Atoms and Nuclei
What is examined
Atoms and Nuclei tests the Rutherford model, Bohr's postulates, hydrogen energy levels and spectra, nuclear size, mass defect and binding energy, radioactivity and its decay laws, and fission and fusion.
Core rules
- Bohr: electrons occupy stationary orbits with mvr = nh/2π; radiation occurs only on transitions, hν = E₂ − E₁.
- Hydrogen: r_n = 0.529 n²/Z Å; E_n = −13.6 Z²/n² eV; velocity v_n ∝ Z/n. Ground-state energy −13.6 eV; ionisation energy 13.6 eV.
- Series: Lyman (n → 1, UV), Balmer (n → 2, visible), Paschen (n → 3, IR). Hα (3 → 2) is 656 nm.
- de Broglie's standing-wave condition explains quantisation: 2πr = nλ.
- Nuclear radius R = R₀A^{1/3}, R₀ ≈ 1.2 fm; nuclear density is nearly constant.
- Mass defect Δm; binding energy BE = Δm × 931.5 MeV u⁻¹. BE per nucleon peaks near Fe-56, so fusion of light nuclei and fission of heavy nuclei release energy.
- Radioactive decay: N = N₀e^{−λt}; T½ = 0.693/λ; activity A = λN. Alpha emission: A − 4, Z − 2; beta-minus: Z + 1.
Worked example
Find the photon energy and wavelength for the transition n = 3 → n = 2 in hydrogen. E₃ = −13.6/9 = −1.51 eV; E₂ = −13.6/4 = −3.40 eV. ΔE = −1.51 − (−3.40) = 1.89 eV. λ = 1240/1.89 ≈ 656 nm. This is the red Hα line.
Traps
Forgetting that atomic energies are negative; using E = +13.6/n²; taking T½ = λ/0.693; and computing binding energy per nucleon without dividing by A.