PH253 - Modern Physics Conceptual Questions
One of the following statements is incorrect. Select it. (a) If the decay of a particle is observed in an inertial frame where it is at rest, the total kinetic energy of the daughter particles is equal to the rest energy of the parent particle. (b) In an inertial reference frame where a system is at rest, the total energy of the system, which may be a complex bound system of constituent systems, depends only on its mass. (c) The energy of a particle depends on its momentum and its mass. (d) If one increases the kinetic energy of a particle by a factor of two, the energy of the particle increases but by less than a factor of two. (e) The energy of a particle cannot be less than its rest energy. (f) A particle is to be considered relativistic if its kinetic energy is comparable to or larger than its rest energy.
(a) If the decay of a particle is observed in an inertial frame where it is at rest, the total kinetic energy of the daughter particles is equal to the rest energy of the parent particle.
Which of the following statements is correct? (a) It is possible to determine the average lifetime of an unstable particle even if the average lifetime is 1 ys. (y=yocto) (b) It is impossible for the uncertainty in the x-coordinate and the uncertainty in the y-coordinate of a particle's position to be simultaneously zero. (c) If a system is stable, it is impossible to measure its energy exactly. (d) For a given uncertainty in the position of a particle, one can use the Heisenberg Uncertainty Principle to determine the uncertainty in the momentum of the particle.
(a) It is possible to determine the average lifetime of an unstable particle even if the average lifetime is 1 ys. (y=yocto)
3. Which of the following is not a property of the stationary states of a system? (a) It is possible to find stationary states for a system even if the potential is changing with time. (b) If the observable properties of the system are changing with time, this can described only in terms of a superposition of stationary states. (c) The properties of a system whose wave function is a stationary state do not change with time. (d) Any state of the system can be described by a superposition of stationary states (e) The energies associated to the stationary states comprise the complete set of allowed energies for the system.
(a) It is possible to find stationary states for a system even if the potential is changing with time Incorrect. If the potential depends on time, the Schrodinger equation cannot have solutions which are a product of two functions, one depending on position only and the other depending on time only.
Which of the following is not associated with Moseley's Law? (a) L-shell X-rays (b) Atomic transitions (c) X-ray energy is proportional to Z-1 (d) Determination of the atomic number from X-ray energy. (e) Nuclear screening.
(a) L-shell X-rays
Which of the following statements is not correct about molecular bonding? (a) Molecules with covalent bonds have larger electric dipole moments than molecules with ionic bonds. (b) When two atoms, such as hydrogen atoms, are brought close together, two states are formed, but only one corresponds to a stable molecule. (c) Binding energy is the difference between the summed rest energies of the individual constituent atoms and the rest energy of the molecule. (d) The binding energy for stable molecules is positive. (e) The total electron spin angular momentum of molecular hydrogen is zero.
(a) Molecules with covalent bonds have larger electric dipole moments than molecules with ionic bonds.
6. Select the following statement which is correct (a) The energy-time uncertainty principle does not involve uncertainty in the measurement of time (b) The cutoff frequency for the photoelectric effect depends on the light intensity. (c) Interference patterns are not observed in double-slit experiments if the intensity of the light is reduced so much that only one photon at a time is incident on the double slit apparatus. (d) There is no connection between the wave-like properties of a system and its particle-like properties
(a) The energy-time uncertainty principle does not involve uncertainty in the measurement of time
If the velocity of a particle is doubled, the magnitude of its momentum (a) increases by more than a factor of two. (b) increases by less than a factor of two. (c) increases by a factor of two. (d) remains the same.
(a) increases by more than a factor of two.
Which of the following statements is not correct? (a) Two events whose space-time separation is space-like cannot be causally connected. (b) A proper time can be defined for any pair of space-time events. (c) The time between two events which occur at the same place is a proper time. (d) The proper length of an object is the length of an object as measured in an inertial frame in which it is at rest. (e) If the proper time between two events is T, no measurement of the time interval between the two events by any other inertial observer can yield a result less than T. (f) The measurement of the length of an object cannot yield a result greater than its proper length.
(b) A proper time can be defined for any pair of space-time events.
2. A particle of mass M decays at rest into two particles of masses m1 and m2, respectively. m1 > m2. Which of the following statements is not correct? p is the symbol for momentum magnitude and K is the symbol for kinetic energy. (a) The kinetic energy of any particle is not exactly proportional to the square of its momentum (b) K1 > K2 (c) M ≥ m1 + m2 (d) p1 = p2 (e) Total kinetic energy is not conserved
(b) K1 > K2
3. A measurement of the magnitude of the orbital angular momentum of the hydrogen atom yields the result sqrt(6h). Which of the following quantities could not have been obtained in a measurement on the hydrogen atom in the same state? (a) E = -3.4 eV (b) Lz = -2h (c) E = -0.85 eV (d) Sz = h/2 (e) Lz = 0
(b) Lz = -2h
19. Consider the following statements about the Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein distributions. Which is not correct? (a) The average number of particles occupying a state of energy E may be greater than one. (b) The Fermi-Dirac distribution applies to electrons in a superconductor below the critical temperature. (c) The Maxwell-Boltzmann distribution is an appropriate distribution to use to describe oscillations of atoms in a solid. (d) Helium can exist as a superfluid or as a rare gas. Even though the particle type is the same in both cases, one would use a di↵erent distribution function for the superfluid than for the rare gas. (e) The distributions describe the average number of particles occupying a particular state of energy E at thermal equilibrium.
(b) The Fermi-Dirac distribution applies to electrons in a superconductor below the critical temperature. For superconductors operating below the critical temperature, the number of electrons occupying states near the energy gap is greater than 1, so Fermi-Dirac statistics do not exactly apply.
An isolated hydrogen atom makes a transition from a n=2 state to the n=1 state. Which of the following statements is correct? (a) The n=2 state has quantum number l=0. (b) The radiation emitted in the transition is comprised of a single line corresponding to an energy of 10.2 eV. (c) The energy of the radiation emitted in the transition has one of two possible values. (d) The energy of the radiation emitted in the transition is exactly 3.4 eV.
(b) The radiation emitted in the transition is comprised of a single line corresponding to an energy of 10.2 eV.
Which of the following statements is inconsistent with the quantum picture of light? (a) The emission spectrum of a blackbody does not depend on the composition of the blackbody if it is in thermal equilibrium. (b) The stopping potential for electrons ejected from an illuminated metal depends on the wavelength and intensity of the light. (c) It is impossible to observe a interference pattern with a double slit apparatus using a light source which occasionally emits a single photon. (d) Laser light is comprised of discrete packets having definite energy and momentum. (e) Laser light illuminating a double-slit apparatus produces an interference pattern.
(b) The stopping potential for electrons ejected from an illuminated metal depends on the wavelength and intensity of the light.
9. Which of the following properties is not possessed by every quantum mechanical wave function? (a) The wave function is single-valued everywhere. (b) The wave function is real. (c) The first derivative of the wave function is continuous everywhere as long as changes in potential are finite. (d) The integral of Ψ*Ψ over all space is 1. (e) The wave function is continuous everywhere.
(b) The wave function is real. Not possessed by every wave function. In general, the wave function may be complex function.
8. Which of the following statements is not correct? (a) A proper time may be defined for the interval between two events if the space-time separation between the two events is time-like. (b) The wavelength at which the intensity of a blackbody peaks is proportional to temperature. (c) Events simultaneous according to one observer may not be simultaneous according to a second observer in relative motion with respect to the first. (d) The sun is an example of a blackbody. (e) The greater the work function for a metal, the higher the cutoff frequency for the photoelectric effect.
(b) The wavelength at which the intensity of a blackbody peaks is proportional to temperature. Incorrect. The higher the temperature, the shorter the wavelength at which the spectrum peaks.
If the hydrogen atom is in a stationary state with principal quantum number equal to 4, which of the following statements is incorrect? (a) If the z component of the orbital angular momentum is measured, there are seven possible outcomes. (b) A measurement of the atom's energy will return the result -0.85 eV. (c) A measurement of the magnitude of the total angular momentum will not give a result equal to 0. (d) A measurement of the magnitude of the total orbital angular momentum of the atom may return the result 3.46h.
(c) A measurement of the magnitude of the total angular momentum will not give a result equal to 0.
Which of the following statements is not correct? (a) If a particle of energy E is incident upon a potential step, there is a nonzero probability that the particle will be reflected even if the energy of the particle is greater than the height of the step. (b) A traveling wave of definite energy E cannot be used to describe a physical particle but a superposition of traveling waves may be used. (c) For a mono-energetic particle of energy E incident upon a potential barrier, the transmission probability approaches 1 only when the the energy of the particle is much greater than the height of the barrier. (d) The decay of a nucleus by alpha emission, the scanning tunneling microscope, and ammonia inversion are examples of quantum tunneling. (e) The allowed energies of a free particle form a continuum.
(c) For a mono-energetic particle of energy E incident upon a potential barrier, the transmission probability approaches 1 only when the the energy of the particle is much greater than the height of the barrier.
Consider a large number of one-electron atoms and imagine that the atoms are one-dimensional. At some instant, the measurement of the position of the electron is measured for half of the atoms and the momentum of the electron is measured for the other half of the atoms. Suppose that the spread in the position measurement results is 0.1 nm. Which of the following statements is inconsistent with this result? Note that the electrons are bound in this case and so a measurement of an electron's velocity is as likely to yield a positive result as it is to yield a negative result. (a) The spread in the momentum measurements is 1.5 keV/c. (b) The uncertainty in the position of the electron is 0.1 nm. (c) If the kinetic energy of the electrons had been measured, the average result would have been about 0.3 eV. (d) The average of the momentum measurements is zero.
(c) If the kinetic energy of the electrons had been measured, the average result would have been about 0.3 eV.
3. Which of the following statements describing the operation of a laser is not correct? (a) Stimulated absorption tends to reduce the intensity of a laser. (b) Population inversion cannot be practically achieved if no metastable states are involved. (c) It is possible to achieve a laser in which the pump state has lower energy than any metastable state involved in the operation of the laser. (d) Considering a photon whose energy is equal to the di↵erence between two atomic levels, the probability per atom in the upper level that a photon stimulates emission is equal to the probability per atom in the lower level that a photon stimulates absorption. (e) If spontaneous emission were the only emssion mechanism available to an atom, lasers would not be possible, but spontaneous emission still plays an important role in the operation of a laser
(c) It is possible to achieve a laser in which the pump state has lower energy than any metastable state involved in the operation of the laser. There is no way to achieve population inversion if the pump state (a short-lived state) is lower in energy than the metastable state involved in lasing radiation.
11. Which of the following statements is incorrect? (a) The quantity E^2-p^2*c^2 has the same value in all inertial reference frames. (b) If observer A measures two events to occur simultaneously but at locations with different x coordinates, the events cannot be simultaneous for any other observer B who is in relative motion in the x-direction with respect to A. (c) The Lorentz transformation relates only position and time measurements by two different inertial observers in relative motion. (d) Two events which have a space-like separation in space-time cannot be causally connected.
(c) The Lorentz transformation relates only position and time measurements by two different inertial observers in relative motion.
5. For a bound system such as the hydrogen atom in which the binding force is the inverse square force (such as the Coulomb force), it can be shown that expectation value of the Coulomb potential energy ( e2 4⇡✏0r ) of the electron (average result of measuring the Coulomb potential energy of the electron) is -2 times the expectation value for the kinetic energy of the electron (average result of measuring the electron kinetic energy). This is known as the virial theorem. This means that the expectation value for the kinetic energy of the electron is -1 times the total energy of the electron. <K> + <U>= E <U>= 2 <K> <K> 2 <K>= E <K>= E where <A> denotes the expectation value of observable quantity A. Which of the following statements is not correct for the electron in the hydrogen atom? (a) The expectation value for the Coulomb potential energy increases as the principal quantum number increases. (Remember the sign of the potential energy.). (b) The motion of the electron in the hydrogen atom is nonrelativistic. (c) The kinetic energy of the electron increases as the principal quantum number increases.
(c) The kinetic energy of the electron increases as the principal quantum number increases. Incorrect. The average kinetic energy of the electron decreases, which is 13.6 eV/n2, decreases as the principal quantum number increases
A free electron gas in thermal equilibrium is an approximate description of conduction electrons in a metal. Which of the following statements is correct? (a) The density of states is independent of the state energy. (b) No quantum states with energy greater than the Fermi energy are occupied at room temperature. (c) The mean kinetic energy of the conduction electrons increases only slightly between temperatures of 0 K (absolute zero) and 298 K (room temperature). (d) At absolute zero, the mean energy of the conduction electrons is the Fermi energy.
(c) The mean kinetic energy of the conduction electrons increases only slightly between temperatures of 0 K (absolute zero) and 298 K (room temperature).
9. Which of the following statements is correct? (a) The Heisenberg Uncertainty Principles are unrelated to the wave-particle duality of physical systems. (b) It is possible to know the momentum of an electron confined to an atom (size approximately 0.1 nm) with an uncertainty less than 1026 kg m/s. (c) The minimum kinetic energy of a localized particle cannot be zero. (d) The slower the rate of change of a system, the greater the uncertainty in its energy. (e) The energy of a muon, which is an unstable particle, can be measured to arbitrarily high precision.
(c) The minimum kinetic energy of a localized particle cannot be zero. Correct. Due to wave-particle duality, a confined system cannot have zero energy.
4. Which of the following concepts is least relevant to understanding the ground state electronic configuration of atoms? (a) minimization of energy (b) electron spin (c) electron mass (d) identical particles (e) antisymmmetry of the total wavefunction under the interchange of particle labels
(c) electron mass. Electron mass is not relevant to explaining the ground state configuration of atoms. All the other concepts are relevant.
6. Which of the following statements is not correct? (a) The wavelike properties of a system are related to its particle-like properties. (b) Doubling the absolute temperature of a blackbody increases its output power by a factor of sixteen. (c) Interference patterns can be observed using weak light sources which emit a single photon at a time. (d) A de Broglie wavelength can be defined for an elementary particle such an electron but not for a much larger system such as an oxygen atom. (e) Increasing the intensity of light incident on a metal by a factor of ten greatly increases the rate at which electrons are emitted from the metal but does not change the maximum kinetic energy of the electrons.
(d) A de Broglie wavelength can be defined for an elementary particle such an electron but not for a much larger system such as an oxygen atom. Incorrect. It can be defined for any system with definite momentum. More generally, no system can be classified as simply a wave or simply a particle.
Which of the following concepts is least relevant to the operation of a laser? (a) stimulated absorption (b) metastable state (c) population inversion (d) Compton scattering (e) spontaneous emission (f) stimulated emission (g) pump state
(d) Compton scattering
1. Which of the following statements is not correct? (a) Doubling the speed of a particle with nonzero mass more than doubles its momentum. (b) The speed of light in vacuum is the same for all inertial observers. (c) The space-time separation between any two events on the world line of a particle with nonzero mass is always time-like. (d) Doubling the momentum of a particle with nonzero mass quadruples its kinetic energy. (e) Two events separated in time by 1 ns and separated in space by 1 m could not be causally connected.
(d) Doubling the momentum of a particle with nonzero mass quadruples its kinetic energy. Incorrect. Only true for classical mechanics,which is an approxmation
For a crystalline solid, which of the following statements is not correct? Assume the solid is one-dimensional and take a to be the lattice spacing. (a) The probability of locating the electron at x is equal to the probability of locating the electron at x+2a. (b) An insulator and a semiconductor (assume pure) are similar in what levels are occupied in the ground state but are very different in what levels are occupied at room temperature. (c) Good conductors are materials in which the unoccupied electron states are nearby in energy where "nearby" means that the difference in energies between occupied and unoccupied states is small compared to kT and/or eV where e is the electronic charge and V is the potential difference applied across the material. (d) For a particular solution to the Schrodinger equation, the wave function at x is equal to the wave function at x+a. (e) The allowed energies within a band are closely spaced but discrete.
(d) For a particular solution to the Schrodinger equation, the wave function at x is equal to the wave function at x+a.
15. Stephen travels from earth to a habitable planet 10 light years away at speed 0.5c. Mary makes the same trip but in the opposite direction at the same speed. Which of the following statements is correct? (The distance to the habitable planet and the speeds of the travelers are as measured by an earth-based observer.) (a) Mary ages more during her trip than Stephen ages during his trip (b) Mary sees the light from earth sun as red-shifted while Stephen sees the light from the earth sun as blue-shifted (c) If Mary and Stephen each send a signal to earth on their birthday, the earth receives more signals from Mary than from Stephen. (d) The birthday signals sent to earth by Mary are received at a higher frequency than the birthday signals sent by Stephen
(d) The birthday signals sent to earth by Mary are received at a higher frequency than the birthday signals sent by Stephen. Both age at the same rate, so the frequency at which birthday signals are emitted in the reference frames of Stephen and Mary are the same. As measured by an earth-based observer, Mary is an approaching source while Stephen is a receding source, so by the relativistic Doppler effect, the birthday signals emitted by Mary arrive at a higher rate than the birthday signals sent by Stephen. The number of signals received for Stephen is still the same as for Mary because Stephen's signals are received over a longer interval.
Which of the following statements is not correct? (a) If one measures the energy of a particle, the outcome is one of the energies associated to stationary states of the particle. (b) Classical physics is a good approximation to quantum mechanics in the regime where the quantum number is very large. (c) The wave function is continuous and single-valued everywhere. (d) The integral of the wave function over all x is 1 for a particle moving in one dimension. (e) The energy of a stationary state can be precisely measured.
(d) The integral of the wave function over all x is 1 for a particle moving in one dimension.
9. Which of the following statements is not correct? (a) The photoelectric effect is an example in which light manifests particle-like properties. (b) The predictions of classical mechanics agree with those of quantum mechanics in the limit of large quantum numbers. (c) The minimum uncertainty in the measurement of the energy of a system depends on the rate at which the system is changing. (d) The wavelike properties of a system are unrelated to the particle-like properties of the system. (e) The electron may be viewed as a complex physical system which manifests particle like properties in some circumstances and wave properties in other circumstances.
(d) The wavelike properties of a system are unrelated to the particle-like properties of the system. The wave-like properties and particlelike properties are related, e.g. p = h/λ.
6. Which of the following orderings describes the relative magnitudes of excitation energies for a typical diatomic molecule? (a) vibrational > rotational > electronic (b) vibrational > electronic > rotational (c) rotational > electronic > vibrational (d) electronic > vibrational > rotational (e) electronic > rotational > vibrational
(d) electronic > vibrational > rotational Excitation energies for electronic states are largest, on the level of an eV or so. Next comes excitation energies for the vibrational states, which are approximately in the range 0.1-1 eV. The rotational states have the lowest excitation energies, in the range 0.01-0.1 eV.
8. Which of the following quantities could be described without reference to Planck's constant? (a) zero-point energy of a particle in a box (b) de Broglie wavelength (c) Schrodinger equation (d) energy of a free particle (e) blackbody radiation
(d) energy of a free particle Except for the energy of a free particle, which can take on any value, none of the other quantities could be explained or defined without a nonzero Planck's constant.
Consider blackbody radiation. Which of the following statements is incorrect? (a) The quantum theory of radiation and the classical theory of radiation disagree on the blackbody spectrum at short wavelengths. (b) Cosmic radiation has a background component which has the features of a blackbody spectrum corresponding to a temperature of 2.7 Kelvin. (c) The blackbody spectrum can be used to determine Planck's constant. (d) A blackbody is defined as an object which absorbs all radiation incident upon it. (e) If one increases the temperature of a blackbody from 100 degrees Centigrade to 200 degrees Centigrade, the wavelength at which the intensity of the blackbody spectrum peaks decreases by a factor of two. (f) The total intensity of a blackbody emitter is proportional to the fourth power of the absolute temperature.
(e) If one increases the temperature of a blackbody from 100 degrees Centigrade to 200 degrees Centigrade, the wavelength at which the intensity of the blackbody spectrum peaks decreases by a factor of two.
14. Which of the following concepts is least important for describing insulator materials? (a) Fermi energy (b) conduction band (c) energy gap (d) valence band (e) holes
(e) holes. One does not need to invoke holes to explain the behavior of insulators
7. A particle of mass m is confined to a one-dimensional box L<x<L. It is in the stationary state described by Ψ(x) = sqrt(1/L)cos(3πx/2L) In which state is the particle? (You may find it helpful to sketch the wavefunction.) (a) third excited state (b) ground state (c) first excited state (d) fourth excited state (e) second excited state
(e) second excited state Wave functions in the classically allowed region are oscillatory. If there is a single classically allowed region as in this case, the ground state has no nodes inside the classical turning points, the first excited state has one node, the second excited state has two nodes, etc. Thus this wave function describes the second excited state.