Modern Physics (the electron, the atom and the nucleus)
Modern Physics tests the electron, the atom and the nucleus: the photoelectric effect, atomic energy levels and spectra, de Broglie wavelength, radioactivity, half-life, nuclear equations and mass–energy equivalence.
Core rules
- A photon has energy E = hf = hc/λ. Einstein’s photoelectric equation is hf = W + KE_max, where W is the work function. The threshold frequency is f₀ = W/h.
- Intensity affects the number of emitted photoelectrons, not their maximum kinetic energy. Maximum kinetic energy depends on photon frequency.
- Atomic energy levels give line spectra: ΔE = hf. Absorption lines occur when electrons move to higher levels; emission lines occur on downward transitions.
- de Broglie wavelength: λ = h/p = h/mv.
- Alpha decay reduces mass number by 4 and atomic number by 2; beta-minus decay leaves mass number unchanged and increases atomic number by 1; gamma emission changes neither.
- Nuclear equations conserve mass number and charge. Half-life is the time for half the nuclei to decay. Mass–energy equivalence is E = mc².
Worked example
Light of wavelength 400 nm strikes a metal of work function 2.0 eV. Photon energy E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸)/(400 × 10⁻⁹) = 4.97 × 10⁻¹⁹ J. Converting: 4.97 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 3.11 eV. Then KE_max = 3.11 − 2.0 = 1.11 eV, about 1.8 × 10⁻¹⁹ J. Longer wavelength means lower photon energy; below the threshold, no emission occurs.
Traps
Convert nanometres to metres. Keep eV and joules separate. Do not say brighter light gives faster photoelectrons. Half-life is not linear. Check both mass number and atomic number in nuclear equations. Mass defect is converted to binding energy.