Modern Physics

Name: AP Physics 2: Algebra-Based Unit 7: Modern Physics
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12–15% of the exam7 lessons · 96 min46 terms

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What this unit covers

The topics below follow the published Physics 2 course framework for Unit 7. This unit is worth 12–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Photoelectric effectAtomic modelsNuclear physicsWave-particle duality

Lessons in this unit

Formulas in Unit 7

Photon energy & the photoelectric equation

E = h · f · KE_max = h · f − φ

φ is the work function — the minimum energy to free an electron from the metal. Electrons are emitted only when hf ≥ φ; the excess energy becomes the electron’s maximum kinetic energy.

Photon energy from a transition

E_photon = E_high − E_low = h · f

The emitted or absorbed photon carries exactly the energy difference between the two levels. A larger energy gap means a higher-frequency (shorter-wavelength) photon.

Half-life & mass–energy

remaining fraction = (1/2)ⁿ, n = t / t₁/₂ · E = m · c²

The half-life t₁/₂ is the time for half of a sample to decay; after n half-lives, a fraction (1/2)ⁿ remains. E = mc² converts the mass lost in a reaction into released energy.

de Broglie wavelength & photon momentum

λ = h / p · p_photon = h / λ

h = 6.63 × 10⁻³⁴ J·s. Wavelength and momentum are inversely related: heavy, fast particles have vanishingly small wavelengths; light, slow particles have larger ones.

Photon relations

E = hf = hc/λ · p = E/c = h/λ · 1 eV = 1.60 × 10⁻¹⁹ J · hc ≈ 1240 eV·nm

The combination hc ≈ 1240 eV·nm is worth memorizing: photon energy in eV is just 1240 divided by the wavelength in nanometers.

Mass defect and binding energy

Δm = (Z·m_proton + N·m_neutron) − m_nucleus · E_binding = Δm·c² · in convenient units: 1 u = 931.5 MeV/c²

The conversion 1 u ↔ 931.5 MeV avoids ever handling c² explicitly, which is why nuclear physics is done in u and MeV.

The decay law

N = N₀ (½)^(t/T) · fraction remaining = (½)^(number of half-lives) · number of half-lives = t / T

For whole numbers of half-lives, halving repeatedly is faster and less error-prone than using the exponent.

Every term in Unit 7

All 46 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: K_max = hf − φ. Below the threshold frequency no electrons are emitted no matter how intense the light, which is evidence for photons of energy E = hf = hc/λ.
Photon energy: E = hf = hc/λ. Shorter wavelength means MORE energy per photon, which is why ultraviolet damages skin and radio waves do not however intense.
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 = h/mv. Everything has one; it is only measurable for very light particles, which is why electron diffraction works and cricket balls do not diffract.
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.
The 1240 eV·nm shortcut: E in eV = 1240 / λ in nm. Removes two unit conversions from every photon problem and is worth memorizing.
Why the electronvolt exists: Atomic energies in joules are awkward powers of ten. Visible photons are 2-3 eV, ionization around 10 eV, nuclear energies in MeV.
Photon momentum: p = E/c = h/λ, despite zero mass. p = mv is a low-speed approximation, not the definition of momentum.
Radiation pressure: Photon momentum is real and transferable — it pushes solar sails and perturbs spacecraft trajectories.
Photoelectric threshold: KE_max = hf − φ. Below the threshold frequency, NO electrons are emitted regardless of intensity.
Intensity versus frequency: More intensity means MORE electrons at the same maximum energy. Only higher frequency gives each electron more energy — the observation that defeated the wave model.
Energy level transitions: A photon is emitted or absorbed with energy exactly equal to the difference between two levels. This is why atomic spectra are discrete lines rather than continua.
Absorption versus emission spectra: Absorption shows dark lines where a cool gas removed photons; emission shows bright lines at the same wavelengths from a hot gas. Same levels, inverted appearance.
Mass defect: Δm = (sum of separated nucleon masses) − (nuclear mass). Subtract in that order; reversing it implies the nucleus falls apart spontaneously.
Binding energy conversion: 1 u = 931.5 MeV/c². Working in u and MeV avoids handling c² and removes most exponent errors.
Binding energy PER NUCLEON is the meaningful figure: Total binding energy grows just because bigger nuclei have more nucleons. Per nucleon it peaks near iron-56 at about 8.8 MeV.
Why fusion and fission both release energy: Both move nucleons toward the iron peak, from opposite sides. Fusing or splitting iron itself would ABSORB energy — which is why stellar cores stop there.
What is conserved in a nuclear equation: Mass number A and charge Z. Total MASS is not conserved — the difference is the released energy.
Alpha versus beta decay: Alpha: A falls by 4, Z by 2. Beta-minus: A unchanged, Z rises by 1, as a neutron becomes a proton.
Half-life removes a constant FRACTION: Not a constant amount. After n half-lives the fraction remaining is (½)ⁿ, which never reaches zero for finite n.
Counting halvings: Faster and safer than exponentials whenever the elapsed time is a whole multiple of the half-life, which on the exam it usually is.
Decay is random: Each nucleus has a fixed probability per unit time and no memory. The exponential law is statistical, emerging from vast numbers of independent events.
What half-life is immune to: Temperature, pressure and chemical combination. It is a nuclear property, which is what makes radiometric dating reliable.
Activity follows the same law: Becquerels are proportional to undecayed nuclei, so activity halves on the same schedule. Activity data and count data are interchangeable.
Why the photon model was needed: The threshold frequency and the independence of electron energy from intensity cannot be explained by continuous wave energy delivery. Both follow immediately from discrete packets.
Evidence for wave-particle duality: Electron diffraction shows particles behaving as waves; the photoelectric effect shows waves behaving as particles. Both are needed, neither alone suffices.
Why atomic spectra are discrete: Electrons occupy quantized energy levels, so an emitted or absorbed photon must carry exactly the difference between two of them.
Ionization energy: The energy to remove an electron entirely, taking it from its level to zero. Equal to the magnitude of that level energy.
Types of radiation, by penetration: Alpha is stopped by paper, beta by a few millimeters of aluminum, gamma needs dense shielding. Penetration is inversely related to ionizing power.
Fusion versus fission energy per nucleon: Fusion of light nuclei releases far more energy per nucleon, because the binding-energy curve rises steeply on the left and only gently declines on the right.

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).
Decide whether the question wants joules or electronvolts before computing, and state the unit at every step. Mixing the two is the dominant error in this unit, and it produces answers off by 19 orders of magnitude.
Work nuclear problems in atomic mass units and MeV using 1 u = 931.5 MeV. Converting to kilograms and joules is not wrong but it multiplies the opportunities for an exponent error.
Count halvings rather than reaching for the exponential whenever the elapsed time is a whole multiple of the half-life. It is faster, self-checking, and exam numbers are almost always chosen to make it work.

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.

194 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 2 study guideAll units, weights and score data in one place All 7 Physics 2 unitsThe full course

Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 7?

Unit 7, Modern Physics, is worth 12–15% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 7?

Modern Physics covers Photoelectric effect, Atomic models, Nuclear physics and Wave-particle duality. We publish 46 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 7?

Read the 7 lessons below first — about 95 minutes — then drill the 46 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.