Atoms and Nuclei
Atoms and Nuclei covers Bohr's model, hydrogen spectral series, nuclear size and density, radioactivity, decay law, half-life, binding energy, fission and fusion. The exam favours short derivations and half-life calculations.
Core rules
- Bohr model: mvr = nh/2π; radius r_n ∝ n²; energy E_n = -13.6/n² eV for hydrogen. Transitions give hν = E₂ - E₁.
- Spectral series: Lyman (ultraviolet, n₁ = 1), Balmer (visible, n₁ = 2), Paschen, Brackett and Pfund in infrared.
- Nucleus: mass number A = Z + N; radius R ≈ R₀A^(1/3), so nuclear density is nearly constant. Mass defect Δm gives binding energy = Δm c².
- Radioactive decay N = N₀e^(-λt); half-life T½ = ln2/λ; activity A = λN. Alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1.
- Fission splits a heavy nucleus; fusion joins light nuclei. Both release energy because binding energy per nucleon increases toward iron.
Worked example
A sample contains 80 g of a radioisotope of half-life 5 years. After 15 years, three half-lives have passed. Remaining mass = 80(1/2)³ = 80/8 = 10 g. The decayed mass is 70 g, not 10 g.
Traps
Confusing atomic number with mass number; using t/T½ as a continuous exponent without checking; forgetting that beta decay changes the element; and treating binding energy per nucleon as maximum at uranium rather than near iron.