shayekh/physics_gre huggingface dataset:
A rock is thrown vertically upward with initial speed $v_{0}$. Assume a friction force proportional to $-v$, where $v$ is the velocity of the rock, and neglect the buoyant force exerted by air. Which of the following is correct?

A. The acceleration of the rock is always equal to $\mathbf{g}$.

B. The acceleration of the rock is equal to $\mathrm{g}$ only at the top of the flight.

C. The acceleration of the rock is always less than $g$.

D. The speed of the rock upon return to its starting point is $v_{0}$.

E. The rock can attain a terminal speed greater than $v_{0}$ before it returns to its starting point.


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
A satellite orbits the Earth in a circular orbit. An astronaut on board perturbs the orbit slightly by briefly firing a control jet aimed toward the Earth's center. Afterward, which of the following is true of the satellite's path?

A. It is an ellipse.

B. It is a hyperbola.

C. It is a circle with larger radius.

D. It is a spiral with increasing radius.

E. It exhibits many radial oscillations per revolution.


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
For blue light, a transparent material has a relative permittivity (dielectric constant) of 2.1 and a relative permeability of 1.0 . If the speed of light in a vacuum is $c$, the phase velocity of blue light in an unbounded medium of this material is

A. $\sqrt{3.1} c$

B. $\sqrt{2.1} c$

C. $\frac{c}{\sqrt{1.1}}$

D. $\frac{c}{\sqrt{2.1}}$

E. $\frac{c}{\sqrt{3.1}}$

Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
The equation $y=A \sin 2 \pi\left(\frac{t}{T}-\frac{x}{\lambda}\right)$, where $A, T$, and $\lambda$ are positive constants, represents a wave whose

A. amplitude is $2 \mathrm{~A}$

B. velocity is in the negative $x$-direction

C. period is $\frac{T}{\lambda}$

D. speed is $\frac{x}{t}$

E. speed is $\frac{\lambda}{T}$



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
Two small spheres of putty, $A$ and $B$, of mass $M$ and $3 M$, respectively, hang from the ceiling on strings of equal length $\ell$. Sphere $A$ is drawn aside so that it is raised to a height $h_{0}$ as shown above and then released. Sphere $A$ collides with sphere $B$; they stick together and swing to a maximum height $h$ equal to
A. $\frac{1}{16} h_{0}$
B. $\frac{1}{8} h_{0}$
C. $\frac{1}{4} h_{0}$
D. $\frac{1}{3} h_{0}$
E. $\frac{1}{2} h_{0}$



Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
A particle is initially at rest at the top of a curved frictionless track. The $x$ - and $y$-coordinates of the track are related in dimensionless units by $y=\frac{x^{2}}{4}$, where the positive $y$-axis is in the vertical downward direction. As the particle slides down the track, what is its tangential acceleration?

A. 0

B. $g$

C. $\frac{g x}{2}$

D. $\frac{g x}{\sqrt{x^{2}+4}}$

E. $\frac{g x^{2}}{\sqrt{x^{2}+16}}$



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
A 2-kilogram box hangs by a massless rope from a ceiling. A force slowly pulls the box horizontally to the side until the horizontal force is 10 newtons. The box is then in equilibrium as shown above. The angle that the rope makes with the vertical is closest to

A. $\arctan 0.5$

B. $\arcsin 0.5$

C. $\arctan 2.0$

D. $\arcsin 2.0$

E. $45^{\circ}$

Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
A 5-kilogram stone is dropped on a nail and drives the nail 0.025 meter into a piece of wood. If the stone is moving at 10 meters per second when it hits the nail, the average force exerted on the nail by the stone while the nail is going into the wood is most nearly

A. 10 N 

B. 100 N 

C. 1000 N 

D. 10,000 N 

E. 100,000 N 

Answer scores (1 = correct):
A wire of diameter 0.02 meter contains $1 \times 10^{28}$ free electrons per cubic meter. For an electric current of 100 amperes, the drift velocity for free electrons in the wire is most nearly

A. $0.6 \times 10^{-29} \mathrm{~m} / \mathrm{s}$

B. $1 \times 10^{-19} \mathrm{~m} / \mathrm{s}$

C. $5 \times 10^{-10} \mathrm{~m} / \mathrm{s}$

D. $2 \times 10^{-4} \mathrm{~m} / \mathrm{s}$

E. $8 \times 10^{3} \mathrm{~m} / \mathrm{s}$

Electric Field

Magnitude



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
An isolated sphere of radius $R$ contains a uniform volume distribution of positive charge. Which of the curves on the graph above correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its center?
A. $A$
B. $B$
C. $C$
D. $D$
E. $E$



Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
Which of the following equations is a consequence of the equation $\nabla \times \mathbf{H}=\dot{\mathbf{D}}+\mathbf{J}$ ?

A. $\nabla \cdot(\dot{\mathbf{D}}+\mathbf{J})=0$

B. $\nabla \times(\dot{\mathbf{D}}+\mathbf{J})=0$

C. $\nabla(\dot{\mathbf{D}} \cdot \mathbf{J})=0$

D. $\dot{\mathbf{D}}+\mathrm{J}=0$

E. $\dot{\mathbf{D}} \cdot \mathbf{J}=\mathbf{0}$


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
A source of 1-kilohertz sound is moving straight toward you at a speed 0.9 times the speed of sound. The frequency you receive is

A. $0.1 \mathrm{kHz}$

B. $0.5 \mathrm{kHz}$

C. $1.1 \mathrm{kHz}$

D. $1.9 \mathrm{kHz}$

E. $10 \mathrm{kHz}$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
Two coherent sources of visible monochromatic light form an interference pattern on a screen. If the relative phase of the sources is varied from 0 to $2 \pi$ at a frequency of 500 hertz, which of the following best describes the effect, if any, on the interference pattern?

A. It is unaffected because the frequency of the phase change is very small compared to the frequency of visible light.

B. It is unaffected because the frequency of the phase change is an integral multiple of $\pi$.

C. It is destroyed except when the phase difference is 0 or $\pi$.

D. It is destroyed for all phase differences because the monochromaticity of the sources is destroyed.

E. It is not destroyed but simply shifts positions at a rate too rapid to be detected by the eye.

Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
For an ideal gas, the specific heat at constant pressure $C_{p}$ is greater than the specific heat at constant volume $C_{\nu}$ because the

A. gas does work on its environment when its pressure remains constant while its temperature is increased

B. heat input per degree increase in temperature is the same in processes for which either the pressure or the volume is kept constant

C. pressure of the gas remains constant when its temperature remains constant

D. increase in the gas's internal energy is greater when the pressure remains constant than when the volume remains constant

E. heat needed is greater when the volume remains constant than when the pressure remains constant


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
A sample of $N$ atoms of helium gas is confined in a 1.0 cubic meter volume. The probability that none of the helium atoms is in a $1.0 \times 10^{-6}$ cubic meter volume of the container is
A. 0
B. $\left(10^{-6}\right)^{N}$
C. $\left(1-10^{-6}\right)^{N}$
D. $1-\left(10^{-6}\right)^{N}$
E. 1


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
Except for mass, the properties of the muon most closely resemble the properties of the
A. electron
B. graviton
C. photon
D. pion
E. proton



Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
Suppose that ${ }_{Z}^{A} X$ decays by natural radioactivity in two stages to ${ }_{Z-1}^{A-4} Y$. The two stages would most likely be which of the following?
$\underline{\text { First Stage }}$
$\underline{\text { Second Stage }}$
A. $\beta^{-}$emission with an antineutrino
$\alpha$ emission
B. $\boldsymbol{\beta}^{-}$emission
$\alpha$ emission with a neutrino
C. $\boldsymbol{\beta}^{-}$emission
$\gamma$ emission
D. Emission of a deuteron Emission of two neutrons
E. $\alpha$ emission $\gamma$ emission


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The wave function $\psi(x)=A \exp \left\{-\frac{b^{2} x^{2}}{2}\right\}$, where $A$ and $b$ are real constants, is a normalized eigenfunction of the Schrödinger equation for a particle of mass $M$ and energy $E$ in a one dimensional potential $V(x)$ such that $V(x)=0$ at $x=0$. Which of the following is correct?

A. $V=\frac{\hbar^{2} b^{4}}{2 M}$

B. $V=\frac{\hbar^{2} b^{4} x^{2}}{2 M}$

C. $V=\frac{\hbar^{2} b^{6} x^{4}}{2 M}$

D. $E=\hbar^{2} b^{2}\left(1-b^{2} x^{2}\right)$

E. $E=\frac{\hbar^{2} b^{4}}{2 M}$


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
The energy levels of the hydrogen atom are given in terms of the principal quantum number $n$ and a positive constant $A$ by the expression

A. $A\left(n+\frac{1}{2}\right)$

B. $A\left(1-n^{2}\right)$

C. $A\left(-\frac{1}{4}+\frac{1}{n^{2}}\right)$

D. $A n^{2}$

E. $-\frac{A}{n^{2}}$

Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
A positive kaon $\left(K^{+}\right)$has a rest mass of $494 \mathrm{MeV} / c^{2}$, whereas a proton has a rest mass of $938 \mathrm{MeV} / c^{2}$. If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly

A. $0.25 c$

B. $0.40 c$

C. $0.55 c$

D. $0.70 c$

E. $0.85 c$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
Two observers $O$ and $O^{\prime}$ observe two events, $A$ and $B$. The observers have a constant relative speed of $0.8 c$. In units such that the speed of light is 1 , observer $O$ obtained the following coordinates:

Event $A: x=3, y=3, z=3, t=3$

Event $B: x=5, y=3, z=1, t=5$

What is the length of the space-time interval between these two events, as measured by $O^{\prime}$ ?
A. 1
B. $\sqrt{2}$
C. 2
D. 3
E. $2 \sqrt{3}$


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
Which of the following statements most accurately describes how an electromagnetic field behaves under a Lorentz transformation?

A. The electric field transforms completely into a magnetic field.

B. If initially there is only an electric field, after the transformation there may be both an electric and a magnetic field.

C. The electric field is unaltered.

D. The magnetic field is unaltered.

E. It cannot be determined unless a gauge transformation is also specified.


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
Which of the following statements concerning the electrical conductivities at room temperature of a pure copper sample and a pure silicon sample is NOT true?

A. The conductivity of the copper sample is many orders of magnitude greater than that of the silicon sample.

B. If the temperature of the copper sample is increased, its conductivity will decrease.

C. If the temperature of the silicon sample is increased, its conductivity will increase.

D. The addition of an impurity in the copper sample always decreases its conductivity.

E. The addition of an impurity in the silicon sample always decreases its conductivity.



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
The battery in the diagram above is to be charged by the generator $G$. The generator has a terminal voltage of 120 volts when the charging current is 10 amperes. The battery has an emf of 100 volts and an internal resistance of $1 \mathrm{ohm}$. In order to charge the battery at 10 amperes charging current, the resistance $R$ should be set at
A. $0.1 \Omega$
B. $0.5 \Omega$
D. $5.0 \Omega$
E. $10.0 \Omega$
C. $1.0 \Omega$


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
A charged particle is released from rest in a region where there is a constant electric field and a constant magnetic field. If the two fields are parallel to each other, the path of the particle is a

A. circle

B. parabola

C. helix

D. cycloid

E. straight line


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
A nickel target $(Z=28)$ is bombarded with fast electrons. The minimum electron kinetic energy needed to produce $\mathrm{x}$-rays in the $K$ series is most nearly 

A. 10 eV 

B. 100 eV 

C. 1000 eV 

D. 10,000 eV 

E. 100,000 eV


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
The hypothesis that an electron possesses spin is qualitatively significant for the explanation of all of the following topics EXCEPT the

A. structure of the periodic table

B. specific heat of metals

C. anomalous Zeeman effect

D. deflection of a moving electron by a uniform magnetic field

E. fine structure of atomic spectra

Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
Eigenfunctions for a rigid dumbbell rotating about its center have a $\phi$ dependence of the form $\psi(\phi)=A e^{i m \phi}$, where $m$ is a quantum number and $A$ is a constant. Which of the following values of $A$ will properly normalize the eigenfunction?

A. $\sqrt{2 \pi}$

B. $2 \pi$

C. $(2 \pi)^{2}$

D. $\frac{1}{\sqrt{2 \pi}}$

E. $\frac{1}{2 \pi}$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
A negative test charge is moving near a long straight wire in which there is a current. A force will act on the test charge in a direction parallel to the direction of the current if the motion of the charge is in a direction

A. toward the wire

B. away from the wire

C. the same as that of the current

D. opposite to that of the current

E. perpendicular to both the direction of the current and the direction toward the wire


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The configuration of the potassium atom in its ground state is $1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}$. Which of the following statements about potassium is true?

A. Its $n=3$ shell is completely filled.

B. Its $4 s$ subshell is completely filled.

C. Its least tightly bound electron has $\ell=4$.

D. Its atomic number is 17.

E. Its electron charge distribution is spherically symmetrical.



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
When the photoelectric equation is satisfied and applicable to this situation, $V$ is the

A. negative value at which the current stops

B. negative value at which the current starts

C. positive value at which the current stops

D. positive value at which the current starts

E. voltage induced when the light is on

Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The photoelectric equation is derived under the assumption that

A. electrons are restricted to orbits of angular momentum $n \hbar$, where $n$ is an integer

B. electrons are associated with waves of wavelength $\lambda=h / p$, where $p$ is momentum

C. light is emitted only when electrons jump between orbits

D. light is absorbed in quanta of energy $E=h \nu$

E. light behaves like a wave


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
The quantity $W$ in the photoelectric equation is the

A. energy difference between the two lowest electron orbits in the atoms of the photocathode

B. total light energy absorbed by the photocathode during the measurement

C. minimum energy a photon must have in order to be absorbed by the photocathode

D. minimum energy required to free an electron from its binding to the cathode material

E. average energy of all electrons in the photocathode



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.

The force on the body is
A. $\frac{1}{2} m v^{2}$
B. $-4 k x^{3}$
C. $k x^{4}$
D. $-\frac{k x^{5}}{5}$
E. $m g$


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.

The Hamiltonian function for this system is
A. $\frac{p^{2}}{2 m}+k x^{4}$
B. $\frac{p^{2}}{2 m}-k x^{4}$
C. $k x^{4}$
D. $\frac{1}{2} m v^{2}-k x^{4}$
E. $\frac{1}{2} m v^{2}$


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The potential energy of a body constrained to move on a straight line is $k x^{4}$ where $k$ is a constant. The position of the body is $x$, its speed $v$, its linear momentum $p$, and its mass $m$.

The body moves from $x_{1}$ at time $t_{1}$ to $x_{2}$ at time $t_{2}$. Which of the following quantities is an extremum for the $x-t$ curve corresponding to this motion, if end points are fixed?

A. $\int_{t_{1}}^{t_{2}}\left(\frac{1}{2} m v^{2}-k x^{4}\right) d t$

B. $\int_{t_{1}}^{t_{2}}\left(\frac{1}{2} m v^{2}\right) d t$

C. $\int_{t_{1}}^{t_{2}}(m x v) d t$

D. $\int_{x_{1}}^{x_{2}}\left(\frac{1}{2} m v^{2}+k x^{4}\right) d x$

E. $\int_{x_{1}}^{x_{2}}(m v) d x$



Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The figure above represents a point mass $m$ attached to the ceiling by a cord of fixed length $\ell$. If the point mass moves in a horizontal circle of radius $r$ with uniform angular velocity $\omega$, the tension in the cord is

A. $m g\left(\frac{r}{\ell}\right)$

B. $m g \cos \left(\frac{\theta}{2}\right)$

C. $\frac{m \omega r}{\sin \left(\frac{\theta}{2}\right)}$

D. $m\left(\omega^{2} r^{2}+g^{2}\right)^{\frac{1}{2}}$

E. $m\left(\omega^{4} r^{2}+g^{2}\right)^{\frac{1}{2}}$



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
If logical 0 is 0 volts and logical 1 is +1 volt, the circuit shown above is a logic circuit commonly known as

A. an OR gate

B. an AND gate

C. a 2-bit adder

D. a flip-flop

E. a fanout



Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
The gain of an amplifier is plotted versus angular frequency $\omega$ in the diagram above. If $K$ and $a$ are positive constants, the frequency dependence of the gain near $\omega=3 \times 10^{5}$ second $^{-1}$ is most accurately expressed by
A. $K e^{-a \omega}$
B. $K \omega^{2}$
C. $K \omega$
D. $K \omega^{-1}$
E. $K \omega^{-2}$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
An experimenter measures 9934 counts during one hour from a radioactive sample. From this number the counting rate of the sample can be estimated with a standard deviation of most nearly
A. 100
B. 200
C. 300
D. 400
E. 500


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
Which of the following nuclei has the largest binding energy per nucleon? (Consider the most abundant isotope of each element.)

A. Helium

B. Carbon

C. Iron

D. Uranium

E. Plutonium


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
A proton beam is incident on a scatterer 0.1 centimeter thick. The scatterer contains $10^{20}$ target nuclei per cubic centimeter. In passing through the scatterer, one proton per incident million is scattered. The scattering cross section is

A. $10^{-29} \mathrm{~cm}^{2}$

B. $10^{-27} \mathrm{~cm}^{2}$

C. $10^{-25} \mathrm{~cm}^{2}$

D. $10^{-23} \mathrm{~cm}^{2}$

E. $10^{-21} \mathrm{~cm}^{2}$



Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
Three masses are connected by two springs as shown above. A longitudinal normal mode with frequency $\frac{1}{2 \pi} \sqrt{\frac{k}{m}}$ is exhibited by

A. $A, B, C$ all moving in the same direction with equal amplitude

B. $A$ and $C$ moving in opposite directions with equal amplitude, and $B$ at rest

C. $A$ and $C$ moving in the same direction with equal amplitude, and $B$ moving in the opposite direction with the same amplitude

D. $A$ and $C$ moving in the same direction with equal amplitude, and $B$ moving in the opposite direction with twice the amplitude

E. none of the above



Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
A uniform stick of length $L$ and mass $M$ lies on a frictionless horizontal surface. A point particle of mass $\boldsymbol{m}$ approaches the stick with speed $v$ on a straight line perpendicular to the stick that intersects the stick at one end, as shown above. After the collision, which is elastic, the particle is at rest. The speed $V$ of the center of mass of the stick after the collision is
A. $\frac{m}{M} v$
B. $\frac{m}{M+m} v$
C. $\sqrt{\frac{m}{M}} v$
D.<smiles>[Y14]1=CCC2CCCC1C2</smiles>
E. $\frac{3 m}{\bar{M}} v$


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
Photons of wavelength $\lambda$ scatter elastically on free protons initially at rest. The wavelength of the photons scattered at $90^{\circ}$ is increased by

A. $\lambda / 137$

B. $\lambda / 1836$

C. $h / m_{e} c$, where $h$ is Planck's constant, $m_{e}$ the rest mass of an electron, and $c$ the speed of light

D. $h / m_{p} c$, where $h$ is Planck's constant, $m_{p}$ the rest mass of a proton, and $c$ the speed of light

E. zero


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
A blackbody at temperature $T_{1}$ radiates energy at a power level of 10 milliwatts $(\mathrm{mW})$. The same blackbody, when at a temperature $2 T_{1}$, radiates energy at a power level of
A. $10 \mathrm{~mW}$
D. $80 \mathrm{~mW}$
B. $20 \mathrm{~mW}$
C. $40 \mathrm{~mW}$
E. $160 \mathrm{~mW}$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
The Franck-Hertz experiment and related scattering experiments show that

A. electrons are always scattered elastically from atoms

B. electrons are never scattered elastically from atoms

C. electrons of a certain energy range can be scattered inelastically, and the energy lost by electrons is discrete

D. electrons always lose the same energy when they are scattered inelastically

E. there is no energy range in which the energy lost by electrons varies continuously


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
A transition in which one photon is radiated by the electron in a hydrogen atom when the electron's wave function changes from $\psi_{1}$ to $\psi_{2}$ is forbidden if $\psi_{1}$ and $\psi_{2}$

A. have opposite parity

B. are orthogonal to each other

C. are zero at the center of the atomic nucleus

D. are both spherically symmetrical

E. are associated with different angular momenta


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
The Hamiltonian operator in the Schrödinger equation can be formed from the classical Hamiltonian by substituting

A. wavelength and frequency for momentum and energy

B. a differential operator for momentum

C. transition probability for potential energy

D. sums over discrete eigenvalues for integrals over continuous variables

E. Gaussian distributions of observables for exact values


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
The Hall effect is used in solid-state physics to measure

A. ratio of charge to mass

B. magnetic susceptibility

C. the sign of the charge carriers

D. the width of the gap between the conduction and valence bands

E. Fermi energy

Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
One feature common to both the Debye theory and the Einstein theory of the specific heat of a crystal composed of $N$ identical atoms is that the

A. average energy of each atom is $3 k T$

B. vibrational energy of the crystal is equivalent to the energy of $3 \mathrm{~N}$ independent harmonic oscillators

C. crystal is assumed to be continuous for all elastic waves

D. speed of the longitudinal elastic waves is less than the speed of the transverse elastic waves

E. upper cutoff frequency of the elastic waves is the same


Answer scores (1 = correct):
A: 0
B: 1
C: 0
D: 0
E: 0
A cube has a constant electric potential $V$ on its surface. If there are no charges inside the cube, the potential at the center of the cube is
A. zero
D. $V / 2$
B. $V / 8$
C. $V / 6$
E. $V$



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 0
E: 1
A charged particle oscillates harmonically along the $x$-axis as shown above. The radiation from the particle is detected at a distant point $P$, which lies in the $x y$-plane. The electric field at $P$ is in the

A. $\pm z$ direction and has a maximum amplitude at $\theta=90^{\circ}$

B. $\pm z$ direction and has a minimum amplitude at $\theta=90^{\circ}$

C. $x y$-plane and has a maximum amplitude at $\theta=90^{\circ}$

D. $x y$-plane and has a minimum amplitude at $\theta=90^{\circ}$

E. $x y$-plane and has a maximum amplitude at $\theta=45^{\circ}$

Dielectric $K$



Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0