Modern Physics
Modern Physics
This domain tests special relativity, quantization of light and energy levels, the photoelectric effect, matter waves, nuclear structure and decay, and conservation laws in nuclear reactions.
Core rules
- Relativity: the speed of light in vacuum is invariant. Moving clocks run slow and moving lengths contract along the motion direction. Relativistic energy E = γmc²; rest energy E₀ = mc².
- Photons: E = hf = hc/λ. The photoelectric effect occurs only when f exceeds the threshold f₀ = φ/h, where φ is the work function. Maximum kinetic energy K_max = hf − φ; intensity affects current, not K_max.
- Atomic levels: ΔE = hf for absorbed or emitted photons. Line spectra are fingerprints of element energy levels.
- Matter waves: λ = h/p = h/(mv). The uncertainty principle sets ΔxΔp ≥ ħ/2.
- Nuclear: conserve nucleon number and charge. Alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1; gamma emission changes neither. Activity halves each half-life: N = N₀(½)^(t/T).
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. Find the maximum kinetic energy of emitted electrons. Using E = 1240 eV·nm / λ, E = 1240/400 = 3.1 eV. Then K_max = 3.1 − 2.0 = 1.1 eV. The 400 nm photon exceeds the threshold, so emission occurs; increasing intensity would increase the number of electrons but not their maximum energy.
Traps
- Thinking brighter light gives faster photoelectrons; only frequency changes K_max.
- Using wavelength in meters with the 1240 eV·nm shortcut without matching units.
- Treating half-life as a linear decrease.
- Forgetting that gamma decay does not change element identity.
- Applying classical addition of velocities near c.