AP Physics 2: Algebra-Based Unit 7: Modern Physics Practice Exam

Assessment for Unit 7: Modern Physics

Estimated Time: 60 minutes

Exam Details

Questions: 31 total (31 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 7: Modern Physics
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (31 Questions)

Select the one best answer for each question.

1. [Skill: 2.B | Topic: 7.1] A monochromatic light source emits photons with a wavelength $\lambda_0$ and energy $E_0$. If the source is adjusted so that it now emits photons with a wavelength of $2\lambda_0$, which of the following expressions correctly represents the energy of a single photon from the adjusted source?

(A)$E_0 / 4$(B)$E_0 / 2$(C)$2E_0$(D)$4E_0$

2. [Skill: 1.A | Topic: 7.1] Particle X and Particle Y are moving through a vacuum. Particle X has a mass $M$ and moves with velocity $v$. Particle Y has a mass $2M$ and moves with velocity $2v$. What is the ratio of the de Broglie wavelength of Particle X to the de Broglie wavelength of Particle Y ($\lambda_X / \lambda_Y$)?

(A)1/4(B)1/2(C)2(D)4

3. [Skill: 6.C | Topic: 7.1] In a controlled experiment, a beam of electrons is fired at a thin gold foil, and a pattern of alternating bright and dark concentric rings is observed on a detection screen. Which of the following claims is best supported by this observation?

(A)Electrons are massless particles that travel at the speed of light.(B)Electrons exhibit wave-like properties such as interference and diffraction.(C)The gold atoms have a continuous range of energy levels that absorb electron momentum.(D)The experiment demonstrates that electrons have a definite position and momentum at all times.

4. [Skill: 1.1 | Topic: 7.2] A physicist is analyzing four different atomic nuclei. The composition of each nucleus is recorded in the table below: - Nucleus 1: 6 protons, 6 neutrons - Nucleus 2: 7 protons, 7 neutrons - Nucleus 3: 6 protons, 8 neutrons - Nucleus 4: 8 protons, 8 neutrons Based on the properties of the atom described in the Bohr model and modern atomic theory, which of the following identifies the nuclei that belong to the same chemical element?

(A)Nucleus 1 and Nucleus 2, because they have the same number of total nucleons.(B)Nucleus 1 and Nucleus 3, because the number of protons defines the identity of the element.(C)Nucleus 2 and Nucleus 4, because they both have an equal number of protons and neutrons.(D)Nucleus 3 and Nucleus 4, because the identity of an element is determined by the number of neutrons in the nucleus.

Refer to the figure below.

5. [Skill: 1.4 | Topic: 7.2] An electron in a hydrogen atom is initially in the $n=3$ energy state and transitions to the $n=2$ energy state. Which of the following best describes the outcome of this transition according to the Bohr model?

(A)The atom absorbs a photon with an energy exactly equal to the difference between the $n=3$ and $n=2$ energy levels.(B)The atom emits a photon with an energy exactly equal to the difference between the $n=3$ and $n=2$ energy levels.(C)The atom emits a continuous spectrum of radiation as the electron spirals from the higher orbit to the lower orbit.(D)The electron gains kinetic energy from the nucleus to move to a lower potential energy state without interacting with light.

6. [Skill: 6.4 | Topic: 7.2] Classical physics predicts that an electron orbiting a nucleus is accelerating and should therefore radiate electromagnetic energy continuously. This would cause the electron to lose energy and spiral into the nucleus, making atoms unstable. How does the Bohr model of the atom resolve this discrepancy with experimental observations of atomic stability and emission spectra?

(A)By assuming the nucleus is composed of both protons and neutrons, which creates a 'strong' force that prevents the electron from spiraling inward.(B)By postulating that electrons exist in 'stationary states' where they do not radiate energy, despite being in an orbital motion.(C)By suggesting that the electron's charge is neutralized by the vacuum of space, preventing the emission of radiation.(D)By replacing the concept of a nucleus with a uniform sphere of positive charge in which electrons are embedded, eliminating orbital acceleration.

Refer to the figure below.

7. [Skill: 1.4 | Topic: 7.3] An energy level diagram for a hypothetical atom is shown below. [Image Cue]: Energy level diagram, Title: Atomic Energy Levels, Vertical axis: Energy in electron-volts (eV), Data points: n=1 at -12.0 eV, n=2 at -7.0 eV, n=3 at -3.0 eV, n=infinity at 0 eV. An electron is currently in the $n=2$ state. Which of the following photons could be absorbed by the atom to cause a transition to a higher energy state?

(A)A photon with energy $3.0\text{ eV}$(B)A photon with energy $4.0\text{ eV}$(C)A photon with energy $5.0\text{ eV}$(D)A photon with energy $7.0\text{ eV}$

8. [Skill: 6.4 | Topic: 7.3] A sample of hydrogen gas is excited by an external energy source, and the resulting light is passed through a diffraction grating. A student observes several discrete, bright lines of different colors on a screen. Which of the following statements best justifies the observation of discrete lines rather than a continuous rainbow of colors?

(A)The speed of light emitted by the atom varies depending on the mass of the nucleus, leading to different refraction angles.(B)The electrons in the atom can only exist in specific, quantized energy states, and photons are emitted only when electrons transition between these states.(C)The diffraction grating filters out all frequencies of light except for those that are multiples of the fundamental frequency of the atom.(D)Energy is conserved only during the absorption of light, while emission allows for a continuous range of photon energies.

9. [Skill: 2.2 | Topic: 7.3] An atom undergoes a transition from an initial energy state $E_i = -2.5\text{ eV}$ to a final energy state $E_f = -10.5\text{ eV}$. If $h$ represents Planck's constant and $c$ represents the speed of light, which of the following expressions correctly calculates the wavelength $\lambda$ of the emitted photon?

(A)$\lambda $= $\frac{hc}{13.0\text{ eV}}$(B)$\lambda $= $\frac{hc}{8.0\text{ eV}}$(C)$\lambda $= $\frac{8.0\text{ eV}}{hc}$(D)$\lambda $= $\frac{hc}{2.5\text{ eV}}$

10. [Skill: 2.B | Topic: 7.4] Star A and Star B are both spherical blackbodies. Star A has a radius $R$ and a surface temperature $T$. Star B has a radius $2R$ and a surface temperature $2T$. What is the ratio of the total power radiated by Star B to the total power radiated by Star A, $\frac{P_B}{P_A}$?

(A)8(B)16(C)32(D)64

11. [Skill: 1.A | Topic: 7.4] A metal rod is placed in an insulated vacuum chamber and heated electrically. Initially, the rod is at room temperature and does not appear to glow. As the temperature of the rod increases to $2500\text{ K}$, it begins to glow a bright yellowish-white. Which of the following best describes the change in the electromagnetic radiation emitted by the rod as its temperature increases?

(A)The emitted radiation changes from a continuous spectrum to a discrete line spectrum.(B)The peak wavelength of the radiation increases, shifting the light toward the infrared end of the spectrum.(C)The total power emitted increases, and the peak wavelength shifts toward shorter wavelengths.(D)The total power emitted remains constant, but the frequency of the peak intensity decreases.

12. [Skill: 1.4 | Topic: 7.5] Monochromatic light of frequency $f$ is incident on a photoactive metal surface with work function $\phi$, where $hf > \phi$. The light source is adjusted so that the intensity of the light is doubled while the frequency remains constant. Which of the following correctly describes the effect of this change on the maximum kinetic energy of the ejected electrons and the number of electrons ejected per second? (A) The maximum kinetic energy doubles, and the number of electrons per second remains the same. (B) The maximum kinetic energy remains the same, and the number of electrons per second remains the same. (C) The maximum kinetic energy doubles, and the number of electrons per second doubles. (D) The maximum kinetic energy remains the same, and the number of electrons per second doubles.

(A)The maximum kinetic energy doubles, and the number of electrons per second remains the same.(B)The maximum kinetic energy remains the same, and the number of electrons per second remains the same.(C)The maximum kinetic energy doubles, and the number of electrons per second doubles.(D)The maximum kinetic energy remains the same, and the number of electrons per second doubles.

13. [Skill: 6.4 | Topic: 7.5] In a laboratory experiment, a beam of light with a wavelength of 600 nm is incident on a metal surface, but no electrons are observed to be emitted. To initiate the emission of electrons from this specific metal, which of the following actions would be most effective? (A) Using a light source with a wavelength of 400 nm. (B) Using a light source with a wavelength of 800 nm. (C) Increasing the intensity of the 600 nm light source. (D) Increasing the total time the 600 nm light shines on the metal.

(A)Using a light source with a wavelength of 400 nm.(B)Using a light source with a wavelength of 800 nm.(C)Increasing the intensity of the 600 nm light source.(D)Increasing the total time the 600 nm light shines on the metal.

Refer to the figure below.

14. [Skill: 1.4 | Topic: 7.6] An X-ray photon with wavelength $\lambda$ and frequency $f$ strikes an electron that is initially at rest. After the collision, the photon is scattered at an angle $\theta$ and has a new wavelength $\lambda'$ and frequency $f'$. Which of the following correctly compares the properties of the incident photon to the scattered photon and provides the best justification based on conservation laws?

(A)$\lambda' > \lambda$ and $f' < f$, because the photon transfers some of its energy to the electron during the collision.(B)$\lambda' < \lambda$ and $f' > f$, because the photon gains momentum from the electron's recoil.(C)$\lambda' = \lambda$ and $f' = f$, because the collision is elastic and the photon's energy is determined only by its speed $c$.(D)$\lambda' > \lambda$ and $f' > f$, because the increase in wavelength must be compensated by an increase in frequency to keep the speed $c$ constant.

15. [Skill: 2.2 | Topic: 7.6] A photon of energy $E_0$ and momentum magnitude $p_0$ collides with a free electron of mass $m_e$ that is initially at rest. The photon is scattered backwards (at an angle of $180^{\circ}$) with energy $E_s$ and momentum magnitude $p_s$. Which of the following expressions correctly represents the magnitude of the momentum of the recoiling electron, $p_e$?

(A)$p_e = p_0 - p_s$(B)$p_e = p_0 + p_s$(C)$p_e = \sqrt{p_0^2 + p_s^2}$(D)$p_e = \frac{E_0 - E_s}{c}$

16. [Skill: 6.4 | Topic: 7.6] Experimental data for Compton scattering shows that the shift in wavelength $\Delta \lambda = \lambda' - \lambda$ depends on the scattering angle $\theta$ but is independent of the material of the target, provided the target contains 'free' or loosely bound electrons. Which of the following claims is best supported by this observation?

(A)The interaction is a collective wave phenomenon involving the entire lattice of the target material.(B)The shift in wavelength is caused by the Doppler effect as the target atoms move away from the source.(C)The interaction is a discrete, two-body collision between a photon and an individual electron.(D)The energy of the incident light is absorbed and re-emitted by the nucleus of the atom.

17. [Skill: 5.B | Topic: 7.7] A heavy nucleus of ${}^{235}_{92}U$ absorbs a slow-moving neutron and undergoes fission, splitting into ${}^{141}_{56}Ba$, ${}^{92}_{36}Kr$, and three additional neutrons. The total mass of the reactants (the uranium nucleus and the initial neutron) is $M_{reactants}$, and the total mass of the products (the barium nucleus, the krypton nucleus, and the three neutrons) is $M_{products}$. If the reaction releases a total energy $Q$, which of the following statements is correct?

(A)$M_{reactants} > M_{products}$ and $Q = (M_{reactants} - M_{products})c^2$(B)$M_{reactants} < M_{products}$ and $Q = (M_{products} - M_{reactants})c^2$(C)$M_{reactants} = M_{products}$ and $Q = M_{reactants}c^2$(D)$M_{reactants} > M_{products}$ and $Q = (M_{reactants} + M_{products})c^2$

18. [Skill: 5.C | Topic: 7.7] A sample of a radioactive isotope is prepared with an initial number of nuclei $N_0$. The isotope has a known decay constant $\lambda$. Which of the following mathematical expressions correctly determines the number of nuclei that have undergone radioactive decay after a time interval $t$ has elapsed?

(A)$N = N_0 e^{-\lambda t}$(B)$N = N_0 (1 - e^{-\lambda t})$(C)$N = N_0 e^{\lambda t}$(D)$N = N_0 (1 - \lambda t)$

19. [Skill: 1.B | Topic: 7.7] Two deuterium nuclei (${}^2_1H$) move toward each other with equal speeds $v$ in a laboratory frame of reference. They undergo a nuclear fusion reaction, producing a helium-3 nucleus (${}^3_2He$) and a single neutron (${}^1_0n$). Which of the following describes the constraints on the system's momentum and energy immediately after the reaction?

(A)The total momentum of the products is $2mv$, and the total mass of the products is equal to the total mass of the reactants.(B)The total momentum of the products is zero, and the total kinetic energy of the products is greater than the initial kinetic energy of the reactants.(C)The total momentum of the products is zero, and the total mass of the products is greater than the total mass of the reactants.(D)The total momentum of the products is $2mv$, and the total kinetic energy of the products is less than the initial kinetic energy of the reactants.

20. [Skill: 1.C | Topic: 7.8] A nucleus of Carbon-14 ($^{14}_{6}C$) is unstable and undergoes radioactive decay to form a nucleus of Nitrogen-14 ($^{14}_{7}N$). Which of the following correctly identifies the particles emitted during this process and the conservation law that requires the emission of the second, neutral particle? [Image Cue]: A nuclear equation showing $^{14}_{6}C \rightarrow ^{14}_{7}N + \text{particle 1} + \text{particle 2}$.

(A)An electron and an antineutrino; conservation of lepton number.(B)A positron and a neutrino; conservation of lepton number.(C)An electron and a neutrino; conservation of charge.(D)A positron and an antineutrino; conservation of nucleon number.

21. [Skill: 6.C | Topic: 7.8] A heavy parent nucleus $X$ with atomic number $Z$ and mass number $A$ undergoes a two-step decay process. First, it undergoes alpha decay to produce daughter nucleus $Y$. Then, nucleus $Y$ undergoes beta-minus decay to produce the final nucleus $Z$. Which of the following correctly describes the composition of the final nucleus $Z$ compared to the original parent nucleus $X$?

(A)Nucleus $Z$ has 3 fewer protons and 1 fewer neutron than nucleus $X$.(B)Nucleus $Z$ has 1 fewer proton and 3 fewer neutrons than nucleus $X$.(C)Nucleus $Z$ has 2 fewer protons and 2 fewer neutrons than nucleus $X$.(D)Nucleus $Z$ has 1 fewer proton and 1 fewer neutron than nucleus $X$.

22. [Skill: 7.A | Topic: 7.8] A sample of Magnesium-27 ($^{27}_{12}Mg$) decays via beta-minus emission. Observations show that immediately following the particle emission, the resulting Aluminum-27 ($^{27}_{13}Al$) nucleus emits a high-energy photon. Which of the following best explains the origin of this photon?

(A)The photon is emitted as an electron moves from an outer atomic shell to an inner shell to fill a vacancy.(B)The photon is emitted because the nucleus was left in an excited state and transitioned to a lower energy state.(C)The photon is emitted to conserve the total number of nucleons which was altered during the beta decay.(D)The photon is emitted to carry away the excess positive charge created when the neutron turned into a proton.

23. [Skill: 2.B | Topic: 7.1] A laser emits monochromatic light with a frequency $f$. The power output of the laser is kept constant, but the source is adjusted to emit light with a frequency of $1.5f$. Which of the following correctly describes the change in the energy of each individual photon emitted by the laser?

(A)The energy of each photon remains the same because the power is constant.(B)The energy of each photon increases by a factor of 1.5.(C)The energy of each photon decreases by a factor of 1.5.(D)The energy of each photon increases by a factor of 2.25.

24. [Skill: 1.4 | Topic: 7.1] Two subatomic particles, Particle X and Particle Y, are moving through a vacuum. Particle X has twice the momentum of Particle Y ($p_X = 2p_Y$). Which of the following correctly compares the de Broglie wavelength $\lambda_X$ of Particle X to the de Broglie wavelength $\lambda_Y$ of Particle Y?

(A)$\lambda_X = 2\lambda_Y$(B)$\lambda_X = 4\lambda_Y$(C)$\lambda_X = \frac{1}{2}\lambda_Y$(D)$\lambda_X = \lambda_Y$

25. [Skill: 6.4 | Topic: 7.1] In a laboratory experiment, a beam of electrons is fired at a double-slit apparatus, and an interference pattern is observed on a detection screen. If the velocity of the electrons in the beam is significantly increased, which of the following best predicts the change in the observed interference pattern?

(A)The maxima in the interference pattern will become more widely spaced because the wavelength of the electrons increases.(B)The maxima in the interference pattern will become more closely spaced because the wavelength of the electrons decreases.(C)The interference pattern will disappear because the electrons will behave strictly as particles at higher velocities.(D)The interference pattern will remain unchanged because the wavelength of an electron depends only on its mass, not its velocity.

26. [Skill: 1.1 | Topic: 7.2] An experimentalist is analyzing three different atomic nuclei with the following compositions: - Nucleus 1: 6 protons, 6 neutrons - Nucleus 2: 6 protons, 7 neutrons - Nucleus 3: 7 protons, 7 neutrons Based on the essential properties of atomic elements, which of the following statements is correct regarding the identity of these nuclei?

(A)Nucleus 1 and Nucleus 2 are the same element because they have the same number of protons.(B)Nucleus 2 and Nucleus 3 are the same element because they have the same number of neutrons.(C)Nucleus 1 and Nucleus 3 are the same element because they have the same total number of nucleons.(D)All three nuclei represent different elements because they have different mass numbers.

Refer to the figure below.

27. [Skill: 1.4 | Topic: 7.2] [Image Cue]: An energy level diagram for a hydrogen atom. Horizontal lines represent energy states labeled $n=1$ (ground state, $-13.6\text{ eV}$), $n=2$ ($-3.4\text{ eV}$), and $n=3$ ($-1.5\text{ eV}$). An arrow points downward from the $n=3$ line to the $n=2$ line. A hydrogen atom is modeled using the Bohr representation. When an electron transitions from the $n=3$ state to the $n=2$ state as shown in the diagram, which of the following best describes the energy of the emitted photon?

(A)The photon energy can be any value between $1.5\text{ eV}$ and $3.4\text{ eV}$ depending on the path taken.(B)The photon energy is exactly $1.9\text{ eV}$, representing the discrete difference between the two quantized states.(C)The photon energy is $4.9\text{ eV}$, which is the sum of the magnitudes of the two energy levels.(D)No photon is emitted because the Bohr model predicts that electrons in circular orbits do not lose energy.

28. [Skill: 6.4 | Topic: 7.2] In the early 20th century, the classical "planetary" model of the atom faced a significant theoretical crisis. According to classical electromagnetism, an electron in circular orbit is accelerating and should continuously radiate energy. Which of the following best explains how the Bohr model addressed this crisis while still utilizing aspects of classical physics?

(A)Bohr postulated that the nucleus is composed of both protons and neutrons, which provides a stabilizing gravitational force.(B)Bohr proposed that electrons move in elliptical rather than circular orbits, which prevents the emission of radiation.(C)Bohr assumed that electrons exist in specific 'stationary states' where they do not radiate energy, despite being in accelerated motion.(D)Bohr suggested that the electric force between the nucleus and the electron is quantized, rather than the energy levels.

29. [Skill: 6.C | Topic: 7.3] An isolated atom is initially in its ground state with an energy of $-10.0\text{ eV}$. The atom has excited states with energies of $-6.0\text{ eV}$ and $-4.0\text{ eV}$. A beam of photons, each with an energy of $4.0\text{ eV}$, is incident on a gas of these atoms. Which of the following best describes the interaction between the photons and the atoms?

(A)The photons are absorbed, and the electrons in the atoms move from the ground state to the $-6.0\text{ eV}$ energy level.(B)The photons are absorbed, and the electrons in the atoms move from the ground state to the $-4.0\text{ eV}$ energy level.(C)The photons are not absorbed because their energy does not match the difference between the ground state and the $-4.0\text{ eV}$ state.(D)The photons are not absorbed because the energy of a single photon must be exactly $10.0\text{ eV}$ to interact with the atom.

Refer to the figure below.

30. [Skill: 1.C | Topic: 7.3] An energy level diagram for a hypothetical atom is shown. The atom undergoes a transition from the $n=3$ state to the $n=2$ state, emitting a photon with wavelength $\lambda_{32}$. It then undergoes a transition from $n=2$ to $n=1$, emitting a photon with wavelength $\lambda_{21}$. If the energy difference between $n=2$ and $n=1$ is significantly greater than the energy difference between $n=3$ and $n=2$ (i.e., $|E_2 - E_1| > |E_3 - E_2|$), which of the following correctly compares the characteristics of the emitted photons?

(A)The frequency $f_{21}$ is less than $f_{32}$, and the wavelength $\lambda_{21}$ is greater than $\lambda_{32}$.(B)The frequency $f_{21}$ is greater than $f_{32}$, and the wavelength $\lambda_{21}$ is greater than $\lambda_{32}$.(C)The frequency $f_{21}$ is greater than $f_{32}$, and the wavelength $\lambda_{21}$ is less than $\lambda_{32}$.(D)The frequency $f_{21}$ is less than $f_{32}$, and the wavelength $\lambda_{21}$ is less than $\lambda_{32}$.

31. [Skill: 2.C | Topic: 7.3] A gas of atoms is found to have a specific energy level at $-2.5\text{ eV}$ and another level at $-5.5\text{ eV}$. When an electron transitions from the higher energy level to the lower energy level, a single photon is emitted. What is the approximate wavelength of the emitted photon? (Use $h = 4.14 \times 10^{-15}\text{ eV}\cdot\text{s}$ and $c = 3.00 \times 10^8\text{ m/s}$)

(A)225 nm(B)310 nm(C)414 nm(D)620 nm

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