Modern Physics
What this domain tests
The photoelectric effect, photon energy, atomic energy levels and spectra, wave–particle duality, nuclear binding energy, radioactive decay and half-life. Questions test whether you keep energies in the correct unit (J or eV) and whether you can write balanced nuclear equations.
Photons and the photoelectric effect
- Photon energy: E = hf = hc/λ.
- Einstein's equation: hf = φ + KEmax, where φ is the work function and KEmax = eVs (Vs is the stopping potential).
- Threshold frequency f₀ = φ/h; below it, ordinary single-photon emission does not occur in the specified weak-illumination model.
- Increasing intensity increases the number of photoelectrons per second, not their maximum kinetic energy.
- Ordinary photoemission does not exhibit the long energy-accumulation delay predicted by the elementary classical picture; this supports the photon description.
Energy levels and nuclear physics
- Spectral lines arise from hf = E₂ − E₁; line spectra are evidence for discrete levels.
- de Broglie wavelength: λ = h/p; for a nonrelativistic massive particle, p = mv.
- Mass defect Δm gives binding energy E = Δmc²; 1 u c² is approximately 931.5 MeV.
- α decay: A falls by 4, Z falls by 2. β⁻ decay: Z rises by 1, A unchanged. γ emission changes neither A nor Z.
- Decay law: N = N₀e^(−λt); half-life t½ = ln2/λ; activity A = λN.
Worked example
Light of wavelength 400 nm falls on sodium (work function 2.28 eV). Find the maximum kinetic energy of the emitted electrons.
Photon energy: E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸)/(4.00 × 10⁻⁷) = 4.97 × 10⁻¹⁹ J = 3.11 eV. KEmax = 3.11 − 2.28 = 0.83 eV (= 1.3 × 10⁻¹⁹ J). Since 0.83 eV > 0, emission occurs; the stopping potential is 0.83 V.
Traps that cost marks
- Claiming brighter light gives faster photoelectrons.
- Mixing eV and J in the same calculation - convert once, then stay consistent.
- Using the count of half-lives incorrectly (20 days with a 5-day half-life is four half-lives, not twenty).
- Changing the wrong number in a nuclear equation: mass number and proton number must both balance.
- Using p = mv outside its nonrelativistic regime, or confusing de Broglie momentum with the separate kinetic-energy expression mv²/2.
- Forgetting that γ emission accompanies α or β decay and does not change A or Z.