Atoms and Nuclei
Two linked chapters: Bohr's model of the hydrogen atom with its radii, energies and spectral series, and nuclear physics with size, binding energy, radioactivity and fission/fusion. The favourite long answers are Bohr's postulates with the derivation of E(n) = −13.6/n² eV, and the radioactive decay law with half-life. Short numericals on photon wavelength in a transition or on mass defect and binding energy are almost certain.
Core rules
- Bohr: electrons occupy orbits with angular momentum mvr = nh/2π; radiation is emitted only on a transition of energy hν = E₂ − E₁.
- Radius r(n) = 0.529 n²/Z Å; energy E(n) = −13.6 Z²/n² eV; for hydrogen, ionisation from the ground state needs 13.6 eV.
- Spectral series: Lyman (to n = 1, ultraviolet), Balmer (to n = 2, visible - Hα at 656 nm), Paschen and beyond in the infrared.
- Nuclear radius R = R₀A^(1/3) with R₀ ≈ 1.2 fm, so volume is proportional to mass number.
- Mass defect Δm converts to binding energy by 1 u = 931.5 MeV; binding energy per nucleon peaks near A ≈ 56 (iron).
- Decay law N = N₀e^(−λt); half-life T½ = 0.693/λ; activity A = λN.
Worked example
Find the wavelength of the photon emitted in the n = 3 to n = 2 transition of hydrogen. E₃ = −13.6/9 = −1.51 eV; E₂ = −13.6/4 = −3.40 eV. ΔE = 3.40 − 1.51 = 1.89 eV. λ = 1240/1.89 ≈ 656 nm - the red Hα line of the Balmer series, which is why it falls in the visible region while Lyman lines do not.
Traps that cost marks
- Using the energy expression without the Z² factor for hydrogen-like ions.
- Reporting a photon energy without its sign logic: ΔE is always positive, though the levels are negative.
- Forgetting to convert mass defect in u to MeV using 931.5.
- Assuming half-life changes with sample size; it does not.