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.
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.
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.
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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.
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 |
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.
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 |
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.
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 |
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.
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 |
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.
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 |
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.
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 |
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.
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 |
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.
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 |
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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.
| 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.
Use this list to confirm you can handle every major skill in Unit 15 before the exam.
Calculate photon energy from frequency, photon frequency from wavelength, and de Broglie wavelength from a particle's momentum or kinetic energy.
Calculate energy levels with E_n = -13.6 eV / n^2, find ionization energy from any level, and identify ground state vs. excited states.
Identify emission and absorption transitions, calculate photon energy and wavelength for a given transition, and explain why each element has a unique spectrum.
Find peak wavelength from temperature and total radiated power from surface area and temperature. Always use Kelvin.
Use K_max = hf - phi to find maximum kinetic energy, threshold frequency, work function, or stopping potential given the other quantities.
Apply Delta lambda = (h/m_e c)(1 - cos theta) for a given scattering angle and explain why the scattered photon has lower energy and longer wavelength.
Write balanced equations for fission, fusion, and all four decay types. Use N = N_0 e^(-lambda t) and t_{1/2} = 0.693/lambda to find remaining nuclei or elapsed time.
Start with wave-particle duality and photon energy (E = hf, lambda = h/p). Then work through the Bohr model energy levels (E_n = -13.6 eV / n^2) and practice reading energy level diagrams to identify emission and absorption transitions. Use the topic guides for 15.1, 15.2, and 15.3 to check your understanding of each concept before moving on.
Work through blackbody radiation (Wien's law and Stefan-Boltzmann law), the photoelectric effect (K_max = hf - phi, threshold frequency, stopping potential), and Compton scattering (Delta lambda = (h/m_e c)(1 - cos theta)) in sequence. For each, practice explaining why classical physics fails and how the quantum model resolves the problem. Use available practice questions to test your equation fluency.
Practice balancing fission and fusion equations by conserving nucleon number and charge. Apply E = mc^2 to find energy released from mass defect. Then work decay kinetics problems using N = N_0 e^(-lambda t) and the half-life relation t_{1/2} = 0.693/lambda. The topic guide for 15.7 and FRQ practice are useful here.
Drill alpha, beta-minus, beta-plus, and gamma decay equations until you can write the daughter nucleus and emitted particles from memory. Check that A, Z, and lepton number are conserved in each. Use the topic guide for 15.8 and practice questions to test your ability to identify decay type from a given nuclear equation.
Review the key terms and the comparison tables across all topics. Work through mixed practice questions covering the full unit. Use the AP score calculator to estimate your estimated score range and identify which topic areas still need focused review.
Open the individual guides for Unit 15 when you want a closer review of one topic.
Use AP-style practice after you review the notes so you can check what you understand.
Practice free-response reasoning and compare your answer with scoring guidance.
Watch past review streams filtered to Unit 15 when you want a video walkthrough.
Open the Fiveable one-page unit review, then explore visual cheatsheets for a quick refresher.
Estimate your broader AP score goal after you review the course and exam format.
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get printablesAP 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.