Atoms and Nuclei
Atoms and Nuclei runs from Rutherford's scattering to Bohr's model and spectral series, then to nuclear size, binding energy, radioactivity and fission or fusion.
Core rules
- Rutherford: most alpha particles pass almost undeflected while a few rebound, so the nucleus is tiny and positive.
- Bohr's postulates: stationary orbits with mvr = nh/2π; radius r(n) = 0.53 n²/Z Å; energy E(n) = −13.6 Z²/n² eV.
- Transitions obey hν = E₂ − E₁. Hydrogen series: Lyman (to n = 1, ultraviolet), Balmer (n = 2, visible), Paschen, Brackett, Pfund.
- Nuclear radius R = R₀A^(1/3) with R₀ ≈ 1.2 fm, so nuclear density is nearly constant.
- Mass defect Δm gives binding energy BE = Δm c²; BE per nucleon peaks near A = 56, which explains energy release in both fission and fusion.
- Decay law N = N₀e^(−λt); half-life T½ = 0.693/λ; activity A = λN.
Worked example
For the hydrogen transition n = 3 to n = 2: ΔE = 13.6(1/4 − 1/9) = 13.6 × 5/36 = 1.89 eV. The photon wavelength is λ = 1240/1.89 ≈ 656 nm, the red Hα line of the Balmer series.
Traps
Writing E(n) as positive; using n rather than n² for energy; quoting total binding energy instead of BE per nucleon when judging stability; confusing half-life with mean life τ = 1/λ.