Modern Physics

What this unit covers

The topics below follow the published Physics 2 course framework for Unit 7. This unit is worth 9–12% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Photons & the Photoelectric Effect13 min · 3 objectivesRelate a photon’s energy to the frequency of light · Explain the photoelectric effect and the role of the work function · Distinguish the effect of increasing light intensity from increasing frequency
• Atomic Models & Energy Levels13 min · 3 objectivesDescribe the Bohr model of quantized electron energy levels · Relate the energy of an emitted or absorbed photon to a transition between levels · Explain why atoms produce discrete line spectra
• The Nucleus & Radioactivity13 min · 3 objectivesDescribe the composition of the nucleus and the meaning of isotopes · Identify alpha, beta, and gamma decay and apply conservation of nucleons and charge · Use half-life to determine how much of a radioactive sample remains
• Wave–Particle Duality13 min · 3 objectivesExplain that light and matter each show both wave and particle behavior · Use the de Broglie relation to connect a particle’s wavelength and momentum · Calculate the momentum of a photon from its wavelength

Formulas in Unit 7

Every term in Unit 7

All 21 terms we publish for Modern Physics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Mass-energy equivalence

E = mc². The mass defect of a nucleus, converted by this relation, is its binding energy.

Photoelectric effect

Light ejects electrons only above a threshold frequency, regardless of intensity — evidence that light is quantized into photons.

Photon energy

E = hf = hc/λ with h = 6.63 × 10⁻³⁴ J·s. Energy depends on frequency alone, which is why intensity cannot compensate for low frequency.

Work function

The minimum energy to free an electron from a metal surface. Maximum kinetic energy of the ejected electron is KE = hf − φ.

Wave-particle duality

Light and matter both show wave and particle behavior depending on the experiment. Neither model alone is complete.

de Broglie wavelength

λ = h/p. Significant only for very small momenta, which is why electron diffraction is observable and a thrown ball's is not.

Energy level diagrams

Electrons occupy discrete levels; a photon is absorbed or emitted only when its energy exactly matches a level difference, producing line spectra.

Nuclear notation

In ᴬ𝖹X, A is mass number (protons plus neutrons) and Z is atomic number. Both are conserved in nuclear equations.

Alpha, beta and gamma decay

Alpha emits a helium nucleus reducing A by 4 and Z by 2; beta-minus converts a neutron to a proton raising Z by 1; gamma emits a photon changing neither.

Half-life

The time for half a sample to decay. After n half-lives, the fraction remaining is (1/2)ⁿ.

Binding energy per nucleon

Peaks near iron-56. Lighter nuclei release energy by fusing and heavier nuclei by fissioning, both moving toward that peak.

Fission vs fusion

Fission splits a heavy nucleus and powers reactors; fusion joins light nuclei, powers stars, and releases more energy per unit mass.

Why intensity does not eject electrons below threshold

Each electron absorbs one photon. If that photon's energy is below the work function, more photons per second simply means more failures.

Stopping potential

The reverse voltage that just prevents the most energetic photoelectrons from arriving; eV_stop = hf − φ.

Photoelectric graph

Plotting maximum kinetic energy against frequency gives a straight line of slope h and vertical intercept −φ.

Compton scattering

A photon scattering off an electron loses energy and lengthens in wavelength — direct evidence that photons carry momentum.

Electron diffraction

Electrons passed through a crystal produce an interference pattern, confirming matter waves and the de Broglie relation.

Emission vs absorption spectra

Emission shows bright lines where excited atoms release photons; absorption shows dark lines at the same wavelengths in a continuous background.

Conservation in nuclear reactions

Mass number, atomic number and charge each balance across the equation. Checking all three catches most errors.

Why binding energy peaks at iron

Below iron, adding nucleons increases the strong-force gain more than the electrostatic penalty; above it, proton repulsion dominates.

Radioactive decay is random

Half-life is a statistical property of a large sample; no individual nucleus has a predictable decay time.

What examiners penalize here

• Separate the two knobs: frequency controls each electron’s energy (KE_max = hf − φ), while intensity controls the *number* of electrons. Exam questions constantly test whether you know that brighter light does not make faster electrons.
• Line spectra are the fingerprint of quantization. Each element’s unique set of energy gaps gives it a unique pattern of spectral lines — the reason spectroscopy can identify the composition of distant stars.
• For half-life problems, first find n = t / t₁/₂, then the surviving fraction is (½)ⁿ. Watch that decay is exponential, not linear — after 2 half-lives one-quarter remains, not zero.
• Two duality relations to keep straight: for a photon E = hf and p = h/λ; for a matter particle λ = h/p. Both hinge on Planck’s constant — the bridge between the wave quantities (f, λ) and the particle quantities (E, p).

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 7 units of AP Physics 2: Algebra-Based

1. Unit 1 · Thermodynamics
2. Unit 2 · Electric Force, Field, and Potential
3. Unit 3 · Electric Circuits
4. Unit 4 · Magnetism and Electromagnetic Induction
5. Unit 5 · Geometric Optics
6. Unit 6 · Waves, Sound, and Physical Optics
7. Unit 7 · Modern Physics