Modern Physics - Multiple Choice Questions

The sodium atom (Z=11) has a single valence electron in the 3s sub shell. A possible excited state of this electron is the 3d state. The properties of this electron can be analyzed, in an approximate way, as if the electric force acting on that electron were due to an effective charge of about

+1e

The Rydberg equation is used to

Calculate the wavelengths of different spectral lines of hydrogen

Solid argon is held together by the van der Waals force. What is the best term to describe its crystal structure?

Close packed crystal

Which distribution function provides the best description of the behavior of electrons in a metal?

Fermi-Dirac

A certain semiconductor has an energy gap of about 1 eV and a certain insulator has an energy gap of about 6 eV. Which of these would you expect to be transparent to all visible light?

insulator

The planetary model of the atom was fundamentally flawed. It failed theoretically because

it was well established experimentally that accelerating electrons emit electromagnetic radiation

Complete the sentence. The average energy pod an electron is metal is

much larger than 3/2 kT, because the electrons follow Fermi-Dirac statistics

A piece of silicon contains a small amount of impurity that forms states located in the energy gap very close to the edge of the conduction band. What category would best describe this material?

n-type semiconductor

As the rotational energy of a molecule increases, what happens to the spacing between the rotational energy states?

The energy spacing increases

Which of the following statements are true about fission reactions?

The fission products themselves are often unstable

To prove the equipartition theorem we need to look at the relationship between

The kinetic energy and the root mean square speed of the molecules

Which statement is true for a diamagnet?

The magnetic susceptibility is negative and small

Which statement is true for a paramagnet?

The magnetic susceptibility is positive and small

In his calculus, Bohr came across a number now called the "Bohr radius". The number is 5.29e-11 m and is

The minimum possible radius of the electrons orbit in hydrogen

What did Rutherfords famous scattering experiment help to prove in his day?

The nucleus of an atom is much smaller than the atom

Which of the following is allowed to change in a radioactive decay process?

The number of electrons

Suppose a nucleus of ^238 _92 U fissions into two nuclei of ^119_46Pd . Compared with the mass of ^238_92U, the total mass of the two ^119_46Pd is:

Smaller

Thermal expansion can be qualitatively understood if we take into account:

The cubic term in the Taylor expansion of the binding potential between atoms

Select the true statement. The Fermi energy depends on

The density of electrons

Use the band theory of semiconductors to choose the most correct statement below.

A semiconductor differs from an insulator in the size of the band gap

Oxygen has the electron configuration 1s^2 2s^2 2p^4. In the ground state, the total m_s of all 8 of the electrons has the largest possible value consistent with the Pauli principle. What is this value?

1

In a stationary state 1.) The probability distribution of the particles is independent of time 2.) The energy of particle oscillates with constant frequency 3.) The momentum of the particles can never be measured accurately 4.) The wave function of the particle is independent of time

1.)

In attempting to describe the atom, Bohr made a set of general assumptions. Which of the following statements is NOT a result or closely aligned with those general assumptions (the assumptions might not be quantum mechanically correct)? 1.) The velocity of the electron around the nucleus is the same in all orbits, although the shape of the orbit changes with higher values of n, the principal quantum number. 2.) The radius of a hydrogen atom can be calculated from a certain combination of fundamental constants. 3.) Stationary states are states where the electron accelerates around the nucleus but does not emit electromagnetic radiation. 4.) Electrons in the hydrogen atom transfer between quantized energy states and can exist nowhere else in the atom but in these energy states.

1.)

Select the correct statement about the transitions between rotational and vibrational modes: 1.) The rotational frequencies are typically lower than the vibrational frequencies 2.) The rotational frequencies are typically about the same as the vibrational frequencies 3.) The rotational frequencies are typically higher than the vibrational frequencies

1.)

Select the correct statement: 1.) In Raman spectroscopy a photon is absorbed and another photon with different frequency is emitted 2.) In Raman spectroscopy a photon is absorbed and an electron is emitted 3.) In Raman spectroscopy a photon is absorbed and another photon with the same frequency is emitted

1.)

Select the true statement: 1.) Fermions are not allowed to be in the same state 2.) Two Fermions have a symmetric wave function 3.) The Pauli exclusion principal works for Bosons 4.) Bosons are not allowed to be in the same state

1.)

Select the true statement: 1.) The density of states, as we defined it here, has units of 1/energy 2.) The Maxwell Boltzmann factor makes the states with higher energy always less occupied than the states with lower energy 3.) The density of state for any given material depends on the temperature

1.)

Which of the following can also be quantum numbers of an l=2 electron in hydrogen? 1.) m_l=0 2.) n=0 3.) n=2 4.) m_l=1/2

1.)

Which of the following is true about Bragg planes? 1.) They are evenly spaced planes within crystal structures of atoms. 2.) There is only one Bragg plane for any given crystal structure. 3.) They are used to scatter alpha particles in gold and other materials.All of these. 4.) They are especially useful for detecting transitions between energy levels in the crystals' atoms.

1.)

Which statement is true about the solution Ψ(𝑥) of the Schrödinger equation? 1.) 2Ψ is also a solution 2.) 1/Ψ is also a solution 3.) |Ψ |^2 is also a solution. 4.) Ψ^2 is also a solution

1.)

You fire alpha particles of about 5 MeV into an unknown target and measure the scattering angle. Which of the following affects the scattering angle of the alpha particles coming off of the target? 1.) The Coulomb force between the alpha particle and the nuclei of the target. 2.) The number of electrons in the target. 3.) The temperature of the target. 4.) The Coulomb force between the alpha particle and the electrons in the target.

1.)

The coulomb energy of two protons at a distance of 1 fermi (10^-15 m) is:

1.4MeV

A certain intrinsic (undoped) semiconducting material has an energy gap of 1.6 eV between the valence and conducting bands. What is the approximate value of the Fermi-Dirac function at the bottom of the conduction band at room temperature (300 K)? Assume that the Fermi energy is half-way in the energy gap. (k = 8.62e-5 eV/K).

10^-14

Some elements like iron, cobalt, and holmium make very good natural magnets. Which of the following statements best describers why? 1.) Atoms in the crystalline structure of the solid metal tend to anti-align their spin and orbital angular momentum 2.) Hund's rule for multi-electron atoms tend to maximize electron spin 3.) The filled s shells with high n and paired electrons create larger atomic radii and therefore the electrons can contribute more to the magnetic field 4.) Large numbers of paired singlet electron spins are essential to good magnets

2.)

The proper way to label the ground state energy of particle in a two-dimensional, square shaped, potential well is: 1.) E_(0,1) 2.) E_(1,1) 3.) E_(0,0) 4.) E_(1,1,1) 5.) E_(1,0) 6.) E_0

2.)

The stationary wave functions in a one dimensional infinite square well potential: 1.) Dependent on time 2.) They can be fully described by using sin and cosine functions 3.) They can be described with sin and cosine functions, but exponential functions are also needed. 4.) They are always real

2.)

Which of the following is assumed when analyzing photons involved in Compton scattering? The photon always recoils with significant energy lost to the electron. 1.) Momentum, but not energy, is conserved when the photon scatters from an electron. 2.) Energy and momentum are treated relativistically in the scattering. 3.) The photon always recoils with significant energy lost to the electron. 4.) The photon behaves like a wave and diffracts at an angle from the electron.

2.)

Which of the following statements is correct about the experiment that first measured the charge of the electron? 1.) The oil drop is suspended because there are no forces acting on the drop. 2.) The mass of the drop was calculated from its terminal velocity. 3.) The value for electron charge had an experimental error of about 35%. 4.) Light hitting the oil drops manipulated their movement in a way to create an interference pattern. 5.) The important result was that Coulomb attraction made all of the oil drops the same mass, regardless of type of oil

2.)

An electron is in the hydrogen atom, with quantum number n=3. What is the number of independent wave functions (consider the angular momentum quantum number l, the magnetic quantum number m_1, and the spin quantum number m_s)?

18

In a Stern-Gerlach type of experiment o an atom (such as sodium) with a single 3s electron, into how many components would the beam be split?

2

Which of the following fusion reactions would you expect to release the most energy per reacting nucleon? 1.) 40 Ca + 40 Ca 2.) 12 C + 12 C 3.) 56 Fe + 56 Fe 4.) 2 H + 2 H

2 H + 2 H

A particle is in a stationary state in quadratic potential with n>>1. According to the solution of the Schrödinger equation, the probability of finding the particle is: 1.) About the same at any position 2.) The greatest in proximity of the classical limits of the motion 3.) Exactly zero in a region where V>E, where E is the total energy of the system 4.) The greatest in the center, around x=0

2.)

Attractive interaction between atoms/ions/molecules can be present due to several reasons. Select the one that is NOT correct. 1.) Sharing a proton between two molecules 2.) Having a tiny spring connecting the two atoms 3.) Fluctuating electric dipoles 4.) Coulomb attraction between opposite charges 5.) Sharing electrons over a larger volume, thereby reducing the energy

2.)

Fill in the blank: The ground state energy of a particle in a two-dimensional infinite, square shaped potential well is ______ . Use 𝐸_0= (𝜋^2 ℏ^2)/2𝑚𝐿^2 1.) 4E_0 2.) 2E_0 3.) E_0 4.) 3E_0

2.)

Select the true statement. The typical Fermi velocity in a metal is 1.) Much smaller than the thermal velocity of the ideal gas 2.) Much larger than the thermal velocity of the ideal gas 3.) Has about the same order of magnitude the thermal velocity the ideal gas

2.)

Which of the following states of the hydrogen atom, as defined by the principal quantum number, angular momentum quantum number, and magnetic quantum number, is allowed? 1.) n=0, l=1, m_l=2 2.) n=5, l=2, m_l=0 3.) n=0, l=1, m_l=1 4.) n=2, l=2, m_l=0 5.) n=5, l=2, m_l=3

2.)

Based on what we know about the hydrogen Aton, we expect that electrons should fill the 1s shell, 2s shell, 2p shell, 3s shell and so on in order of the principal quantum number. The energy does not depend on the orbital angular momentum quantum number. Instead, for heavier elements we find that the 4s sub shell fills before the 3d sub shell. Select the correct statements that contribute to the explanation of this effect. 1.) Electrons that experience less shielding of the nuclear charge have higher energy 2.) Electrons with higher angular momentum value has zero probability being at the nucleus and therefore they are better shielded from the nuclear charge 3.) Electrons fill the lowest energy levels available to them, subject to the Pauli exclusion principle

2.) and 3.)

According to the equipartition theorem, the specific heat of the O2 gas is

2.5R

A particle is in a stationary state in a quadratic potential with n=1. According to the solution of the Schrödinger equation, the probability of finding the particle is: 1.) Exactly zero in a region where V>E, where E is the total energy of the system 2.) About the same at any position 3.) The greatest in the center, around x=0 4.) The greatest in proximity of the classical limits of the motion

3.)

A particle oscillates in a quadratic potential. According to classical physics, the probability of finding the particle is: 1.) About the same at any position 2.) The greatest in the center, around x=0 3.) The greatest at the position where the potential energy V(x) is the highest 4.) Non-zero in a region where V>E, where E is the total energy of the system

3.)

One of these transitions is NOT allowed. Which one? Number represent (n, l, m_1, m_s) 1.) (4,2,-1,-1/2)->(3,1,0,-1/2) 2.) (2,0,0,1/2)->(3,1,1,1/2) 3.) (2,0,0,1/2)->(3,0,0,1/20 4.) (4,2,-1,-1/2)->(2,1,0,-1/2)

3.)

Select the correct statement: 1.) In infrared spectroscopy a photon is absorbed and another proton with the same frequency is emitted 2.) In infrared spectroscopy a photon is absorbed and another photon with different frequency is emitted 3.) In infrared spectroscopy a photon is absorbed and nothing is emitted 4.) In infrared spectroscopy a photon is absorbed and an electron is emitted

3.)

The de Broglie wavelength of which of the following objects would be smallest if the objects all had the same momentum? 1.) Electron 2.) Proton 3.) All the same wavelength 4.) Bowling ball 5.) Tennis ball

3.)

The de Broglie wavelength of which of the following objects would be smallest if the objects had the same velocity? 1.) Electron 2.) All the same wavelength 3.) Bowling ball 4.) Proton 5.) Tennis ball

3.)

The stationary wave functions in a one dimensional finite square well potential: 1.) Dependent on time 2.) They can be fully described by using sin and cosine functions 3.) They can be described with sin and cosine functions, but exponential functions are also needed. 4.) They are always real

3.)

Which of the following statements about blackbody radiation is NOT correct? 1.) The classical theory of intensity vs. wavelength, the Rayleigh-Jeans formula, of blackbody radiation is only correct at large wavelengths. 2.) The wavelength of peak relative intensity emitted from a blackbody is proportional to 1/T, the temperature of the blackbody. 3.) In Planck's radiation law the intensity of blackbody radiation is strictly proportional to 1/𝜆5 . 4.) The power per unit area given by blackbody radiation is proportional to T4.

3.)

Which of the following statements is most correct about the uncertainty principle? 1.) On large length scales, the uncertainty principle dominates our understanding of the physical world. 2.) Our instruments will eventually be able to measure more precisely than the principle presently allows. 3.) It is impossible to know exactly both the position and the momentum of a particle simultaneously. 4.) An electron with some momentum can be trapped into an arbitrarily small box. 5.) A particle limited in space can occupy any energy.

3.)

Which of the following statements is true about the Maxwell speed distribution? 1.) A molecule of has moving at the most probably speed has more kinetic energy than does the same molecule moving at the average speed 2.) The mean speed and root-mean-square speed are different names for the same value 3.) The distribution of molecules from largest to smallest goes 1.) most probable speed, 2.) mean speed, 3.) root-mean-square speed 4.) A higher proportion of molecules have the root-mean-square speed than the average speed

3.)

In quantum mechanics the particles of the same type cannot be distinguished from each other. What follows from this statement? (Pick two): 1.) The wave function of two particles must be symmetric 2.) The wave function of two particles must be anti-symmetric 3.) The wave function of two particles can be either symmetric or anti-symmetric 4.) The Pauli principle

3.) and 4.)

If electrons did not have spin, how many elements would occupy the second row in the periodic table?

4

Which statistical distribution might describe the energy distribution of photons from the Sun?

Bose-Einstein

An electron and a positron annihilate each other in vacuum. Two photons are produced, flying off in opposite directions. Analyze the situation using relativistic momentum and energy and choose the false statement below. 1.) The photons can have the same wavelength, but it is not necessary. 2.) If the resulting photons have the same wavelength, then the electron and positron must have had equal momenta. 3.) The kinetic energies of the positron and electron influences the frequency of the gamma rays produced in the annihilation. 4.) There can be two photons produced (as in the above example), but only one photon is produced in some cases. 5.) The rest energies of the positron and electron influence the frequency of the gamma rays produced in the annihilation.

4.)

For a two-dimensional infinite potential well the wavefunction is 𝜓(𝑥,𝑦)=𝐴 (sin 𝑛1 𝜋𝑥/𝐿1)(sin 𝑛2 𝜋𝑦/𝐿2). The quantum numbers n1 and n2 are integers and they can be: 1.) n1=0 and n2>0 2.) m1>0 and n2=0 3.) n1= and n2=0 4.) n1>0 and n2>0

4.)

The wave function 𝚿(2,1,1,1/2), 𝚿(3,1,1,1/2) and 𝚿(3,1,1,1/2) are normalized solutions of the time-independent Schrödinger equation for the electron in the hydrogen atom (we label the wave functions as 𝚿(n,l,m_l,m_s), where n is the principal quantum number, l is the angular momentum quantum number, m_1 is the magnetic quantum number, and m_s is the spin quantum number). WE combine two of these wave functions as seen below. Which combination is also a normalized solution of the time-independent Schrödinger equation? 1.) 1/2(𝚿(2,1,1,1/2)+𝚿(2,0,1,1/2)) 2.) 1/√2(𝚿(2,1,1,1/2)+𝚿(3,0,-1,1/2)) 3.) 1/√2(𝚿(2,1,1,1/2)+(𝚿(3,0,1,1/2)) 4.) 1/√2(𝚿(2,1,1,1/2)+(𝚿(2,0,1,1/2))

4.)

When de Broglie's matter waves are applied to electrons in the Bohr atom, which of the following occurs? 1.) The electron is found to have in its orbit an integral number of half-wavelengths. 2.) Bohr's quantization assumption for electron orbits is modified to incorporate the wave properties of the electron. 3.) The angular momentum of the electron in the atom is constant, with longer wavelengths at larger quantum numbers. 4.) de Broglie's results allow an integral number of wavelengths in the electron orbits.

4.)

Which of the following is an important difference between the infinite square-well potential and the finite square-well potential? 1.) The number of energy levels is limited in the infinite square-well potential but not limited in the finite square-well potential 2.) The energy levels are quantized only in the finite square-well potential 3.) Only the energy levels in the finite square-well potential depend on Planks constant 4.) Particles can exist in classically forbidden regions outside the finite square-well potential 5.) The infinite square-well potential utilizes Schrodingers equation to describe particle motion while the finite square-well potential does not

4.)

Which of the following statements is correct about the double slit experiment with electrons? 1.) Electrons are particles, not waves, and therefore there will be no interference. 2.) With a careful measurement we can determine which slit was used by the electron to reach the screen, and we can still record the interference. 3.) If we make sure that the apparatus has only one electron in it, and we send single electrons repeatedly for a long time, there will be no interference. 4.) A single electron passes through both of the slits simultaneously.

4.)

The Aufbau principle works well for lighter elements, but at higher atomic number it does not work perfectly. Mark the elements that violate the aufbau priniciple: 1.) Cobalt [Ar] 3d^7 4s^2 2.) Mangenese [Ar] 3d^5 4s^2 3.) Nickle [Ar] 3d^8 4s^2 4.) Zinc [Ar] 3d^10 4s^2 5.) Copper [Ar] 3d^10 4s^1 6.) Iron [Ar] 3d^6 4s^2 7.) Gold [Xe] 4f^15 5d^10 6s^1 8.) Chromium [Ar] 3d^5 4s^1 9.) Vanadium [Ar] 3d^3 4s^2 10.) Vanadium [Ar] 3d^3 4s^2

5.) and 7.) and 8.)

Which one is NOT a required property of the wave function (assuming finite potentials)? 1.) The wave function has to be a single-valued function. 2.) The wave function has to be finite 3.) At far away distances the wave function must approach zero 4.) The first derivative of the wave function has to be continuous. 5.) The wave function has to be continuous. 6.) The second derivative of the wave function has to be continuous.

6.)

Relative to the z axis, how many possible directions are there in space for the orbital angular momentum vector that represents an electron in a 4f state (n=4, l=3)?

7

For an atom of hydrogen without the effects of an external magnetic field, an electron transition from the 3P sub shell to the 2P sub shell is called a forbidden transition. Why is this so?

An atom that changes energy through transitioning must either absorb or emit a photon.

When you increase only the frequency of the incoming light onto the emitter, you measure

An increase in the necessary stopping voltage

In the photoelectric measurement, when you increase only the intensity of the light onto the emitter, you measure

An increased current

In the radioactive decays of fission fragments, the most commonly emitted particles are (select two):

Electrons and neutrons

Metals are good thermal conductors because:

Electrons move freely in metals

Around room temperature, the specific heat of the H2S gas is close to 3R. This is likely to happen because:

H2S is not a linear molecule and there is large moment of inertia around all 3 axes (x,y,z)

How did Planck modify the classical theory of blackbody radiation to correctly determine his radiation law?

He assumed light was absorbed and emitted in quanta

How did Thompson measure the charge to mass ratio of the electron?

He passed cathode rays through electric and magnetic fields and measured the deflection

Fusion releases energy because the binding energy per nucleon:

Increases with increasing mass numbers at low mass numbers

Select the correct statement. The Madelung energy:

Is the energy of one of the ions interacting with all other ions in the solid.

The ultraviolet catastrophe

Is the result of applying classical physics to thermal radiation

In system K an object moves in the positive x direction with a speed of 0.8c. K moves relative to K in the positive x direction with a speed of 0.3c. In classical physics the speed of the object observed from K is 0.5c. Using relativistic kinematics the speed will be

Larger than 0.5c

Consider a H+2 ion . The energy of the electron is the lowest when the protons are at the equilibrium separation. If the distance between the protons is decreased the energy will go up. This happens primarily because:

The electron is pushed to a smaller volume and its kinetic energy goes up

What is the bremsstrahlung process?

The emission of a photon from an electron being accelerated by a nucleus

The binding of of a nucleus is:

The energy needed to take apart a nucleus into its constituent protons and neutrons

Is Ψ=𝐴𝑒^(−𝛼|𝑥|) 𝑒^(𝑖𝜔t) a possible wavefunction?

No, because its first derivative is not continuous

Consider a H+ ion. The energy of the electron is the lowest when the protons are at the equilibrium separation. If the distance between the protons is increased the energy will go up. This happens primarily because:

The electron is farther away from the protons and its potential energy goes up

Finish the sentence: The space dependent part of the wave function of two electrons can be the same if the

Spins are opposite

In the H2 molecule the bonding molecular orbital can be constructed from the atomic orbital by taking:

Symmetric combination of orbitals and opposite spins of electrons

Finish the sentence: The wave function of two identical particles is

Symmetric if the particles have spin 1

A gas of atoms can be described with classical rather than quantum statistics only if:

The average spacing between atoms is much larger than their de-Broglie wavelength

Energy released in the fission of ^238 U because:

The binding energy per nucleon decreases with A for larger A

The phase velocity is

The velocity of a point on the wave at a given phase

The group velocity is

The velocity of the wave packet

The number of neutrons in a nucleus is:

Usually greater than the number of protons

A particle moves along the x-axis in the positive direction with energy E > 0. It encounters a potential well with potential V = −V0 < 0 at x = 0 and extending to x = L. Is it possible that the particle is fully transmitted?

Yes, but only at certain special values of L and V_0

A particle moves along the x-axis in the positive direction with energy E. It encounters a barrier with potential V < E at x = 0 and extending to x = L. Is there any chance for the particle to be reflected?

Yes. The wave function allow for a finite probability for the particle to be reflected

A particle moves along the x-axis in the positive direction with energy E. It encounters a barrier with potential V > E at x = 0 and extending to x = L. Is there any chance for the particle to be transmitted?

Yes. The wave function allow for a finite probability for the particle to be transmitted

Thompson model for the atom was called plum pudding model because

considered the atom as a soft, positively charged sphere (the pudding) with the electrons (the plums) embedded

The quantum number m_l provides information about what property of a hydrogen atom?

z component of the orbital angular momentum