Modern Physics

Eight topics on what happens when energy comes in lumps. Photons, whose energy is set by colour and never by brightness, the Bohr model and the standing-wave condition that makes its levels discrete, spectra read as differences between levels, blackbody radiation fixed by temperature alone, the photoelectric effect and its two independent knobs, Compton scattering as a two-body collision, and nuclear physics, where the books balance in nucleons and deliberately not in mass.

AP exam 12-15%8 topics

Topics

15.1

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

Types of Radioactive Decay

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Photon energy

E = hf = hc/λ. Set by FREQUENCY alone. Intensity counts photons per second, and never changes E

Matched unit pairs

h = 6.63 × 10⁻³⁴ J·s with λ in METRES → joules. hc = 1240 eV·nm with λ in NANOMETRES → eV. Never blend them

Size check

visible photons are a few eV. An answer far from that is a unit slip. 1 eV = 1.60 × 10⁻¹⁹ J

Wave-particle duality

ONE description; which behaviour appears depends on what the experiment measures. Nothing about the light switches

de Broglie wavelength

λ = h/p, for EVERY particle. INVERSE: faster means shorter, so a faster electron diffracts less

Bohr radius

r(n) = n² × 0.053 nm. Grows as n²

Hydrogen levels

E(n) = −13.6/n² eV. Magnitude falls as 1/n², so the levels CROWD toward 0 as n climbs

Reading the signs

−13.6 eV is the LOWEST level, not the highest. Deeper means more tightly bound

Standing-wave condition

nλ = 2πr closes the orbit on itself, which is where discrete levels come from

Transition photon

E(photon) = |E(final) − E(initial)|, a DIFFERENCE. Absorption goes UP, emission goes DOWN

Ionization

the jump to E = 0, so 13.6 eV from the ground state. Surplus energy becomes the freed electron's kinetic energy

Wien's law

λ(max) T = 2.90 × 10⁻³ m·K. INVERSE: hotter peaks BLUER

Stefan-Boltzmann

P = σeAT⁴, in KELVIN. Tripling T multiplies the power by 81

Blackbody spectrum

shape fixed by TEMPERATURE alone, not by the material. A good absorber is a good emitter

Photoelectric effect

K(max) = hf − φ. φ belongs to the METAL, f to the light. No intensity appears in it

Two independent knobs

FREQUENCY sets K(max) and the stopping voltage. INTENSITY sets how many electrons, the current

Stopping voltage plot

V(stop) against f: slope = h/e, vertical intercept = −φ/e, horizontal intercept = f₀ = φ/h

Compton scattering

a two-body COLLISION: incoming photon, scattered photon, recoiling electron. The photon does not vanish

Compton shift

Δλ = (h/m(e)c)(1 − cosθ), depending on the ANGLE only. Then λ' = λ + Δλ

Two separate books

nucleon number A and charge Z BALANCE. Mass does NOT: the defect leaves as energy

Mass-energy

E = Δmc². 1 u of defect ≈ 931 MeV

Stability

ranked by binding energy PER NUCLEON, peaking near iron at about 8.8 MeV. Total binding energy just grows with size

Why both work

moving TOWARD the iron peak from either side releases energy: fusion below it, fission above it

Half-life

each interval removes half of WHAT REMAINS: 1/2, 1/4, 1/8, never zero

Decay laws

N = N₀(½)^(t/t½) = N₀e^(−λt), with λ = 0.693/t½

What half-life depends on

the ISOTOPE alone. Not the amount, the temperature, the chemistry, or how long it has already sat

Alpha decay

A − 4, Z − 2. Emits a helium-4 nucleus

Beta-minus

A unchanged, Z + 1. A neutron becomes a proton: electron PLUS antineutrino

Beta-plus

A unchanged, Z − 1. A proton becomes a neutron: positron PLUS neutrino

Gamma decay

A and Z BOTH unchanged: the nucleus drops to a lower energy level. Same nuclide before and after

Balancing a decay

write every superscript and subscript, sum each row on each side, and let the arithmetic name the daughter

Why the neutrino is there

lepton number is conserved too, and it carries a share of the energy, which is why beta electrons come out with a SPREAD

Unit 15 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 8 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

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Check what stuck.

Units 9 through 15, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 42questions

46topics

168codes covered

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