AP Physics 2 Unit 15 Review: Modern Physics

Q: What's on the AP Physics 2 Unit 15 progress check (MCQ and FRQ)?

The AP Physics 2 Unit 15 progress check includes both MCQ and FRQ parts drawn from all 8 Modern Physics topics. The MCQ section tests conceptual understanding of the photoelectric effect, Compton scattering, blackbody radiation, atomic structure, and nuclear decay. The FRQ part asks you to apply quantum theory reasoning, interpret spectra, or work through nuclear processes quantitatively. Practice with matched questions at /ap-physics-2-revised/unit-15 .

Q: How do I practice AP Physics 2 Unit 15 FRQs?

The best way to practice AP Physics 2 Unit 15 FRQs is to focus on the topics that generate the most free-response questions: the photoelectric effect, emission and absorption spectra, and nuclear decay processes. FRQs in this unit typically ask you to explain phenomena using quantum theory, calculate photon energy or stopping voltage, or analyze nuclear equations. Practice by writing out full explanations, not just plugging numbers, since College Board awards points for reasoning. Find Unit 15 FRQ practice at /ap-physics-2-revised/unit-15 .

Q: Where can I find AP Physics 2 Unit 15 practice questions?

For AP Physics 2 Unit 15 practice questions, including multiple-choice and practice test sets, head to /ap-physics-2-revised/unit-15 . There you'll find MCQ practice covering the photoelectric effect, Bohr model, Compton scattering, blackbody radiation, and nuclear decay, plus FRQ-style problems. Mixing MCQ and FRQ practice is the most effective way to prepare for the 12-15% of exam questions this unit represents.

Q: How should I study AP Physics 2 Unit 15?

Start with the photoelectric effect and quantum theory since those concepts anchor everything else in Unit 15. Once you understand wave-particle duality and discrete energy levels, the Bohr model of atomic structure and emission spectra will click into place. From there, work through Compton scattering and blackbody radiation, then finish with fission, fusion, and radioactive decay. A few concrete steps that help: draw energy-level diagrams for the Bohr model, practice writing and balancing nuclear equations for decay types, and do timed MCQ sets to reinforce the conceptual reasoning College Board tests. Unit 15 is 12-15% of the exam, so it's worth steady, spaced review rather than a last-minute cram. Find study resources at /ap-physics-2-revised/unit-15 .

12–15% of AP multiple choice
8 topics
AP exam review verified for 2027

Unit 15 covers the quantum and nuclear physics that make up 12-15% of the AP Physics 2 exam. You will use E = hf, K_max = hf - phi, the Bohr energy formula, Wien's law, the Stefan-Boltzmann law, the Compton shift equation, E = mc², and N = N0 e^(-lambda t) to explain and calculate phenomena that classical mechanics cannot handle.

Fiveable's AP Physics 2 Unit 15 review covers 8 topics, with guided practice questions for the unit.

start with 15.1 start unit practiceReview with a tutorFree, 24/7, real people, from UPchieve

AP Physics 2 unit 15 topics

15.1

Quantum Theory and Wave-Particle Duality

Introduces photons (E = hf), the de Broglie wavelength (lambda = h/p), and the evidence from double-slit experiments and electron diffraction that both light and matter exhibit wave and particle behavior.

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15.2

The Bohr Model of Atomic Structure

Covers atomic structure (protons, neutrons, electrons), nuclear notation, isotopes, and the Bohr model's quantized circular orbits for hydrogen, including the energy formula E_n = -13.6 eV / n^2.

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15.3

Emission and Absorption Spectra

Explains how photon emission and absorption correspond to electron transitions between discrete energy levels, producing unique line spectra for each element, read from energy level diagrams.

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15.4

Blackbody Radiation

Describes how objects emit a continuous thermal spectrum governed by Wien's displacement law (lambda_max = b/T) and the Stefan-Boltzmann law (P = A sigma T^4), and why Planck's quantization was needed to explain the observed spectrum.

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15.5

The Photoelectric Effect

Covers electron ejection by light, the threshold frequency, the work function, and the equation K_max = hf - phi, demonstrating that photon energy (not intensity) determines the kinetic energy of ejected electrons.

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15.6

Compton Scattering

Treats photon-electron collisions using conservation of energy and momentum. The Compton shift Delta lambda = (h/m_e c)(1 - cos theta) shows photons carry momentum and lose energy when scattered.

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15.7

Fission, Fusion, and Nuclear Decay

Covers the strong force, mass-energy equivalence (E = mc^2), conservation of nucleon number, fission and fusion energy release, and exponential radioactive decay kinetics (N = N_0 e^(-lambda t)).

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15.8

Types of Radioactive Decay

Describes alpha, beta-minus, beta-plus, and gamma decay, including the particles emitted, changes in A and Z, and conservation of nucleon number, charge, and lepton number in each process.

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Practice AP Physics 2 unit 15 questions

Try AP-style questions on unit 15, then use the review notes below for anything you miss.

Example stimulus-based MCQs

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diagram

Stimulus-based practice question

The figure shows a nuclear decay sequence for a parent nucleus with mass number A = 220 and atomic number Z = 86. The nucleus first undergoes alpha decay to form Daughter 1, then Daughter 1 undergoes beta-minus decay to form Daughter 2. A student compares the neutron numbers of Daughter 1 and Daughter 2.

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Question

Which of the following correctly compares the neutron number N of Daughter 1 to the neutron number N of Daughter 2?

N(Daughter 1) is 1 less than N(Daughter 2)

N(Daughter 1) is 1 greater than N(Daughter 2)

N(Daughter 1) is 2 greater than N(Daughter 2)

N(Daughter 1) equals N(Daughter 2)

graph

Stimulus-based practice question

A student performs a Compton scattering experiment and records the energy of the scattered photon as a function of scattering angle θ. The figure shows the resulting graph. The student claims the data support the particle model of light rather than the classical wave model.

answer in practice

Question

Which choice best evaluates the student's claim using the evidence in the figure?

Supported, because the data show higher photon energy at larger angles.

Supported, because the data show lower photon energy at larger angles.

Not supported, because the wave model predicts this angle dependence from Doppler shift.

Not supported, because any change in photon energy fits both models equally well.

Example FRQs

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FRQ

Photoelectric effect and stopping potential in sodium

1. A laboratory investigates several modern physics phenomena using a hot filament source, a hydrogen gas discharge tube, a clean sodium metal surface in a vacuum photoelectric apparatus, an x-ray source with a graphite target, and a sealed sample of radioactive nuclei, as shown in Figure 1. Light from the filament is approximated as blackbody radiation. The hydrogen discharge tube emits light due to electron transitions between atomic energy levels. Photons from selected sources are directed onto matter to study both particle-like and wave-like behavior of electromagnetic radiation and the quantized behavior of atoms and nuclei.

Figure 1. Five-station modern-physics laboratory: blackbody filament, hydrogen emission spectrum, sodium photoelectric effect, x-ray scattering from graphite, and radioactive decay counting.

Figure 2. Intensity I versus wavelength λ for two blackbody filaments; one curve peaks at 970 nm and the other peaks at 580 nm.

Figure 3. Hydrogen energy levels with a transition from n = 4 to n = 2.

Complete the following tasks in Figures 2 and 3.

•

In Figure 2, indicate which curve corresponds to the filament at the higher absolute temperature.

•

In Figure 3, the transition shown is from $n=4$ to $n=2$ . Indicate whether the photon is emitted or absorbed during the transition.

ii.

For hydrogen, the energy of level $n$ is given by $E_n=-\dfrac{13.6\ \text{eV}}{n^2}$ .

Derive an expression for the wavelength $\lambda_{4\to2}$ of the photon associated with the $n=4$ to $n=2$ transition, in terms of fundamental constants. Then calculate $\lambda_{4\to2}$ in nanometers.

Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Vacuum photoelectric-effect apparatus with sodium cathode, adjustable stopping potential Vₛ, and voltmeter reading at zero current.

Indicate whether the measured stopping potential is consistent with the photoelectric effect model for sodium. Monochromatic light of wavelength $\lambda = 350\ \text{nm}$ shines on a clean sodium surface in a vacuum photoelectric apparatus, as shown in Figure 4. The work function of sodium is $\phi = 2.30\ \text{eV}$ . The stopping potential measured is $V_s = 0.90\ \text{V}$ . Use $h = 6.63× 10^{-34}\ \text{J}·\text{s}$ , $c = 3.00× 10^8\ \text{m/s}$ , and $1\ \text{eV}=1.60× 10^{-19}\ \text{J}$ .

Consistent
Not consistent

Justify your answer with a calculation using energy conservation for the photoelectric effect.

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FRQ

Photoelectric effect and stopping potential with wavelength

4. A physics student investigates the photoelectric effect using two different monochromatic light sources that illuminate a clean metal surface in a vacuum. Figure 1 shows the experimental setup. The emitted electrons are collected by an electrode, and an adjustable retarding potential difference $V_s$ is applied to reduce the current to zero. The student can also change the wavelength of the incident light while keeping the intensity low enough that at most one photon interacts with one electron at a time. The work function of the metal is $\phi = 2.20\ \text{eV}$ .

Figure 1. Photoelectric-effect apparatus with adjustable stopping potential V_s (retarding potential) between a clean metal cathode and a collector anode in vacuum; emitted electrons are measured with an ammeter while monochromatic light illuminates the cathode.

Light source 1 has wavelength $\lambda_1 = 350\ \text{nm}$ and light source 2 has wavelength $\lambda_2 = 550\ \text{nm}$ .

A student claims that the stopping potential $V_s$ needed to reduce the current to zero is greater when using light source 1 than when using light source 2.

Indicate whether the student's claim is correct or incorrect. Without manipulating equations, justify your answer by referencing how the energy carried by an individual photon depends on wavelength and how that affects the maximum kinetic energy of the emitted electrons.

Derive an expression for the stopping potential $V_s$ as a function of the wavelength $\lambda$ of the incident light for this metal. Express your answer in terms of $\lambda$ , $\phi$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Indicate whether the expression you derived in part B is or is not consistent with your answer from part A. Briefly justify your answer by describing how $V_s$ changes when $\lambda$ decreases from $550\ \text{nm}$ to $350\ \text{nm}$ .

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FRQ

Photoelectric effect and stopping potential

2. A student investigates the photoelectric effect using a vacuum phototube with a sodium photocathode, as shown in Figure 1. Monochromatic light of adjustable wavelength is incident on the photocathode. The student measures the stopping potential $V_s$ needed to reduce the photoelectric current to zero for different wavelengths. The work function of sodium is $\phi = 2.30\ \text{eV}$ .

Figure 1. Vacuum phototube photoelectric-effect apparatus with adjustable stopping potential V_s, sodium photocathode, collector, and meters for voltage and photocurrent.

Construct an energy diagram (energy on a vertical axis) that represents the interaction of a single photon with the sodium surface for this trial. Your diagram must include and label (i) the incident photon energy $E_\gamma$ , (ii) the work function $\phi$ of the metal, and (iii) the maximum kinetic energy $K_{\max}$ of the emitted electron as inferred from the stopping potential. During one trial, the incident light has wavelength $\lambda = 365\ \text{nm}$ and the stopping potential is measured to be $V_s = 1.10\ \text{V}$ .

Derive an expression for the stopping potential $V_s$ in terms of $\lambda$ , $\phi$ , and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Assume the maximum kinetic energy of emitted electrons is related to the stopping potential by $K_{\max} = eV_s$ and photon energy is $E_\gamma = hc/\lambda$ .

Figure 2. Axes for graphing stopping potential V_s as a function of inverse wavelength 1/λ for the photoelectric effect.

On the axes provided in Figure 2, sketch the expected relationship between $V_s$ and $1/\lambda$ for wavelengths that produce photoelectrons. Draw a straight best-fit line with an arrow indicating the direction of increasing photon energy. Label the physical meaning of (i) the slope and (ii) the $V_s$ -axis intercept in terms of fundamental constants and/or $\phi$ . The student repeats the experiment for several wavelengths and chooses to graph $V_s$ versus $1/\lambda$ to create a linear representation.

Indicate which source, if either, will produce emitted photoelectrons from the sodium surface. The student considers using two different light sources on the same sodium photocathode.

Source 1: monochromatic light of wavelength $\lambda = 540\ \text{nm}$ with intensity $I_1 = 2.0\ \text{mW}\,\text{cm}^{-2}$ .

Source 2: monochromatic light of wavelength $\lambda = 365\ \text{nm}$ with a lower intensity $I_2 = 0.50\ \text{mW}\,\text{cm}^{-2}$ .

Assume the photocathode area illuminated is the same for both sources and the work function remains $\phi = 2.30\ \text{eV}$ .

Source 1 only
Source 2 only
Both sources
Neither source

Briefly justify your answer by referencing at least one feature of your answers to parts A, B, or C.

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AP Physics 2 unit 15 practice test

A timed, AP-style test built only from unit 15 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.

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Unit 15 review notes

15.1

Wave-particle duality and photon basics

Quantum theory was developed because classical physics failed to explain atomic spectra, blackbody radiation, and the photoelectric effect. Light behaves as both a wave (interference, diffraction) and a particle (photons). Electrons and other matter particles also exhibit wave behavior, confirmed by electron diffraction experiments like Davisson-Germer. The de Broglie wavelength lambda = h/p applies to any particle with momentum p.

Photon energy: E = hf, where h = 6.626 x 10^-34 J·s and f is frequency. Photons are massless and electrically neutral.
Speed of photons: All photons travel at c = 3.00 x 10^8 m/s in free space. In a medium with index of refraction n, speed = c/n.
de Broglie wavelength: lambda = h/p. Any particle with momentum p has an associated wavelength, giving it wave-like properties.
Wave-particle duality evidence: Single photons and electrons both produce interference patterns in double-slit experiments, confirming wave behavior even for individual particles.
Quantization in bound systems: Particles confined to a region (like electrons in atoms) can only have discrete energy and momentum values, not a continuous range.

If a photon has frequency 6.0 x 10^14 Hz, its energy is E = hf = (6.626 x 10^-34)(6.0 x 10^14) = 3.98 x 10^-19 J. An electron with momentum 9.1 x 10^-25 kg·m/s has de Broglie wavelength lambda = h/p = 7.3 x 10^-10 m.

Property	Wave model of light	Photon (particle) model of light
Explains interference and diffraction	Yes	No (single photon)
Explains photoelectric effect threshold	No	Yes
Carries momentum	Indirectly (radiation pressure)	Yes, p = h/lambda
Energy depends on	Amplitude (intensity)	Frequency only

15.2

Bohr model and atomic structure

The Bohr model pictures electrons in circular orbits around a small, positively charged nucleus made of protons and neutrons. Only orbits where the circumference fits a whole number of de Broglie wavelengths are allowed (2 pi r = n lambda), which quantizes angular momentum and energy. For hydrogen, the energy of level n is E_n = -13.6 eV / n^2. The model correctly predicts hydrogen's spectral lines but does not generalize to multi-electron atoms.

Nuclear notation: An element is written as A over Z X, where Z is the proton number (atomic number) and A is the mass number (protons + neutrons).
Isotopes and ions: Isotopes have the same Z but different neutron counts. Ions have a nonzero net charge due to electron gain or loss.
Hydrogen energy levels: E_n = -13.6 eV / n^2. Ground state is n = 1 (E = -13.6 eV). Ionization requires 13.6 eV from the ground state.
Coulomb force in orbits: The electrostatic attraction between the electron and nucleus provides the centripetal force: k e^2 / r^2 = m v^2 / r.
Standing wave condition: 2 pi r = n lambda = n h/p. This forces only discrete radii and energies to be allowed.

For hydrogen in the n = 3 state, E_3 = -13.6 / 9 = -1.51 eV. The atom is in an excited state and can emit photons by dropping to n = 2 or n = 1.

Quantity	n = 1 (ground)	n = 2	n = 3
Energy (eV)	-13.6	-3.4	-1.51
Orbit radius	Smallest (a0)	4a0	9a0
Ionization energy needed (eV)	13.6	3.4	1.51

15.3

Emission and absorption spectra

An atom emits a photon when an electron drops from a higher to a lower energy level; it absorbs a photon when an electron jumps up. The photon's energy must exactly match the energy difference between the two levels: E_photon = hf = delta E. Because energy levels are discrete, each element produces a unique set of spectral lines that can be used to identify it. Emission spectra show bright lines on a dark background; absorption spectra show dark lines on a continuous background.

Photon emission: Electron drops from n_i to n_f (n_f < n_i). Photon energy = E_i - E_f = hf.
Photon absorption: Electron jumps from n_f to n_i (n_i > n_f). Photon must have exactly the right frequency; other frequencies pass through.
Energy level diagram: Horizontal lines represent allowed energies. Downward arrows are emission; upward arrows are absorption. The ionization threshold is E = 0.
Spectral line uniqueness: Each element has a unique set of allowed transitions, producing a fingerprint spectrum used in spectroscopy.
Connecting energy to wavelength: E = hf = hc/lambda. A larger energy gap produces a shorter wavelength (higher frequency) photon.

A hydrogen electron drops from n = 3 to n = 2. Delta E = -1.51 - (-3.4) = 1.89 eV. The emitted photon has f = 1.89 eV / h = 4.57 x 10^14 Hz, which falls in the visible red (Balmer series).

Spectrum type	Appearance	Produced when	Example
Emission	Bright lines on dark background	Excited gas emits photons	Hydrogen discharge tube
Absorption	Dark lines on continuous background	Cool gas absorbs from white light	Fraunhofer lines in sunlight

15.4

Blackbody radiation

A blackbody absorbs all incident radiation and emits a continuous spectrum that depends only on its temperature. Classical physics predicted infinite intensity at short wavelengths (the ultraviolet catastrophe), but Planck resolved this by assuming light energy is quantized in units of hf. Two key equations describe blackbody behavior: Wien's displacement law gives the peak wavelength, and the Stefan-Boltzmann law gives total emitted power.

Wien's displacement law: lambda_max = b / T, where b = 2.898 x 10^-3 m·K. Higher temperature shifts the peak to shorter wavelengths.
Stefan-Boltzmann law: P = A sigma T^4, where sigma = 5.67 x 10^-8 W/(m^2·K^4). Total power emitted scales with the fourth power of absolute temperature.
Planck's quantization fix: Planck assumed oscillators emit energy only in multiples of hf, eliminating the ultraviolet catastrophe and matching observed spectra.
Continuous spectrum: Blackbody radiation spans all wavelengths, unlike atomic line spectra. The shape of the curve shifts and grows with temperature.
Temperature must be in Kelvin: Both Wien's law and the Stefan-Boltzmann law require absolute temperature. Convert Celsius to Kelvin before calculating.

The Sun's surface is about 5800 K. Wien's law gives lambda_max = 2.898 x 10^-3 / 5800 = 500 nm, which is green light, consistent with the Sun's peak visible output.

Law	Equation	What it predicts
Wien's displacement law	lambda_max = b/T	Wavelength of peak emission
Stefan-Boltzmann law	P = A sigma T^4	Total power radiated by surface

15.5

The photoelectric effect

When light of sufficient frequency strikes a metal surface, electrons are ejected. The key result is that the maximum kinetic energy of ejected electrons depends on the frequency of light, not its intensity. Increasing intensity increases the number of ejected electrons (current) but not their energy. This behavior is only explained by treating light as photons, each carrying energy hf.

Photoelectric equation: K_max = hf - phi, where phi is the work function (minimum energy to eject an electron) and hf is the photon energy.
Threshold frequency: f_0 = phi / h. Below this frequency, no electrons are ejected regardless of intensity.
Work function: phi is the minimum energy needed to free an electron from the metal surface. It is a material property, measured in eV.
Stopping potential: The reverse voltage V_stop needed to halt the fastest ejected electrons: e V_stop = K_max.
Intensity vs. frequency: Intensity controls how many photons arrive per second (current), not the energy per photon. Only frequency determines K_max.

Light of frequency 8.0 x 10^14 Hz hits a metal with work function 2.0 eV. K_max = hf - phi = (6.626 x 10^-34)(8.0 x 10^14) / (1.6 x 10^-19) - 2.0 = 3.31 - 2.0 = 1.31 eV.

Variable changed	Effect on K_max	Effect on photoelectric current
Increase frequency (above f_0)	Increases linearly	No direct effect
Increase intensity	No effect	Increases (more photons)
Change metal (higher phi)	Decreases	May stop emission if hf < phi

15.6

Compton scattering

In Compton scattering, a photon collides with a free electron and transfers some of its energy and momentum to the electron. The scattered photon emerges with a longer wavelength (lower energy) than the incoming photon. The wavelength shift depends only on the scattering angle theta, not on the photon's initial wavelength. This result is explained by treating the photon as a particle with momentum p = h/lambda and applying conservation of energy and momentum.

Compton shift equation: Delta lambda = (h / m_e c)(1 - cos theta), where m_e c = 9.11 x 10^-31 kg and c = 3.00 x 10^8 m/s. The factor h/(m_e c) = 2.43 x 10^-12 m is the Compton wavelength.
Scattering angle dependence: At theta = 0 (forward scatter), Delta lambda = 0. At theta = 180 degrees (backscatter), Delta lambda is maximum = 2h/(m_e c).
Photon momentum: p = h/lambda = E/c. Photons carry momentum even though they are massless, which is why they can transfer momentum to electrons.
Conservation laws applied: Both energy and momentum are conserved in the photon-electron collision, treated as a particle-particle interaction.
Evidence for photon particle nature: Classical wave theory predicts no wavelength shift in scattering. The observed shift confirms photons behave as particles with definite momentum.

A photon scatters at theta = 90 degrees. Delta lambda = (h / m_e c)(1 - cos 90) = (2.43 x 10^-12)(1 - 0) = 2.43 x 10^-12 m = 2.43 pm. The scattered photon has a longer wavelength and lower energy.

Scattering angle theta	cos theta	Delta lambda
0 degrees (forward)	1	0
90 degrees	0	h/(m_e c) = 2.43 pm
180 degrees (backscatter)	-1	2h/(m_e c) = 4.86 pm

15.7

Fission, fusion, and radioactive decay kinetics

Nuclear reactions are governed by the strong force, conservation of nucleon number, conservation of charge, conservation of momentum, and mass-energy equivalence. Fusion combines light nuclei into a heavier one, releasing energy because the product is more tightly bound. Fission splits a heavy nucleus into smaller fragments, also releasing energy. Radioactive decay is the spontaneous transformation of an unstable nucleus, and the number of remaining nuclei decreases exponentially over time.

Mass-energy equivalence: E = mc^2. Mass defect (the difference between reactant and product masses) converts to released energy in nuclear reactions.
Conservation of nucleon number: The total number of protons plus neutrons is the same before and after any nuclear reaction. Use this to balance nuclear equations.
Fusion vs. fission: Fusion: small nuclei combine (e.g., deuterium + tritium to helium-4 + neutron). Fission: heavy nucleus splits (e.g., U-235 + neutron to two mid-mass fragments + neutrons). Both release energy.
Exponential decay law: N = N_0 e^(-lambda t), where lambda is the decay constant and t is time. The number of nuclei decreases by half every half-life t_{1/2}.
Half-life and decay constant: t_{1/2} = ln(2) / lambda = 0.693 / lambda. After n half-lives, N = N_0 / 2^n.

A sample starts with 8.0 x 10^12 nuclei and has a half-life of 10 years. After 30 years (3 half-lives), N = 8.0 x 10^12 / 2^3 = 1.0 x 10^12 nuclei remain.

Process	What happens	Energy released because
Fusion	Two light nuclei combine	Product nucleus is more tightly bound per nucleon
Fission	Heavy nucleus splits	Fragments are more tightly bound per nucleon than parent
Radioactive decay	Unstable nucleus emits particle or photon	Daughter nucleus is at lower energy state

15.8

Types of radioactive decay

Four decay modes are tested in AP Physics 2. In every case, nucleon number, charge, and lepton number are conserved. Writing and balancing nuclear decay equations requires tracking mass number A and atomic number Z on both sides. Gamma decay does not change A or Z; it only releases energy from a nuclear excited state.

Alpha decay: Nucleus emits an alpha particle (He-4, 2 protons + 2 neutrons). A decreases by 4, Z decreases by 2. Example: U-238 to Th-234 + alpha.
Beta-minus decay: A neutron converts to a proton; the nucleus emits an electron (beta minus) and an antineutrino. A unchanged, Z increases by 1.
Beta-plus decay: A proton converts to a neutron; the nucleus emits a positron (beta plus) and a neutrino. A unchanged, Z decreases by 1.
Gamma decay: An excited nucleus releases energy as a high-energy photon (gamma ray). A and Z are unchanged. Often follows alpha or beta decay.
Lepton number conservation: In beta decays, a neutrino or antineutrino is emitted to conserve lepton number. Beta-minus emits antineutrino; beta-plus emits neutrino.

Carbon-14 undergoes beta-minus decay: C-14 (Z=6) to N-14 (Z=7) + electron + antineutrino. Check: A = 14 = 14, charge = 6 = 7 + (-1), lepton number conserved by antineutrino.

Decay type	Particle emitted	Change in A	Change in Z
Alpha	He-4 nucleus	-4	-2
Beta-minus	Electron + antineutrino	0	+1
Beta-plus	Positron + neutrino	0	-1
Gamma	Photon only	0	0

Key terms

Term	Definition
Photon energy	The energy carried by a single photon, equal to hf, where h is Planck's constant and f is the photon's frequency. Used in photoelectric effect, spectra, and Compton scattering calculations.
quantization	The property that energy and momentum take only discrete values for bound systems. Explains why atomic spectra show lines rather than a continuous range of frequencies.
ground state	The lowest allowed energy state of an atom (n = 1 for hydrogen, E = -13.6 eV). An electron in the ground state requires the most energy to be ionized.
excited state	Any allowed energy state above the ground state. An electron in an excited state can spontaneously emit a photon and drop to a lower level.
threshold frequency	The minimum photon frequency needed to eject an electron from a metal surface via the photoelectric effect. Below this frequency, no electrons are emitted regardless of light intensity.
Maximum kinetic energy	The kinetic energy of the fastest electrons ejected in the photoelectric effect, given by K_max = hf - phi. Increases linearly with photon frequency above the threshold.
photon momentum	The momentum carried by a photon: p = h/lambda = E/c. Photons transfer momentum to electrons in Compton scattering, explaining the observed wavelength shift.
Wien's law	lambda_max = b/T, where b = 2.898 x 10^-3 m·K. Gives the peak wavelength of a blackbody spectrum; higher temperature shifts the peak to shorter wavelengths.
Stefan-Boltzmann law	P = A sigma T^4. The total power radiated by a blackbody surface scales with the fourth power of absolute temperature. Temperature must be in Kelvin.
continuous spectrum	A spectrum with intensity distributed across all wavelengths, as emitted by a blackbody. Contrasts with the discrete line spectrum produced by atomic transitions.
nucleon	A proton or neutron in the nucleus. Nucleon number (mass number A) is conserved in all nuclear reactions and decay processes.
lepton number	A conserved quantity in nuclear decays. Beta-minus decay produces an antineutrino; beta-plus decay produces a neutrino, each to keep lepton number balanced.

How to review unit 15

Topics students miss most

Miss rates come from Fiveable multiple-choice practice.

15.6

Compton Scattering

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15.7

Fission, Fusion, and Nuclear Decay

46%120 tries

15.5

The Photoelectric Effect

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Common unit 15 mistakes

Confusing intensity and frequency in the photoelectric effect

Increasing light intensity increases the number of ejected electrons (current) but does not change K_max. Only increasing frequency above the threshold raises K_max. A common error is predicting that brighter light ejects faster electrons.

Using Celsius instead of Kelvin in blackbody equations

Both Wien's law and the Stefan-Boltzmann law require absolute temperature in Kelvin. Plugging in a Celsius value gives a completely wrong answer. Always convert: T(K) = T(C) + 273.

Forgetting to conserve both A and Z in nuclear equations

Students often balance mass number A but forget to check atomic number Z, or vice versa. In every nuclear reaction and decay, both the total nucleon count and total charge must be equal on both sides.

Misidentifying which decay type changes A vs. Z

Alpha decay changes both A (by -4) and Z (by -2). Beta decays change only Z (by +1 or -1) while A stays the same. Gamma decay changes neither. Mixing these up leads to wrong daughter nuclei.

Applying the Compton shift formula to bound electrons

The Compton shift equation Delta lambda = (h/m_e c)(1 - cos theta) applies to photon collisions with free electrons. For tightly bound electrons, the photon scatters without a wavelength shift (Thomson scattering). Using the Compton formula in the wrong context is a frequent error.

How this unit shows up on the AP exam

Explaining phenomena qualitatively before calculating

AP Physics 2 free-response questions frequently ask you to explain why a phenomenon occurs before or instead of calculating a numerical answer. For Unit 15, this means being able to state why increasing light intensity does not increase K_max in the photoelectric effect, why the Compton shift depends on scattering angle, or why classical physics predicted the ultraviolet catastrophe. Practice writing one-to-two sentence explanations that name the physical principle (quantization, photon model, conservation of momentum) and connect it directly to the observation.

Balancing nuclear equations and applying conservation laws

Multiple-choice and free-response items in Unit 15 commonly require you to complete or verify a nuclear equation by conserving nucleon number and charge. You may be given a decay or reaction with one unknown particle and asked to identify it, or asked to explain which conservation law rules out a proposed reaction. Practice writing balanced equations for all four decay types and for fission and fusion reactions, checking both A and Z on each side.

Connecting graphs and diagrams to quantum concepts

Unit 15 exam questions often present an energy level diagram, a blackbody intensity-wavelength curve, or a photoelectric effect graph (K_max vs. frequency) and ask you to extract information or make predictions. For energy level diagrams, practice identifying the transition that produces a given photon wavelength. For blackbody curves, practice reading off peak wavelength and predicting how the curve shifts with temperature. For photoelectric graphs, practice finding work function from the x-intercept and Planck's constant from the slope.

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Topic study guides

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FRQ practice

Practice free-response reasoning and compare your answer with scoring guidance.

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Cram archive videos

Watch past review streams filtered to Unit 15 when you want a video walkthrough.

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Official unit cheatsheet

Open the Fiveable one-page unit review, then explore visual cheatsheets for a quick refresher.

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Score calculator

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Unit 15 printables

Print the unit cheatsheets ($3) or unit exams ($5) for Unit 15. Yours to keep, no subscription needed.

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Frequently Asked Questions

What's on the AP Physics 2 Unit 15 progress check (MCQ and FRQ)?

The AP Physics 2 Unit 15 progress check includes both MCQ and FRQ parts drawn from all 8 Modern Physics topics. The MCQ section tests conceptual understanding of the photoelectric effect, Compton scattering, blackbody radiation, atomic structure, and nuclear decay. The FRQ part asks you to apply quantum theory reasoning, interpret spectra, or work through nuclear processes quantitatively. Practice with matched questions at /ap-physics-2-revised/unit-15.

How do I practice AP Physics 2 Unit 15 FRQs?

The best way to practice AP Physics 2 Unit 15 FRQs is to focus on the topics that generate the most free-response questions: the photoelectric effect, emission and absorption spectra, and nuclear decay processes. FRQs in this unit typically ask you to explain phenomena using quantum theory, calculate photon energy or stopping voltage, or analyze nuclear equations. Practice by writing out full explanations, not just plugging numbers, since College Board awards points for reasoning. Find Unit 15 FRQ practice at /ap-physics-2-revised/unit-15.

Where can I find AP Physics 2 Unit 15 practice questions?

For AP Physics 2 Unit 15 practice questions, including multiple-choice and practice test sets, head to /ap-physics-2-revised/unit-15. There you'll find MCQ practice covering the photoelectric effect, Bohr model, Compton scattering, blackbody radiation, and nuclear decay, plus FRQ-style problems. Mixing MCQ and FRQ practice is the most effective way to prepare for the 12-15% of exam questions this unit represents.

How should I study AP Physics 2 Unit 15?

Start with the photoelectric effect and quantum theory since those concepts anchor everything else in Unit 15. Once you understand wave-particle duality and discrete energy levels, the Bohr model of atomic structure and emission spectra will click into place. From there, work through Compton scattering and blackbody radiation, then finish with fission, fusion, and radioactive decay. A few concrete steps that help: draw energy-level diagrams for the Bohr model, practice writing and balancing nuclear equations for decay types, and do timed MCQ sets to reinforce the conceptual reasoning College Board tests. Unit 15 is 12-15% of the exam, so it's worth steady, spaced review rather than a last-minute cram. Find study resources at /ap-physics-2-revised/unit-15.

Ready to review Unit 15?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

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