Modern Physics: Photoelectric Effect, Atomic Models, Nuclear Physics, Relativity
Modern physics questions reward precision with units. The photoelectric effect is almost always examined quantitatively, atomic energy levels through photon wavelengths, and nuclear decay through half-life or mass defect. Relativity appears at the level of the two postulates and the time-dilation and length-contraction relations.
Photoelectric effect
Light arrives as photons of energy E = hf = hc/λ. Emission occurs only if hf exceeds the work function W; the maximum kinetic energy is K_max = hf − W, and the threshold frequency is f₀ = W/h. The stopping potential satisfies eV_s = K_max. Crucially, intensity controls the number of photons per second (the photocurrent), not the maximum kinetic energy - that depends only on frequency and the metal.
Atoms and nuclei
Atoms emit or absorb photons satisfying hf = E₂ − E₁ between discrete levels; line spectra are the fingerprint of those levels. De Broglie wavelength λ = h/p. Nuclei: binding energy comes from the mass defect, E = Δmc², with Δm in kilograms for joules. Radioactive decay is exponential, N = N₀(1/2)^(t/T), where T is the half-life; activity falls in the same proportion. Alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1.
Relativity basics
The speed of light is the same for all inertial observers, and physics laws have the same form in all inertial frames. Then t = γt₀ (moving clocks run slow) and L = L₀/γ (moving lengths contract along the motion), with γ = 1/√(1 − v²/c²). Rest energy is E₀ = mc²; total energy includes kinetic energy.
Worked example
Light of wavelength 400 nm falls on a metal of work function 2.2 eV. Find the maximum kinetic energy and the stopping potential. Using hc = 1240 eV·nm, the photon energy is 1240/400 = 3.1 eV. Then K_max = 3.1 − 2.2 = 0.90 eV. Since eV_s = K_max, the stopping potential is 0.90 V. No electrons are emitted if the wavelength exceeds hc/W = 1240/2.2 ≈ 564 nm.
Traps that cost marks
- Mixing electronvolts and joules inside one equation (1 eV = 1.6 × 10⁻¹⁹ J).
- Claiming brighter light gives faster photoelectrons.
- Treating half-life as a linear decrease, or forgetting that after n half-lives the fraction left is (1/2)ⁿ.
- Using the mass defect in atomic mass units when joules are required, without converting.
- Confusing proper time (measured in the rest frame of the event) with the dilated time.