shayekh/physics_gre huggingface dataset:
A gas-filled cell of length 5 centimeters is inserted in one arm of a Michelson interferometer, as shown in the figure above. The interferometer is illuminated by light of wavelength 500 nanometers. As the gas is evacuated from the cell, $\mathbf{4 0}$ fringes cross a point in the field of view. The refractive index of this gas is most nearly

A. 1.02

B. 1.002

C. 1.0002

D. 1.00002

E. 0.98

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Lattice forces affect the motion of electrons in a metallic crystal, so that the relationship between the energy $E$ and wave number $k$ is not the classical equation $E=\hbar^{2} k^{2} / 2 m$, where $m$ is the electron mass. Instead, it is possible to use an effective mass $m^{*}$ given by which of the following?

A. $m^{*}=\frac{1}{2} \hbar^{2} k\left(\frac{d k}{d E}\right)$

B. $m^{*}=\frac{\hbar^{2} k}{\left(\frac{d k}{d E}\right)}$

C. $m^{*}=\hbar^{2} k\left(\frac{d^{2} k}{d E^{2}}\right)^{\frac{1}{3}}$

D. $m^{*}=\frac{\hbar^{2}}{\left(\frac{d^{2} E}{d k^{2}}\right)}$

E. $m^{*}=\frac{1}{2} \hbar^{2} m^{2}\left(\frac{d^{2} E}{d k^{2}}\right)$


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The matrix $A=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]$

has three eigenvalues $\lambda_{i}$ defined by $A v_{i}=\lambda_{i} v_{i}$. Which of the following statements is NOT true?

A. $\lambda_{1}+\lambda_{2}+\lambda_{3}=0$

B. $\lambda_{1}, \lambda_{2}$, and $\lambda_{3}$ are all real numbers.

C. $\lambda_{2} \lambda_{3}=+1$ for some pair of roots.

D. $\lambda_{1} \lambda_{2}+\lambda_{2} \lambda_{3}+\lambda_{3} \lambda_{1}=0$

E. $\lambda_{i}{ }^{3}=+1, i=1,2,3$


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A: 0
B: 1
C: 0
D: 0
E: 0
In perturbation theory, what is the first order correction to the energy of a hydrogen atom (Bohr radius $a_{0}$ ) in its ground state due to the presence of a static electric field $E$ ?

A. Zero

B. $e E a_{0}$

C. $3 e E a_{0}$

D. $\frac{8 e^{2} E a_{0}^{3}}{3}$

E. $\frac{8 e^{2} E^{2} a_{0}^{3}}{3}$



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A: 1
B: 0
C: 0
D: 0
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A uniform rod of length 10 meters and mass 20 kilograms is balanced on a fulcrum with a 40 -kilogram mass on one end of the rod and a 20-kilogram mass on the other end, as shown above. How far is the fulcrum located from the center of the rod?

A. $0 \mathrm{~m}$

B. $1 \mathrm{~m}$

C. $1.25 \mathrm{~m}$

D. $1.5 \mathrm{~m}$

E. $2 \mathrm{~m}$



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C: 1
D: 0
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A ball is thrown out of the passenger window of a car moving to the right (ignore air resistance). If the ball is thrown out perpendicular to the velocity of the car, which of the following best depicts the path the ball takes, as viewed from above?

A.



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An object is thrown horizontally from the open window of a building. If the initial speed of the object is $20 \mathrm{~m} / \mathrm{s}$ and it hits the ground $2.0 \mathrm{~s}$ later, from what height was it thrown? (Neglect air resistance and assume the ground is level.)

A. $4.9 \mathrm{~m}$

B. $9.8 \mathrm{~m}$

C. $10.0 \mathrm{~m}$

D. $19.6 \mathrm{~m}$

E. $39.2 \mathrm{~m}$


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B: 0
C: 0
D: 1
E: 0
A resistor in a circuit dissipates energy at a rate of $1 \mathrm{~W}$. If the voltage across the resistor is doubled, what will be the new rate of energy dissipation?

A. $0.25 \mathrm{~W}$

B. $0.5 \mathrm{~W}$

C. $1 \mathrm{~W}$

D. $2 \mathrm{~W}$

E. $4 \mathrm{~W}$



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B: 0
C: 0
D: 0
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An infinitely long, straight wire carrying current $I_{1}$ passes through the center of a circular loop of wire carrying current $I_{2}$, as shown above. The long wire is perpendicular to the plane of the loop. Which of the following describes the magnetic force on the loop?

A. Outward, along a radius of the loop.

B. Inward, along a radius of the loop.

C. Upward, along the axis of the loop.

D. Downward, along the axis of the loop.

E. There is no magnetic force on the loop.


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De Broglie hypothesized that the linear momentum and wavelength of a free massive particle are related by which of the following constants?

A. Planck's constant

B. Boltzmann's constant

C. The Rydberg constant

D. The speed of light

E. Avogadro's number


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A: 1
B: 0
C: 0
D: 0
E: 0
An atom has filled $n=1$ and $n=2$ levels. How many electrons does the atom have?

A. 2

B. 4

C. 6

D. 8

E. 10

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B: 0
C: 0
D: 0
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The root-mean-square speed of molecules of mass $m$ in an ideal gas at temperature $T$ is

A. 0

B. $\sqrt{\frac{2 k T}{m}}$

C. $\sqrt{\frac{3 k T}{m}}$

D. $\sqrt{\frac{8 k T}{\pi m}}$

E. $\frac{k T}{m}$


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B: 0
C: 1
D: 0
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The energy from electromagnetic waves in equilibrium in a cavity is used to melt ice. If the Kelvin temperature of the cavity is increased by a factor of two, the mass of ice that can be melted in a fixed amount of time is increased by a factor of

A. 2

B. 4

C. 8

D. 16

E. 32



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The figure above represents the orbit of a planet around a star, $S$, and the marks divide the orbit into 14 equal time intervals, $t=T / 14$, where $T$ is the orbital period. If the only force acting on the planet is Newtonian gravitation, then true statements about the situation include which of the following?

I. Area $A=\operatorname{area} B$

II. The star $S$ is at one focus of an elliptically shaped orbit.

III. $T^{2}=C a^{3}$, where $a$ is the semimajor axis of the ellipse and $C$ is a constant.

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III


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A massless spring with force constant $k$ launches a ball of mass $m$. In order for the ball to reach a speed $v$, by what displacement $s$ should the spring be compressed?

A. $s=v \sqrt{\frac{k}{m}}$

B. $s=v \sqrt{\frac{m}{k}}$

C. $s=v \sqrt{\frac{2 k}{m}}$

D. $s=v \frac{m}{k}$

E. $s=v^{2} \frac{m}{2 k}$

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C: 0
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A quantum mechanical harmonic oscillator has an angular frequency $\omega$. The Schrödinger equation predicts that the ground state energy of the oscillator will be

A. $-\frac{1}{2} \hbar \omega$

B. 0

C. $\frac{1}{2} \hbar \omega$

D. $\hbar \omega$

E. $\frac{3}{2} \hbar \omega$


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C: 1
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In the Bohr model of the hydrogen atom, the linear momentum of the electron at radius $r_{n}$ is given by which of the following? ( $n$ is the principal quantum number.)

A. $n \hbar$

B. $n r_{n} \hbar$

C. $\frac{n \hbar}{r_{n}}$

D. $n^{2} r_{n} \hbar$

E. $\frac{n^{2} \hbar}{r_{n}}$



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The figure above represents a log-log plot of variable $y$ versus variable $x$. The origin represents the point $x=1$ and $y=1$. Which of the following gives the approximate functional relationship between $y$ and $x$ ?

A. $y=6 \sqrt{x}$

B. $y=\frac{1}{2} x+6$

C. $y=6 x+0.5$

D. $y=\frac{1}{6} x^{2}$

E. $y=6 x^{2}$


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B: 0
C: 0
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Two experimental techniques determine the mass of an object to be $11 \pm 1 \mathrm{~kg}$ and $10 \pm 2 \mathrm{~kg}$. These two measurements can be combined to give a weighted average. The uncertainty of the weighted average is equal to which of the following?

A. $\frac{1}{2} \mathrm{~kg}$

B. $\frac{2}{\sqrt{5}} \mathrm{~kg}$

C. $\frac{2}{\sqrt{3}} \mathrm{~kg}$

D. $2 \mathrm{~kg}$

E. $\sqrt{5} \mathrm{~kg}$

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If the five lenses shown below are made of the same material, which lens has the shortest positive focal length?

A.



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Unpolarized light is incident on a pair of ideal linear polarizers whose transmission axes make an angle of $45^{\circ}$ with each other. The transmitted light intensity through both polarizers is what percentage of the incident intensity?

A. $100 \%$

B. $75 \%$

C. $50 \%$

D. $25 \%$

E. $0 \%$


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A very long, thin, straight wire carries a uniform charge density of $\lambda$ per unit length. Which of the following gives the magnitude of the electric field at a radial distance $r$ from the wire?

A. $\frac{1}{2 \pi \varepsilon_{0}} \frac{\lambda}{r}$

B. $\frac{1}{2 \pi \varepsilon_{0}} \frac{r}{\lambda}$

C. $\frac{1}{2 \pi \varepsilon_{0}} \frac{\lambda}{r^{2}}$

D. $\frac{1}{4 \pi \varepsilon_{0}} \frac{\lambda^{2}}{r^{2}}$

E. $\frac{1}{4 \pi \varepsilon_{0}} \lambda \ln r$



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C: 0
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The bar magnet shown in the figure above is moved completely through the loop. Which of the following is a true statement about the direction of the current flow between the two points $a$ and $b$ in the circuit?

A. No current flows between $a$ and $b$ as the magnet passes through the loop.

B. Current flows from $a$ to $b$ as the magnet passes through the loop.

C. Current flows from $b$ to $a$ as the magnet passes through the loop.

D. Current flows from $a$ to $b$ as the magnet enters the loop and from $b$ to $a$ as the magnet leaves the loop.

E. Current flows from $b$ to $a$ as the magnet enters the loop and from $a$ to $b$ as the magnet leaves the loop.


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The surface of the Sun has a temperature close to $6,000 \mathrm{~K}$ and it emits a blackbody (Planck) spectrum that reaches a maximum near $500 \mathrm{~nm}$. For a body with a surface temperature close to $300 \mathrm{~K}$, at what wavelength would the thermal spectrum reach a maximum?

A. $10 \mu \mathrm{m}$

B. $100 \mu \mathrm{m}$

C. $10 \mathrm{~mm}$

D. $100 \mathrm{~mm}$

E. $10 \mathrm{~m}$


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
At the present time, the temperature of the universe (i.e., the microwave radiation background) is about $3 \mathrm{~K}$. When the temperature was $12 \mathrm{~K}$, typical objects in the universe, such as galaxies, were

A. one-quarter as distant as they are today

B. one-half as distant as they are today

C. separated by about the same distances as they are today

D. two times as distant as they are today

E. four times as distant as they are today


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C: 0
D: 0
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For an adiabatic process involving an ideal gas having volume $V$ and temperature $T$, which of the following is constant? $\left(\gamma=C_{P} / C_{V}\right)$

A. $T V$

B. $T V^{\gamma}$

C. $T V^{\gamma-1}$

D. $T^{\gamma} V$

E. $T^{\gamma} V^{-1}$

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C: 1
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An electron has total energy equal to four times its rest energy. The momentum of the electron is

A. $m_{e} c$

B. $\sqrt{2} m_{e} c$

C. $\sqrt{15} m_{e} c$

D. $4 m_{e} c$

E. $2 \sqrt{15} m_{e} c$


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C: 1
D: 0
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Two spaceships approach Earth with equal speeds, as measured by an observer on Earth, but from opposite directions. A meterstick on one spaceship is measured to be $60 \mathrm{~cm}$ long by an occupant of the other spaceship. What is the speed of each spaceship, as measured by the observer on Earth?

A. $0.4 c$

B. $0.5 c$

C. $0.6 c$

D. $0.7 c$

E. $0.8 c$


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B: 1
C: 0
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A meter stick with a speed of $0.8 c$ moves past an observer. In the observer's reference frame, how long does it take the stick to pass the observer?

A. $1.6 \mathrm{~ns}$

B. $2.5 \mathrm{~ns}$

C. $4.2 \mathrm{~ns}$

D. $6.9 \mathrm{~ns}$

E. $8.3 \mathrm{~ns}$


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C: 0
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Consider a set of wave functions $\psi_{i}(x)$. Which of the following conditions guarantees that the functions are normalized and mutually orthogonal? (The indices $i$ and $j$ take on the values in the set $\{1,2, \ldots, n\}$. )

A. $\psi_{i}^{*}(x) \psi_{j}(x)=0$

B. $\psi_{i}^{*}(x) \psi_{j}(x)=1$

C. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=0$

D. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=1$

E. $\int_{-\infty}^{\infty} \psi_{i}^{*}(x) \psi_{j}(x) d x=\delta_{i j}$


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The normalized ground state wave function of hydrogen is $\psi_{100}=\frac{2}{(4 \pi)^{1 / 2} a_{0}^{3 / 2}} e^{-r / a_{0}}$, where $a_{0}$ is the Bohr radius. What is the most likely distance that the electron is from the nucleus?

A. 0

B. $\frac{a_{0}}{2}$

C. $\frac{a_{0}}{\sqrt{2}}$

D. $a_{0}$

E. $2 a_{0}$

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C: 0
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The lifetime for the $2 p \rightarrow 1 s$ transition in hydrogen is $1.6 \times 10^{-9} \mathrm{~s}$. The natural line width for the radiation emitted during the transition is approximately

A. $100 \mathrm{~Hz}$

B. $100 \mathrm{kHz}$

C. $100 \mathrm{MHz}$

D. $100 \mathrm{GHz}$

E. $100 \mathrm{THz}$


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B: 0
C: 1
D: 0
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A spring of force constant $k$ is stretched a certain distance. It takes twice as much work to stretch a second spring by half this distance. The force constant of the second spring is

A. $k$

B. $2 k$

C. $4 k$

D. $8 k$

E. $16 k$


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B: 0
C: 0
D: 1
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On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of the same mass that is initially at rest. After the collision, the first block moves at an angle $\theta$ to its initial direction and has a speed $v / 2$. The second block's speed after the collision is

A. $\frac{\sqrt{3}}{4} v$

B. $\frac{v}{2}$

C. $\frac{\sqrt{3}}{2} v$

D. $\frac{\sqrt{5}}{2} v$

E. $v+\frac{v}{2} \cos \theta$


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B: 0
C: 1
D: 0
E: 0
Which of the following gives Hamilton's canonical equation(s) of motion? ( $H$ is the Hamiltonian, $q_{i}$ are the generalized coordinates, and $p_{i}$ are the generalized momenta.)

A. $q_{i}=\frac{\partial H}{\partial p_{i}}, \quad p_{i}=-\frac{\partial H}{\partial q_{i}}$

B. $q_{i}=\frac{\partial H}{\partial \dot{q}_{i}}, \quad p_{i}=\frac{\partial H}{\partial \dot{p}_{i}}$

C. $\dot{q}_{i}=\frac{\partial H}{\partial q_{i}}, \quad \dot{p}_{i}=-\frac{\partial H}{\partial p_{i}}$

D. $\dot{q}_{i}=\frac{\partial H}{\partial p_{i}}, \quad \dot{p}_{i}=-\frac{\partial H}{\partial q_{i}}$

E. $\frac{d}{d t}\left(\frac{\partial H}{\partial p_{i}}\right)-\frac{\partial H}{\partial q_{i}}=0$

\begin{tabular}{|l|}
\hline Oil \\
\hline Water \\
\hline
\end{tabular}


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A layer of oil with density $800 \mathrm{~kg} / \mathrm{m}^{3}$ floats on top of a volume of water with density $1,000 \mathrm{~kg} / \mathrm{m}^{3}$. A block floats at the oil-water interface with $1 / 4$ of its volume in oil and 3/4 of its volume in water, as shown in the figure above. What is the density of the block?

A. $200 \mathrm{~kg} / \mathrm{m}^{3}$

B. $850 \mathrm{~kg} / \mathrm{m}^{3}$

C. $950 \mathrm{~kg} / \mathrm{m}^{3}$

D. $1,050 \mathrm{~kg} / \mathrm{m}^{3}$

E. $1,800 \mathrm{~kg} / \mathrm{m}^{3}$

Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
An incompressible fluid of density $\rho$ flows through a horizontal pipe of radius $r$ and then passes through a constriction of radius $r / 2$. If the fluid has pressure $P_{0}$ and velocity $v_{0}$ before the constriction, the pressure in the constriction is

A. $P_{0}-\frac{15}{2} \rho v_{0}^{2}$

B. $P_{0}-\frac{3}{2} \rho v_{0}^{2}$

C. $\frac{P_{0}}{4}$

D. $P_{0}+\frac{3}{2} \rho v_{0}^{2}$

E. $P_{0}+\frac{15}{2} \rho v_{0}^{2}$


Answer scores (1 = correct):
A: 1
B: 0
C: 0
D: 0
E: 0
A thermodynamic system, initially at absolute temperature $T_{1}$, contains a mass $m$ of water with specific heat capacity $c$. Heat is added until the temperature rises to $T_{2}$. The change in entropy of the water is

A. 0

B. $T_{2}-T_{1}$

C. $m c T_{2}$

D. $m c\left(T_{2}-T_{1}\right)$

E. $m c \ln \left(\frac{T_{2}}{T_{1}}\right)$


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B: 0
C: 0
D: 0
E: 1
Heat $Q$ is added to a monatomic ideal gas under conditions of constant volume, resulting in a temperature change $\Delta T$. How much heat will be required to produce the same temperature change, if it is added under conditions of constant pressure?

A. $\frac{3}{5} Q$

B. $Q$

C. $\frac{5}{3} Q$

D. $2 Q$

E. $\frac{10}{3} Q$

Answer scores (1 = correct):
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B: 0
C: 1
D: 0
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A heat pump is to extract heat from an outdoor environment at $7^{\circ} \mathrm{C}$ and heat the environment indoors to $27^{\circ} \mathrm{C}$. For each $15,000 \mathrm{~J}$ of heat delivered indoors, the smallest amount of work that must be supplied to the heat pump is approximately

A. $500 \mathrm{~J}$

B. $1,000 \mathrm{~J}$

C. $1,100 \mathrm{~J}$

D. $2,000 \mathrm{~J}$

E. $2,200 \mathrm{~J}$



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The capacitor in the circuit above is charged. If switch $S$ is closed at time $t=0$, which of the following represents the magnetic energy, $U$, in the inductor as a function of time? (Assume that the capacitor and inductor are ideal.)

A.



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A pair of electric charges of equal magnitude $q$ and opposite sign are separated by a distance $\ell$, as shown in the figure above. Which of the following gives the approximate magnitude and direction of the electric field set up by the two charges at a point $P$ on the $y$-axis, which is located a distance $r \gg \ell$ from the $x$-axis?
Magnitude
Direction
A. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$+y$
B. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$+x$
C. $\frac{1}{4 \pi \epsilon_{0}} \frac{2 q}{r^{2}}$
$-x$
D. $\frac{1}{4 \pi \epsilon_{0}} \frac{q \ell}{r^{3}}$
$+x$
E. $\frac{1}{4 \pi \epsilon_{0}} \frac{q \ell}{r^{3}}$


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Consider two very long, straight, insulated wires oriented at right angles. The wires carry currents of equal magnitude $I$ in the directions shown in the figure above. What is the net magnetic field at point $P$ ?

A. $\frac{\mu_{0} I}{2 \pi a}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$

B. $-\frac{\mu_{0} I}{2 \pi a}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$

C. $\frac{\mu_{0} I}{\pi a} \hat{\mathbf{z}}$

D. $-\frac{\mu_{0} I}{\pi a} \hat{\mathbf{z}}$

E. 0


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A beam of muons travels through the laboratory with speed $v=\frac{4}{5} c$. The lifetime of a muon in its rest frame is $\tau=2.2 \times 10^{-6} \mathrm{~s}$. The mean distance traveled by the muons in the laboratory frame is

A. $530 \mathrm{~m}$

B. $660 \mathrm{~m}$

C. $880 \mathrm{~m}$

D. $1,100 \mathrm{~m}$

E. $1,500 \mathrm{~m}$


Answer scores (1 = correct):
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B: 0
C: 1
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A particle of mass $M$ decays from rest into two particles. One particle has mass $m$ and the other particle is massless. The momentum of the massless particle is

A. $\frac{\left(M^{2}-m^{2}\right) c}{4 M}$

B. $\frac{\left(M^{2}-m^{2}\right) c}{2 M}$

C. $\frac{\left(M^{2}-m^{2}\right) c}{M}$

D. $\frac{2\left(M^{2}-m^{2}\right) c}{M}$

E. $\frac{4\left(M^{2}-m^{2}\right) c}{M}$



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In an experimental observation of the photoelectric effect, the stopping potential was plotted versus the light frequency, as shown in the figure above. The best straight line was fitted to the experimental points. Which of the following gives the slope of the line? (The work function of the metal is $\phi$.)

A. $\frac{h}{\phi}$

B. $\frac{h}{e}$

C. $\frac{e}{h}$

D. $\frac{e}{\phi}$

E. $\frac{\phi}{e}$



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Two sinusoidal waveforms of the same frequency are displayed on an oscilloscope screen, as indicated above. The horizontal sweep of the oscilloscope is set to $100 \mathrm{~ns} / \mathrm{cm}$ and the vertical gains of channels 1 and 2 are each set to $2 \mathrm{~V} / \mathrm{cm}$. The zero-voltage level of each channel is given at the right in the figure. The phase difference between the two waveforms is most nearly

A. $30^{\circ}$

B. $45^{\circ}$

C. $60^{\circ}$

D. $90^{\circ}$

E. $120^{\circ}$


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In the diamond structure of elemental carbon, the nearest neighbors of each $\mathrm{C}$ atom lie at the corners of a

A. square

B. hexagon

C. cube

D. tetrahedron

E. octahedron

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According to the BCS theory, the attraction between Cooper pairs in a superconductor is due to

A. the weak nuclear force

B. the strong nuclear force

C. vacuum polarization

D. interactions with the ionic lattice

E. the Casimir effect


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During a hurricane, a $1,200 \mathrm{~Hz}$ warning siren on the town hall sounds. The wind is blowing at $55 \mathrm{~m} / \mathrm{s}$ in a direction from the siren toward a person $1 \mathrm{~km}$ away. With what frequency does the sound wave reach the person? (The speed of sound in air is $330 \mathrm{~m} / \mathrm{s}$.)

A. $1,000 \mathrm{~Hz}$

B. $1,030 \mathrm{~Hz}$

C. $1,200 \mathrm{~Hz}$

D. $1,400 \mathrm{~Hz}$

E. $1,440 \mathrm{~Hz}$


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D: 0
E: 0
Sound waves moving at $350 \mathrm{~m} / \mathrm{s}$ diffract out of a speaker enclosure with an opening that is a long rectangular slit $0.14 \mathrm{~m}$ across. At about what frequency will the sound first disappear at an angle of $45^{\circ}$ from the normal to the speaker face?

A. $500 \mathrm{~Hz}$

B. $1,750 \mathrm{~Hz}$

C. $2,750 \mathrm{~Hz}$

D. $3,500 \mathrm{~Hz}$

E. $5,000 \mathrm{~Hz}$


Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
An organ pipe, closed at one end and open at the other, is designed to have a fundamental frequency of $\mathrm{C}(131 \mathrm{~Hz})$. What is the frequency of the next higher harmonic for this pipe?

A. $44 \mathrm{~Hz}$

B. $196 \mathrm{~Hz}$

C. $262 \mathrm{~Hz}$

D. $393 \mathrm{~Hz}$

E. $524 \mathrm{~Hz}$

Inputs



Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
For the logic circuit shown above, which of the following Boolean statements gives the output $E$ in terms of inputs $A, B, C$, and $D$ ?

A. $E=\overline{A+B}+\overline{C \cdot D}$

B. $E=\overline{A+B} \cdot \overline{C \cdot D}$

C. $E=\overline{\bar{A}+\bar{B}} \cdot \overline{C \cdot D}$

D. $E=\overline{A \cdot B} \cdot \overline{C \cdot D}$

E. $E=\overline{\bar{A} \cdot \bar{B}} \cdot \overline{C \cdot D}$


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
Which of the following lasers utilizes transitions that involve the energy levels of free atoms?

A. Diode laser

B. Dye laser

C. Free-electron laser

D. Gas laser

E. Solid-state laser

Answer scores (1 = correct):
A: 0
B: 0
C: 0
D: 1
E: 0
Which of the following expressions is proportional to the total energy for the levels of a oneelectron Bohr atom? ( $m$ is the reduced mass, $Z$ is the number of protons in the nucleus, $-e$ is the charge on the electron, and $n$ is the principal quantum number.)

A. $\frac{m Z e^{2}}{n}$

B. $\frac{m Z e^{2}}{n^{2}}$

C. $\frac{m Z^{2} e^{4}}{n^{2}}$

D. $\frac{m^{2} Z^{2} e^{2}}{n^{2}}$

E. $\frac{m^{2} Z^{2} e^{4}}{n^{2}}$


Answer scores (1 = correct):
A: 0
B: 0
C: 1
D: 0
E: 0
True statements about the absorption and emission of energy by an atom include which of the following?

I. An atom can only absorb photons of light that have certain specific energies.

II. An atom can emit photons of light of any energy.

III. At low temperature, the lines in the absorption spectrum of an atom coincide with the lines in its emission spectrum that represent transitions to the ground state.

A. I only

B. III only

C. I and II only

D. I and III only

E. I, II, and III


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