Modern Physics: Relativity, Quantum Phenomena, and Atomic/Nuclear Structure
What this domain tests
The photoelectric effect and photon model, atomic energy levels and spectra, radioactivity and half-life, nuclear equations, mass–energy equivalence and qualitative relativity.
Core rules
- Photon energy E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J s.
- Photoelectric emission occurs only if f ≥ f₀; maximum KE = hf − work function. Intensity changes the number of emitted electrons, not their maximum energy.
- Line spectra arise when electrons fall between discrete energy levels: ΔE = hf.
- Alpha decay: A falls by 4, Z by 2. Beta-minus: Z rises by 1, A unchanged. Gamma: neither A nor Z changes.
- Half-life: after n half-lives the fraction remaining is (½)ⁿ.
- E = mc²; the mass defect appears as energy. Fission splits heavy nuclei; fusion joins light ones.
- Relativity: the speed of light is the same for all observers; moving clocks run slow and lengths contract.
Worked example
Light of wavelength 500 nm falls on a metal of work function 2.0 eV. Photon energy = hc/λ = (6.63 × 10⁻³⁴ × 3.0 × 10⁸)/(5.0 × 10⁻⁷) = 3.98 × 10⁻¹⁹ J ≈ 2.48 eV. Maximum KE = 2.48 − 2.0 = 0.48 eV (about 7.7 × 10⁻²⁰ J). Reasoning: the work function is the minimum escape energy, so the surplus becomes the electron's kinetic energy.
Traps that cost marks
- Believing brighter light produces faster photoelectrons.
- Writing nuclear equations that do not balance A and Z.
- Treating half-life as though half the original sample disappears permanently.
- Mixing joules and electronvolts without converting (1 eV = 1.6 × 10⁻¹⁹ J).
- Quoting a photon energy that depends on intensity rather than frequency.