Compton scattering is when a high-energy photon (like an X-ray) collides with a free (or weakly bound) electron and behaves like a particle. Treat the photon and electron as a two-body collision and apply conservation of energy and momentum in two dimensions: the outgoing photon has lower energy (so lower frequency and longer wavelength) and the electron recoils. The Compton wavelength shift is Δλ = (h / m_e c)(1 − cos θ), where θ is the photon scattering angle, h is Planck’s constant, m_e the electron rest mass, and c the speed of light. Compton scattering provided direct evidence that light comes in quantized photons (E = hf) because only a particle-picture plus conservation laws predicts the observed wavelength shift. For AP Physics 2, be ready to do the 2-D conservation derivation and use Δλ to relate angle and wavelength change. Review the topic study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-15), and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Because a photon behaves like a particle with energy E = hf and momentum p = h/λ, Compton scattering is just an elastic collision between that photon and a (initially) free electron. Conservation of energy and conservation of momentum must both hold. To satisfy both, some of the photon’s energy must be transferred to the electron as kinetic energy, so the scattered photon ends up with less energy (lower f) and a longer wavelength. The amount lost depends on how much the photon’s direction changes—that’s the Compton shift Δλ = (h / mec)(1 − cos θ). Treating light as photons and applying 2-D momentum conservation is exactly the CED explanation (15.6.A.2.i). For a focused review, see the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of light as both a wave and a particle—sometimes the particle picture explains what you see better. In Compton scattering the photon behaves like a tiny billiard ball: it has energy E = hf and momentum p = h/λ, so when it collides with a (nearly) free electron you apply conservation of energy and momentum like any elastic collision. That collision transfers discrete energy to the electron, so the scattered photon has lower energy (longer wavelength). The quantitative result is the Compton shift Δλ = (h / m_e c)(1 − cos θ); the factor h / (m_e c) ≈ 2.43×10^−12 m is the Compton wavelength of the electron. Experiments (Compton scattering, the photoelectric effect) show photons deliver energy in packets, not continuously—that’s why the particle model is necessary. For AP exam work: you must be able to treat a photon as a particle, use E = hf and p = h/λ, and apply 2D conservation of momentum and energy to derive or use the Compton formula (CED 15.6.A). For extra review and practice see the topic study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-15), and 1000+ practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: they’re different ways photons interact with electrons. Photoelectric effect: a photon is completely absorbed by a bound (metal) electron. If hf > φ (work function), the electron is ejected with maximum KE = hf − φ. It shows a threshold frequency and that light transfers quantized energy (photoelectrons, kinetic-energy relation). This is what AP often tests qualitatively and with the Kmax = hf − φ equation. Compton scattering: a photon collides with a (effectively) free electron and is scattered—the photon is not destroyed but loses energy, so its wavelength increases. The wavelength shift depends on scattering angle: Δλ = (h / m_e c)(1 − cos θ). You use conservation of energy and momentum (particle picture) to analyze it. Compton provides particle-nature evidence for higher-energy photons (X-rays). On the exam you may be asked to compare, derive, or apply these relations. For a focused review, see the Compton study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the particle picture of the photon: E = hf and p = h/λ. In Compton scattering a photon (energy hf, momentum h/λ) hits a free electron at rest. Apply conservation of energy and conservation of momentum (vector form, so conserve x- and y-components). Step outline: 1. Energy: hf + mec^2 = hf' + γmec^2 (photon loses energy; electron gains relativistic kinetic energy). 2. Momentum (x, y): h/λ = (h/λ') cosθ + p_e,x and 0 = (h/λ') sinθ + p_e,y (take incoming photon along +x; θ is photon scattering angle). 3. Square and add the momentum components to eliminate the electron momentum, and combine with the energy equation. Use relations p_photon = h/λ and relativistic energy-momentum for the electron (E_e^2 = (p_ec)^2 + (mec^2)^2). 4. Algebra yields the Compton shift: Δλ = λ' − λ = (h / (mec))(1 − cosθ). On the AP exam you may be asked to derive or apply Δλ, or to set up the two conservation equations and solve for λ' or electron energy. For a clear review and practice, see the Compton scattering study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and more practice problems at Fiveable (https://library.fiveable.me/practice/ap-physics-2-revised).

Because the photon gives some of its energy and momentum to the (initially) free electron in the collision, the photon that comes out has less energy. Lower photon energy means lower frequency and, by E = hf (or E = hc/λ), a longer wavelength. You can show this quantitatively by treating the interaction as a two-body collision and applying conservation of energy and momentum; that derivation leads to the Compton shift formula Δλ = h/(m_e c) (1 − cos θ). The shift is zero if θ = 0° (no change in direction), and largest for backscatter (θ = 180°). This effect is direct evidence that light behaves as particles (photons) and is included in the AP CED under Topic 15.6 (use conservation of energy/momentum and λ = h/p). For a focused review and worked examples, see the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and try practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Theta (θ) in the Compton shift formula Δλ = (h / m_e c)(1 − cos θ) is the scattering angle of the photon—i.e., the angle between the photon’s outgoing direction and its original incoming direction after it collides with a (approximately) free electron. It comes from applying conservation of energy and momentum to the photon–electron collision (CED 15.6.A.1, 15.6.A.2.i). Key points to remember for the AP exam: - θ = 0° (photon keeps same direction) ⇒ cosθ = 1 ⇒ Δλ = 0 (no wavelength change). - θ = 180° (backscatter) ⇒ cosθ = −1 ⇒ Δλ = 2h / m_e c (maximum shift, the Compton wavelength × 2). - The magnitude of the wavelength change depends only on θ (and constants h, m_e, c), showing how direction change links to energy/momentum transfer (CED 15.6.A.3). For a quick review, check the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf). For more practice across Unit 15, see the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-15) and the large set of practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Compton scattering shows light comes in photons because the observed X-ray wavelength shift behaves exactly like an elastic particle collision: treat the incoming light as a photon with energy E = hf and momentum p = h/λ, apply conservation of energy and momentum for a photon + free electron collision, and you get the Compton shift Δλ = (h / (m_e c))(1 − cos θ). That angle-dependent increase in wavelength (and corresponding loss of photon energy transferred to the recoiling electron) can’t be explained by classical waves—it matches the particle (photon) model. AP relevance: you should be able to do the 2-D conservation derivation and use E = hf and λ = h/p (CED 15.6.A.1–A.3). For a quick review, check the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-15), and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised) to drill the derivation and sample questions.

The change in wavelength depends on scattering angle because Compton scattering is just a two-body collision where the photon gives some momentum to a (initially) free electron. Treat the photon as a particle (E = hf, p = h/λ) and apply conservation of energy and conservation of momentum in two dimensions. The algebra leads to the Compton shift formula Δλ = (h / m_e c)(1 − cos θ). Physically that 1 − cos θ term comes from how much the photon’s direction (and therefore its momentum component along the original direction) changes: if θ = 0° (forward scattering) cos θ = 1 so Δλ = 0 (no energy lost), while if θ = 180° (backscatter) cos θ = −1 and Δλ = 2h / m_e c (maximum shift). This is exactly what the CED expects: explain Compton scattering by treating photons as particles and using conservation laws (15.6.A and 15.6.A.2). For a clear step-by-step derivation, check the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

After the photon hits the (essentially) free electron in Compton scattering, the electron recoils—it gains kinetic energy and momentum. By conserving energy and momentum (usually treated in two dimensions on the AP exam), the photon loses some energy so its frequency decreases and its wavelength increases by Δλ = h/(m_e c) (1 − cos θ). The electron’s kinetic energy equals the photon’s initial energy minus the scattered photon’s energy, and its direction depends on the collision geometry (you can solve for its speed and angle with conservation equations). If the electron was loosely bound in an atom, it’s effectively treated as free for the CED treatment; stronger bindings require different processes. For a clear CED-aligned explanation and worked examples, see the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf). For extra practice, Fiveable has many AP Physics 2 problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the Compton shift formula: Δλ = (h / (m_e c)) (1 − cos θ). Steps to solve problems: 1. Identify knowns: initial photon wavelength λi (or energy/frequency), scattering angle θ, or final wavelength λf. Remember hf = E and λ = h/p if you need momentum/energy conversions (CED 15.6.A.2). 2. If given energies: convert to wavelength using λ = hc / E (or f = E/h then λ = c/f). 3. Plug into Δλ equation to get the change in wavelength. If you know λi, then λf = λi + Δλ. If asked for θ, solve 1 − cos θ = (Δλ)(m_e c / h). 4. Check limits: θ = 0 → Δλ = 0 (no change); θ = 180° → Δλ = 2h/(m_e c) (maximum shift). 5. Use conservation of energy and momentum only if problem asks for electron kinetic energy or scattering angles (CED 15.6.A.2.i). For AP-style practice, use the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and more practice problems at (https://library.fiveable.me/practice/ap-physics-2-revised).

Compton scattering matters because it gives clear, experimental proof that light behaves as particles (photons), not just waves. In Compton’s X-ray experiments a scattered photon loses energy and gains wavelength in a way you can only explain by treating the photon like a particle that collides with a (nearly) free electron. Applying conservation of energy and momentum (in two dimensions) leads to the Compton shift Δλ = h/(m_e c) (1 − cos θ), where h/(m_e c) ≈ 2.43×10^−12 m. That relationship directly supports E = hf and λ = h/p and shows quantized energy transfer—exactly the kind of evidence the AP CED asks you to understand (15.6.A.1–A.3). For quick review of the derivation and practice problems, see the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf). For broader unit review and lots of practice questions, check the Unit 15 page (https://library.fiveable.me/ap-physics-2-revised/unit-15) and Fiveable’s practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

In Compton scattering the photon’s energy, frequency, momentum, and wavelength all change because the photon transfers energy and momentum to a (nearly) free electron. Key relations you should know from the CED: E = hf and for a photon p = h/λ (so λ = h/p). After scattering the photon has lower energy (E decreases), lower frequency (f decreases), and a longer wavelength (λ increases). The wavelength change depends only on the scattering angle θ: Δλ = λ' − λ = (h / m_e c) (1 − cos θ), where the Compton wavelength h/(m_e c) ≈ 2.43×10^−12 m. You can convert wavelength change to energy change using E = hc/λ (so a larger λ means smaller E). This effect is derived by applying conservation of energy and momentum to the photon–electron collision and is direct evidence that light behaves like particles (photons). For a clear AP-aligned review and practice, see the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and the practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Short answer: Compton scattering can in principle occur with any photon, but it’s only measurable for high-energy photons like X-rays (and gamma rays). Why: The Compton shift formula Δλ = h/(mec) (1 − cos θ) gives an absolute wavelength change up to 2h/(mec) ≈ 4.9×10^−12 m. That shift is a large fraction of X-ray wavelengths (~10^−10 m) so you can detect it. For visible light (λ ~ 5×10^−7 m) that same Δλ is tiny and effectively unobservable, so you won’t see a Compton effect in ordinary optics. Compton scattering also requires the photon to collide with a (nearly) free electron so experiments typically use loosely bound or free electrons—another reason X-rays are used. On the AP: use conservation of energy and momentum and the CED Δλ expression to explain why Compton scattering was key evidence for light’s particle nature (see the Topic 15.6 study guide: https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf). For extra practice, check Fiveable’s AP Physics 2 practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Do the collision like any 2D particle problem: enforce conservation of energy and conservation of momentum in both x and y directions, then eliminate the electron’s unknowns to get the Compton result. Start assumptions: electron initially at rest, incoming photon energy E = hf and momentum p = hf/c. After scattering the photon has E' = hf' and angle θ (measured from original direction); electron has momentum pe and angle φ. Write the equations: - Energy: hf + mec^2 = hf' + γmec^2 (or equivalently hf = hf' + K_e) - Momentum x: (hf/c) = (hf'/c) cosθ + pe cosφ - Momentum y: 0 = (hf'/c) sinθ − pe sinφ Square and add the two momentum equations to eliminate φ and pe, substitute energy relation to eliminate pe (or use relativistic relation E_e^2 = (p_ec)^2 + (m_ec^2)^2). After algebra you get the Compton shift: Δλ = λ' − λ = (h / (m_e c)) (1 − cosθ). On the AP exam you should show the two-component momentum setup and the energy equation, then eliminate the electron’s variables to reach Δλ. For worked steps and practice problems, check the Topic 15.6 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-7/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) and hundreds of AP-style practice questions (https://library.fiveable.me/practice/ap-physics-2-revised).