Modern Physics
The Modern Physics domain covers photons, the photoelectric effect, atomic energy levels, wave–particle duality, nuclear decay, half-life, mass–energy equivalence, and basic relativity. Many questions are one-step calculations, so the main risk is unit confusion between joules and electron-volts.
Photons and the photoelectric effect
Photon energy: E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J·s and hc ≈ 1.24 × 10³ eV·nm. The photoelectric effect has a threshold frequency; below it, no electrons are emitted no matter how intense the light. Above it, K_max = hf − φ, where φ is the work function. Intensity changes the number of electrons, not their maximum kinetic energy.
Atomic spectra and duality
Atoms emit or absorb photons at discrete energies: hf = E_high − E_low. Line spectra are evidence for quantized energy levels. De Broglie wavelength: λ = h/p = h/(mv).
Nuclear physics
Alpha decay removes ⁴₂He: A decreases by 4 and Z by 2. Beta-minus decay converts a neutron to a proton: Z increases by 1, A unchanged. Gamma emission releases energy without changing A or Z. Half-life: N = N₀(1/2)^(t/T). Mass–energy: E = mc².
Relativity
The speed of light is the same for all inertial observers. Moving clocks run slow (time dilation), moving lengths contract along the motion direction, and mass and energy are equivalent.
Worked example
A sample with a half-life of 5.0 days starts at 80 g. How much remains after 15 days? 15 days ÷ 5.0 days = 3 half-lives. N = 80 × (1/2)³ = 80/8 = 10 g. Do not subtract half the original mass each time; halve the remaining mass.
Traps
- Mixing J and eV without converting (1 eV = 1.60 × 10⁻¹⁹ J).
- Using intensity to predict electron kinetic energy.
- Treating half-life as linear.
- Forgetting that beta decay changes the element.
- Using h = 6.63 × 10⁻³⁴ eV·s instead of J·s.