atomic energy level or state with n = 2 and l = 1 is called a 2p state.

11.28. An electron orbiting an atom results in a current loop with a magnetic moment mu = __, where L = __ is the magnitude of the orbital angular momentum. a. -e*(2m)*L; m*v/r b. -e/(2m)*L; m*v/r c. -e*(2m)*L; m*v*r d. -e/(2m)*L; m*v*r e. none of the above

d. An electron orbiting an atom results in a current loop with a magnetic moment mu = -e/(2m)*L, where L = m*v*r is the magnitude of the orbital angular momentum.

11.18. Boundary conditions require that the principal quantum number n __ the orbital angular momentum quantum number l. a. is equal to b. is less than c. is greater than or equal to d. is greater than e. none of the above

d. Boundary conditions require that the principal quantum number n is greater than the orbital angular momentum quantum number l.

7.3. Bragg's law states that n*lambda = __, where n is an integer, lambda is the wavelength of the x-rays, d is the spacing between planes of atoms, theta is the diffracted angle. a. d*sin(theta) b. d/sin(theta) c. 2*d/sin(theta) d. 2*d*sin(theta) e. none of the above

d. Bragg's law states that n*lambda = 2*d*sin(theta), where n is an integer, lambda is the wavelength of the x-rays, d is the spacing between planes of atoms, theta is the diffracted angle.

12.6. Consider a helium atom with two protons in its nucleus, and two electrons in its electronic shells. Experimental results from He atoms can be understood by applying the relevant __ and __.without having to actually compute the __ functions of the many-electron interactions in the atom. a. electrons; protons; wave b. electrons; protons; particle c. boundary states; selection effects; particle d. boundary conditions; selection rules; wave e. none of the above

d. Consider a helium atom with two protons in its nucleus, and two electrons in its electronic shells. Experimental results from He atoms can be understood by applying the relevant boundary conditions and selection rules without having to actually compute the wave functions of the many-electron interactions in the atom.

7.10. Electrons were observed to __ Ni crystal much like __. a. to be absorbed by; heat b. to be emitted by; light c. refract from; x-rays d. diffract from; x-rays e. none of the above

d. Electrons were observed to diffract from Ni crystal much like x-rays.

10.5. For a particle in a 3-D square-well the time-independent Schrodinger equation becomes __. a. -(hcross/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + E*psi b. -(hcross*2m)/(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) = E*psi c. -(hcross^2*2m)/(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) + E*psi d. -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) = E*psi e. none of the above

d. For a particle in a 3-D square-well the time-independent Schrodinger equation becomes -(hcross^2/2m)*(del^2 psi/del x^2 + del^2 psi/del y^2 +del^2 psi/del z^2) = E*psi.

6.9. For non-relativistic particles, the phase velocity u = lambda*f = __, where omega is the angular frequency, k is the wave vector, E is the energy, p is the momentum, m is the mass of the particle, hcross is Planck's constant divided by 2pi, and v is the velocity of the particle. a. omega*k = E*p= p*2m= hcross/p = v/2 b. omega*k = E*p= p/2m= hcross/p = v/2 c. omega+k = E+p= p/2m= hcross/p = v/2 d. omega/k = E/p= p/2m= hcross/p = v/2 e. none of the above

d. For non-relativistic particles, the phase velocity u = lambda*f = omega/k = E/p= p/2m= hcross/p = v/2, where omega is the angular frequency, k is the wave vector, E is the energy, p is the momentum, m is the mass of the particle, hcross is Planck's constant divided by 2pi, and v is the velocity of the particle.

4.14. If an alpha particle is scattered by N electrons, then the total scattering angle is given approximately by Theta.total ~= __, where theta is the angle through which the alpha particle is scattered by one electron. a. N*theta b. N*SQRT(theta) c. SQRT(N*theta) d. SQRT(N)*theta e. none of the above

d. If an alpha particle is scattered by N electrons, then the total scattering angle is given approximately by Theta.total ~= SQRT(N)*theta, where theta is the angle through which the alpha particle is scattered by one electron.

5.4. In Rutherford scattering, the number of scattered particles is __ proportional to __ atomic numbers of the incident particle and the target scatterer. a. inversely; the b. directly; the c. inversely; the square of the d. directly; the square of the e. none of the above

d. In Rutherford scattering, the number of scattered particles is directly proportional to the square of the atomic numbers of the incident particle and the target scatterer.

5.7. In Rutherford scattering, the number of scattered particles is __ proportional to the target thickness for __ targets. a. inversely; thin b. inversely; thick c. directly; thick d. directly; thin e. none of the above

d. In Rutherford scattering, the number of scattered particles is directly proportional to the target thickness for thin targets.

4.27. In Rutherford scattering, when the atomic number of the incoming atom (Z1) increases, the impact parameter b __. a. decreases b. increases c. stays the same d. increases and then decreases e. none of the abovedecreases and then increases (...really?)

d. In Rutherford scattering, when the atomic number of the incoming atom (Z1) increases, the impact parameter b increases.

12.20. In a Helium atom, the second electron has the following values for its four quantum numbers __, __, __, and __. a. 1; 0; 0; 1/2 b. 1; 0; 0; 1 c. 1; 0; 0; -1 d. 1; 0; 0; -1/2 e. none of the above

d. In a Helium atom, the second electron has the following values for its four quantum numbers 1, 0, 0, and -1/2.

7.24. In quantum mechanics, __ are those quantities such as position, velocity, momentum, and energy that can be experimentally measured. Given Bohr's principle of __, in any given instance we must use __ the particle description __ the wave description. a. atomic observables; uncertainty; either; or b. atomic observables; uncertainty; both; and c. physical observables; complementarity; both; and d. physical observables; complementarity; either; or e. none of the above

d. In quantum mechanics, physical observables are those quantities such as position, velocity, momentum, and energy that can be experimentally measured. Given Bohr's principle of complimentarity, in any given instance we must use either the particle description or the wave description.

9.5. In quantum mechanics, we change from __ to __ variables by using the __ P(x,t) __ the particle at a particular x. a. discrete; continuous; momentum; of b. physical; temporal; energy; of c. continuous; discrete; time duration of existence; of d. discrete; continuous; probability; of observing e. none of the above

d. In quantum mechanics, we change from discrete to continuous variables by using the probability P(x,t) of observing the particle at a particular x.

6.10. In the Bohr model, the Electron is a __ in an orbit around the __ of a Hydrogen atom. This __ will have nodes and be __ number of __. a. orbiting wave; proton; wave; a fractional; wavelengths b. oscillating wave; electron; wave; an integral; frequencies c. moving wave; electron; wave; a fractional; frequencies d. standing wave; proton; wave; an integral; wavelengths e. none of the above

d. In the Bohr model, the Electron is a standing wave in an orbit around the proton of a Hydrogen atom. This wave will have nodes and be an integral number of wavelengths.

10.21. In the Schrodinger Wave Equation for a two-body situation, the Eigen Function is __. a. E b. V c. H d. psi(x,y,z) e. none of the above

d. In the Schrodinger Wave Equation for a two-body situation, the Eigen Function is psi(x,y,z).

8.3. In the Schrodinger equation, i = __, and is __ number. a. sqrt(-1); a rea b. sqrt(1); an integer c. sqrt(2); a real d. sqrt(-1); an imaginary e. none of the above

d. In the Schrodinger equation, i = sqrt(-1), and is an imaginary number.

10.12. In the case of a particle in a square-well potential, the resulting kx, ky and kz are related by kx^2 + ky^2 + kz^2 = __. a. 2mE * hcross^2 b. 2mE + hcross^2 c. 2mE - hcross^2 d. 2mE / hcross^2 e. none of the above

d. In the case of a particle in a square-well potential, the resulting kx, ky and kz are related by kx^2 + ky^2 + kz^2 = 2mE / hcross^2.

8.26. In the separated form of the time-independent Schrodinger Wave Equation, the left side of the equation depends __, and the right side depends __. Hence each side must be equal to a __. a. on time; on momentum; variable b. on time and energy; on position and momentum; constant c. only on energy; only on time; variable d. only on time; only on spatial coordinates; constant e. none of the above

d. In the separated form of the time-independent Schrodinger Wave Equation, the left side of the equation depends only on time, and the right side depends only on spatial coordinates. Hence each side must be equal to a constant.

10.16. In the solution to the Schrodinger equation for a particle in an infinite square-well, for a cubic box, E = __. a. (hcross^2*pi^2/2mL^2) / (nx^2 + ny^2 + nz^2) b. (hcross^2*pi^2/2mL^2) + (nx^2 + ny^2 + nz^2) c. (hcross^2*pi^2/2mL^2) - (nx^2 + ny^2 + nz^2) d. (hcross^2*pi^2/2mL^2)*(nx^2 + ny^2 + nz^2) e. none of the above

d. In the solution to the Schrodinger equation for a particle in an infinite square-well, for a cubic box, E = (hcross^2*pi^2/2mL^2)*(nx^2 + ny^2 + nz^2).

6.24. In the which-slit double-slit electron experiment, the __ of the photons (that are used to determine which slit the __ went through) is sufficiently great to strongly modify the __ of the __ itself, thus changing the direction of the __ and so, changing the __. a. energy; photon; momentum; photon; electron; reflection pattern b. energy; electron; momentum; electron; photon; diffraction pattern c. momentum; photon; momentum; electron; electron; scattering pattern d. momentum; electron; momentum; electron; electron; interference pattern e. none of the above

d. In the which-slit double-slit electron experiment, the momentum of the photons (that are used to determine which slit the electron went through) is sufficiently great to strongly modify the momentum of the electron itself, thus changing the direction of the electron and so, changing the interference pattern.

5.14. One of Bohr's assumptions in developing his model of the atom is that __ states or orbits must exist in atoms. In those states, orbiting electrons __ energy. These orbits have a __ energy. a. oscillating; do not radiate; oscillating b. oscillating; radiate; fixed c. stationary; radiate; decreasing d. stationary; do not radiate; fixed e. none of the above

d. One of Bohr's assumptions in developing his model of the atom is that stationary states or orbits must exist in atoms. In those states, orbiting electrons do not radiate energy. These orbits have a fixed energy.

4.19. One of the assumptions of Rutherford Scattering is that the target scatterer is __ that it does __ significantly. Therefore, the initial and final __ of the alpha particle are equal. a. not massive; not recoil; kinetic energies b. so massive; not recoil; potential energies c. not massive; recoil; potential energies d. so massive; not recoil; kinetic energies e. none of the above

d. One of the assumptions of Rutherford Scattering is that the target scatterer is so massive that it does not recoil significantly. Therefore, the initial and final kinetic energies of the alpha particle are equal.

8.20. One of the properties of a valid wave function is that in order to avoid __ values of the probability, the wave function must be __ valued. a. infinite; single b. infinite; multi c. finite; multi d. multiple; single e. none of the above

d. One of the properties of a valid wave function is that in order to avoid multiple values of the probability, the wave function must be single valued.

5.29. Rutherford Backscattering Spectrometry, ion-beam analysis, commonly uses __ energy __ions, also known as __ particles, as the incoming probe beam. a. keV; He; alpha b. eV; H; beta c. MeV; H; gamma d. MeV; He; alpha e. none of the above

d. Rutherford Backscattering Spectrometry, ion-beam analysis, commonly uses MeV energy He ions, also known as alpha particles, as the incoming probe beam.

4.23. __ experiments help us study components of __ that are too __ to be observed directly. a. Planck scattering; waves; light b. Newtonian scattering; matter; small c. Rutherford scattering; waves; large d. Rutherford scattering; matter; small e. none of the above

d. Rutherford scattering experiments help us study components of matter that are too small to be observed directly.

12.11. The Pauli exclusion principle applies to __ particles of __ spin. a. all; integer b. some; integer c. some; half-integer d. all; half-integer e. none of the above

d. The Pauli exclusion principle applies to all particles of half-integer spin.

7.13. The angular frequency of a matter wave is w = __. a. pi/T b. pi*T c. 2*pi*T d. 2*pi/T e. none of the above

d. The angular frequency of a matter wave is w = 2*pi/T.

4.4. The discoveries of __, __ and __ indicate that the atom is __ fundamental unit of matter. a. radioactivity; X-rays; electrons; the b. relativity; gamma-rays; electrons; the c. radioactivity; gamma-rays; photons; not the d. radioactivity; X-rays; electrons; not the e. none of the above

d. The discoveries of radioactivity, X-rays and electrons; indicate that the atom is not the fundamental unit of matter.

6.14. The displacement of matter waves is a solution to the wave equation del squared psi over del x squared = __. a. 1/v * del squared psi over del t squared b. v * del squared psi over del t squared c. v^2 /del squared psi over del t squared d. 1/v^2 * del squared psi over del t squared e. none of the above

d. The displacement of matter waves is a solution to the wave equation del squared psi over del x squared = 1/v^2 * del squared psi over del t squared.

8.15. The kinetic energy of the wave-particle (solution to Schrodinger equation) is given by KE = __, where p is the momentum, and m is the mass of the particle. a. p/2m b. p*m c. p^2*2m d. p^2/2m e. none of the above

d. The kinetic energy of the wave-particle (solution to Schrodinger equation) is given by KE = p^2/2m, where p is the momentum, and m is the mass of the particle.

13.1. The last group of the periodic table includes __. a. halogens b. alkaline earths c. alkalis d. inert gases e. none of the above

d. The last group of the periodic table includes inert gases.

6.19. The localization of the wave packet over a small region to describe a __ requires __ range of wave numbers. Conversely, __ range of wave numbers __ produce a wave packet localized within a small distance. a. wave; a large; a small; can b. wave; a small; a large; cannot c. particle; a small; a large; can d. particle; a large; a small; cannot e. none of the above

d. The localization of the wave packet over a small region to describe a particle requires a large range of wave numbers. Conversely, a small range of wave numbers cannot produce a wave packet localized within a small distance.

11.2. The negative in the expression for the quantized energy means that the electron and the proton __. a. are waves b. are particles c. have negative momentum d. are bound together e. none of the above

d. The negative in the expression for the quantized energy means that the electron and the proton are bound together.

8.13. The physical meaning of the Schrodinger wave equation is Total __ = kinetic __ + potential __. a. momentum; momentum; momentum b. position; position; position c. time; time; time d. energy; energy; energy e. none of the above

d. The physical meaning of the Schrodinger wave equation is Total energy = kinetic energy + potential energy.

5.22. The ratio of the electron's orbital velocity (in the ground state) and the speed of light is the __ constant. a. Planck b. universal c. large structure d. fine-structure e. none of the above

d. The ratio of the electron's orbital velocity (in the ground state) and the speed of light is the fine-structure constant.

8.29. The solution to the time-independent Schrodinger Wave Equation results in a __ that is called a __ state. a. moving particle; kinetic b. standing particle; potential c. moving wave; dynamic d. standing wave; stationary e. none of the above

d. The solution to the time-independent Schrodinger Wave Equation results in a standing wave that is called a stationary state.

7.14. The wave equation for a matter wave is given by psi(x,t) = __. a. A/sin(k*x - w*t) b. A*sin(k/x - w*t) c. A*sin(k*x - w/t) d. A*sin(k*x - w*t) e. none of the above

d. The wave equation for a matter wave is given by psi(x,t) = A*sin(k*x - w*t).

6.30. The wave function determines the likelihood (or probability) of finding a particle at a particular position in space at a given time. P(y)dy = __. a. |psi(y,t)| dy b. |psi(y,t)| + dy c. |psi(y,t)|^2 + dy d. |psi(y,t)|^2 dy e. none of the above

d. The wave function determines the likelihood (or probability) of finding a particle at a particular position in space at a given time. P(y)dy = |psi(y,t)|^2 dy

4.5. Thomson's atomic model is also known as the __ model. a. Bohr b. planetary c. rice pudding d. plum pudding e. none of the above

d. Thomson's atomic model is also known as the plum pudding model.

4.17. When Rutherford scattered alpha particles off of a gold foil, the experimental results were __ Thomson's __ model of the atom. a. consistent with; plum-pudding b. consistent with; satellite c. not consistent with; satellite d. not consistent with; plum-pudding e. none of the above

d. When Rutherford scattered alpha particles off of a gold foil, the experimental results were not consistent with Thomson's plum-pudding model of the atom.

4.12. When an alpha particle hits an electron, the maximum angle of scattering of the alpha particle is given by ThetaMax =__, where Me is the mass of the electron and Malpha is the mass of the alpha particle. a. 2*Me*Malpha b. Me*Malpha c. 2*Me*Malpha d. 2*Me/Malpha e. none of the above

d. When an alpha particle hits an electron, the maximum angle of scattering of the alpha particle is given by ThetaMax = 2*Me/Malpha, where Me is the mass of the electron and Malpha is the mass of the alpha particle.