Modern Physics: Atomic, Nuclear and Quantum Phenomena
Scope of the domain
This domain covers photons and the photoelectric effect, atomic energy levels and spectra, wave–particle duality, nuclear structure, radioactive decay and mass–energy. The exam asks you to calculate photon and de Broglie quantities, apply conservation laws to decay equations, and use half-life and E = Δmc².
Core rules
- Photon energy E = hf = hc/λ, with h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m/s.
- Photoelectric equation: hf = Φ + KEmax, where Φ is the work function. Threshold frequency f₀ = Φ/h. Light below f₀ produces no emission, whatever its intensity.
- Intensity controls the number of photons per second, so it changes the rate of emission but not the maximum kinetic energy.
- Stopping potential: eVₛ = KEmax. Convert between eV and J using 1 eV = 1.60 × 10⁻¹⁹ J.
- Line spectra arise from electrons moving between discrete energy levels: E₂ − E₁ = hf.
- de Broglie wavelength λ = h/p = h/(mv).
- Nuclear notation ᴬ_Z X: A = protons + neutrons, Z = protons. Isotopes have the same Z but different A.
- Alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1; beta-plus lowers Z by 1; gamma changes neither.
- Mass defect Δm releases energy E = Δmc². Half-life is the time for half the nuclei to decay: N = N₀(½)^(t/T).
Worked example
A sample of 80 mg has a half-life of 5.0 days. After 20 days, the number of half-lives is 20 ÷ 5.0 = 4. Remaining mass = 80 × (½)⁴ = 80 ÷ 16 = 5.0 mg. For a photon of wavelength 500 nm, E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) ÷ 5.00 × 10⁻⁷ = 3.98 × 10⁻¹⁹ J, which is 2.49 eV.
Traps that cost marks
- Mixing joules and electronvolts without converting.
- Treating radioactive decay as linear rather than halving repeatedly.
- Forgetting that beta-minus decay increases the atomic number but leaves A unchanged.
- Claiming brighter light gives faster photoelectrons; only higher frequency does.
- Using the photon energy formula with frequency in kHz or wavelength in nm without converting.
- Ignoring conservation of A and Z when completing a decay equation.