Modern Physics
Modern Physics covers special relativity, quantization, atomic energy levels, and nuclear decay. Items usually pair one calculation with a conceptual claim about photons or reference frames.
Core rules
- Photon energy. E = hf = hc/λ, with hc ≈ 1240 eV·nm - a shortcut worth memorizing.
- Photoelectric effect. K_max = hf − φ. No emission occurs below f₀ = φ/h, no matter the intensity. Stopping potential V_s = K_max/e.
- de Broglie wavelength. λ = h/p.
- Bohr model. Eₙ = −13.6 eV/n² for hydrogen; an emitted or absorbed photon carries exactly the level difference.
- Relativity. γ = 1/√(1 − v²/c²); Δt = γΔt₀ and L = L₀/γ.
- Decay. N = N₀(1/2)^(t/T½); activity halves every half-life.
Worked example
Light of 400 nm strikes a metal whose work function is 2.0 eV. Photon energy = 1240/400 = 3.1 eV, so K_max = 3.1 − 2.0 = 1.1 eV and the stopping potential is 1.1 V. Doubling the intensity doubles the number of emitted electrons but leaves K_max at 1.1 eV, because each individual photon still delivers 3.1 eV.
Traps
- Believing brighter light produces faster photoelectrons.
- Mixing joules and electron-volts within one calculation.
- Confusing half-life with mean lifetime.
- Applying γ where v ≪ c and reporting a dilated time when the factor rounds to 1.000 - recognize the classical limit instead.