Atoms and Nuclei
What the exam tests
Questions cover Rutherford scattering, Bohr model, hydrogen spectral series, radius and energy levels, nuclear composition, mass defect, binding energy, radioactivity, decay law, half-life, fission and fusion.
Core rules
- Bohr postulate: mvr = nh/(2π). For hydrogen-like atoms, r_n = 0.529 n^2/Z Å and E_n = −13.6 Z^2/n^2 eV.
- Spectral lines obey hν = E_upper − E_lower. The Balmer series ends on n = 2 and lies largely in the visible region.
- Nucleus contains protons and neutrons; A = Z + N. Isotopes have same Z, different N.
- Mass defect Δm = total mass of nucleons − nuclear mass. Binding energy BE = Δm c^2; BE per nucleon peaks near iron, explaining fission of heavy nuclei and fusion of light nuclei.
- Radioactive decay: N = N0e^(−λt); half-life T = ln2/λ; activity A = λN.
- Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1; gamma changes neither A nor Z.
Worked example
Find the wavelength of the photon emitted when hydrogen falls from n = 3 to n = 2. E3 = −13.6/9 = −1.51 eV and E2 = −13.6/4 = −3.40 eV. The energy difference is 1.89 eV. Using λ = 1240/E(eV) nm gives λ ≈ 656 nm, the red H-alpha line of the Balmer series.
Traps
Bohr energies are negative; the ground state is n = 1, not n = 0. Ionisation energy from the ground state is 13.6 eV. Half-life is a statistical concept; after two half-lives one quarter remains, not zero. Alpha and beta decays change the element; gamma does not. Binding energy per nucleon, not total binding energy, indicates stability.