Review AP Physics 2 Unit 15 to understand how quantum theory replaced classical physics at atomic and subatomic scales. This unit covers wave-particle duality, atomic spectra, blackbody radiation, the photoelectric effect, Compton scattering, and nuclear processes including fission, fusion, and radioactive decay.
Use the topic guides, practice questions, FRQ practice, and AP score calculator available for this unit to build and check your understanding before exam day.
Classical physics could not explain why heated objects glow the way they do, why atomic spectra show discrete lines instead of a continuous rainbow, or why shining dim high-frequency light ejects electrons while bright low-frequency light does not. Quantum theory was developed to answer exactly these questions.
Topics 15.1-15.3 establish the core quantum ideas: photons carry energy E = hf, matter has a de Broglie wavelength lambda = h/p, and electrons in atoms occupy only discrete energy levels. The Bohr model quantizes hydrogen's orbits, and transitions between levels produce the specific photon frequencies seen in emission and absorption spectra.
Topics 15.4-15.6 are the three phenomena that proved light must be quantized. Blackbody spectra follow Wien's law and the Stefan-Boltzmann law. The photoelectric effect shows that electron emission depends on frequency, not intensity, described by K_max = hf - phi. Compton scattering shows photons carry momentum p = h/lambda and lose energy in collisions with electrons.
Topics 15.7-15.8 cover the strong force, mass-energy equivalence, fission, fusion, and radioactive decay. Every nuclear reaction conserves nucleon number, charge, and momentum. Decay rates follow N = N0 e^(-lambda t), and the four decay types (alpha, beta-minus, beta-plus, gamma) each change the nucleus in predictable ways governed by conservation laws.
The central shift in Unit 15 is recognizing that energy and momentum are not continuous at atomic scales. Photons and electrons both exhibit wave and particle behavior depending on how they are observed. This quantization explains atomic spectra, the photoelectric effect, Compton scattering, and blackbody radiation in ways classical physics simply cannot. Nuclear physics extends this logic: mass itself is a form of energy, and unstable nuclei decay by strict conservation rules that determine which particles are emitted and how much energy is released.
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.
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.
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.
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.
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.
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.
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)).
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.
This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.
Across 1.1k multiple-choice practice attempts for this unit.
Practice activity included in this snapshot.
Across 4 scored free-response attempts for this unit.
Review Compton Scattering with attention to how the concept appears in AP-style source and evidence questions.
Review Fission, Fusion, and Nuclear Decay with attention to how the concept appears in AP-style source and evidence questions.
Review The Photoelectric Effect with attention to how the concept appears in AP-style source and evidence questions.
Review The Bohr Model of Atomic Structure with attention to how the concept appears in AP-style source and evidence questions.
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.
| 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 |
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.
| 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 |
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.
| 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 |
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.
| 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 |
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.
| 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 |
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.
| 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 |
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.
| 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 |
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.
| 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 |
Try stimulus-based AP practice questions and written prompts after you review the notes.
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.
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.
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 to . Indicate whether the photon is emitted or absorbed during the transition.
For hydrogen, the energy of level is given by .
Derive an expression for the wavelength of the photon associated with the to transition, in terms of fundamental constants. Then calculate 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 shines on a clean sodium surface in a vacuum photoelectric apparatus, as shown in Figure 4. The work function of sodium is . The stopping potential measured is . Use , , and .
Consistent
Not consistent
Justify your answer with a calculation using energy conservation for the photoelectric effect.
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 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 .
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 and light source 2 has wavelength .
A student claims that the stopping potential 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 as a function of the wavelength of the incident light for this metal. Express your answer in terms of , , 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 changes when decreases from to .
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 needed to reduce the photoelectric current to zero for different wavelengths. The work function of sodium is .
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 , (ii) the work function of the metal, and (iii) the maximum kinetic energy of the emitted electron as inferred from the stopping potential. During one trial, the incident light has wavelength and the stopping potential is measured to be .
Derive an expression for the stopping potential in terms of , , 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 and photon energy is .
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 and 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 -axis intercept in terms of fundamental constants and/or . The student repeats the experiment for several wavelengths and chooses to graph versus 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 with intensity .
Source 2: monochromatic light of wavelength with a lower intensity .
Assume the photocathode area illuminated is the same for both sources and the work function remains .
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.
| 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. |
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.
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.
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.
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.
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.
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.
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.
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.
Open the individual guides for Unit 15 when you want a closer review of one topic.
browse guidesUse AP-style practice after you review the notes so you can check what you understand.
start practicePractice free-response reasoning and compare your answer with scoring guidance.
practice FRQsUse unit cheatsheets for a quick visual review after you work through the notes.
open cheatsheetsEstimate your broader AP score goal after you review the course and exam format.
open calculatorAP Physics 2 Unit 15 covers 8 topics in Modern Physics: Quantum Theory and Wave-Particle Duality, the Bohr Model of Atomic Structure, Emission and Absorption Spectra, Blackbody Radiation, the Photoelectric Effect, Compton Scattering, Fission, Fusion, and Nuclear Decay, and Types of Radioactive Decay. Together these topics explain how quantum theory replaced classical physics at the atomic and subatomic scale. See all 8 topics at /ap-physics-2-revised/unit-15.
Unit 15: Modern Physics makes up 12-15% of the AP Physics 2 exam, making it one of the more heavily weighted units. It covers quantum theory, the photoelectric effect, atomic structure, nuclear decay, fission, and fusion. Expect several multiple-choice questions and potential FRQ components drawn from these topics on exam day.
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.
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.
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.
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.