Modern physics: photoelectric effect, atomic and nuclear models, quantum concepts
Modern physics
This domain tests the photoelectric effect, atomic energy levels and spectra, nuclear models, radioactive decay, binding energy and basic quantum ideas such as the de Broglie wavelength. Calculations often use electronvolts, so conversion discipline matters.
Core rules
- Photon: E=hf=hc/λ. A useful shortcut is E(eV)≈1240/λ(nm).
- Photoelectric effect: K_max=hf−φ, where φ is the work function. Stopping potential satisfies eV_s=K_max. Below the threshold frequency, no emission occurs regardless of intensity.
- Bohr atom: E_n=−13.6/n² eV for hydrogen. A photon is absorbed or emitted with energy equal to the level difference: hf=E_f−E_i.
- de Broglie: λ=h/p=h/(mv), showing wave–particle duality.
- Nuclear: binding energy is the mass defect times c²; binding energy per nucleon peaks near iron-56. Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1; gamma emission changes neither.
- Half-life: N=N0(1/2)^(t/T½); activity falls by the same factor.
Worked example
Light of wavelength 400 nm strikes a metal with work function 2.0 eV. The photon energy is 1240/400=3.1 eV. Thus K_max=3.1−2.0=1.1 eV, and the stopping potential is 1.1 V. The maximum speed follows from K_max=½mv², but only after converting to joules: 1.1×1.6×10⁻¹⁹=1.76×10⁻¹⁹ J. Increasing intensity increases the number of photoelectrons, not their maximum energy.
Traps
Using wavelength in metres in the 1240 shortcut; mixing eV and J; thinking brighter light gives faster photoelectrons; treating half-life as a linear decrease; forgetting that gamma emission does not change the element; using n=0 in the Bohr formula; confusing binding energy with total rest energy.