Physics: Modern Physics

Modern Physics: what is tested

This domain covers quantum phenomena, atomic and nuclear physics, and relativity. The exam tests photon energy, the photoelectric effect, de Broglie wavelength, energy levels, radioactive decay, mass–energy equivalence, and relativistic time dilation.

Core rules

• Photon energy E = hf = hc/λ. A useful value is hc ≈ 1240 eV·nm. Intensity changes the number of photons, not the maximum kinetic energy.
• Photoelectric equation: K_max = hf − φ, where φ is the work function. Emission occurs only above the threshold frequency f₀ = φ/h; stopping potential satisfies eV_s = K_max.
• De Broglie wavelength: λ = h/p. For a non-relativistic electron, p = mv and K = p²/(2m).
• Hydrogen levels: E_n = −13.6/n² eV. A transition emits a photon of energy E_initial − E_final when the electron drops to a lower level.
• Radioactive decay: N = N₀(1/2)^(t/T₁/₂). Activity falls by the same factor per half-life; half-life is not a linear decay time.
• Mass defect: E = Δmc². Relativity gives time dilation t = γt₀ and length contraction L = L₀/γ, with γ = 1/√(1 − v²/c²).

Worked example

Light of wavelength 400 nm strikes a metal with work function 2.0 eV. The photon energy is E = 1240/400 = 3.1 eV. Therefore K_max = 3.1 − 2.0 = 1.1 eV, and the stopping potential is 1.1 V. The emitted electrons have a range of kinetic energies up to 1.1 eV; increasing the light intensity increases the photocurrent but does not raise K_max.

Traps that cost marks

Convert electronvolts to joules when using SI equations: 1 eV = 1.60 × 10⁻¹⁹ J. Do not use intensity to explain a changed stopping potential. For photon emission, subtract the lower final energy from the higher initial energy and take the magnitude. Half-life problems often require a fractional number of half-lives. Relativistic formulas are not needed at everyday speeds; γ is very close to 1 there.