Atomic and Nuclear Physics
Atomic and Nuclear Physics covers Bohr's model, spectral series, nuclear size, binding energy, radioactivity, and fission and fusion. Expect a Bohr energy-level calculation and a half-life problem.
Core rules
- Bohr postulates: quantized orbits with mvr = nh/2π, and radiation only during transitions, hν = E₂ − E₁.
- Hydrogen levels E_n = −13.6/n² eV; radius r_n = 0.53 n²/Z Å; Lyman, Balmer and Paschen series end at n = 1, 2 and 3.
- Rydberg: 1/λ = R(1/n₁² − 1/n₂²), with R = 1.097×10⁷ m⁻¹.
- Nuclear radius R = R₀A^(1/3), R₀ ≈ 1.2 fm, so nuclear density is nearly the same for all nuclei.
- Mass defect Δm = (Z m_p + N m_n) − M; binding energy BE = Δm c²; 1 u = 931.5 MeV. BE per nucleon peaks near Fe-56, so fission of heavy nuclei and fusion of light nuclei both release energy.
- Decay: N = N₀e^(−λt); half-life T½ = 0.693/λ; mean life τ = 1/λ.
- α emission: A → A − 4, Z → Z − 2. β⁻ emission: Z → Z + 1, A unchanged. γ emission: no change in A or Z.
Worked example
A radioisotope has T½ = 20 min. What fraction remains after 60 min? 60/20 = 3 half-lives, so the fraction remaining is (1/2)³ = 1/8, that is 12.5%, and 87.5% has decayed. Always convert the elapsed time into a number of half-lives first.
Traps
Using T½ where the decay constant belongs; swapping the A and Z changes for α and β; forgetting to square c in Δm c²; and comparing stability by total binding energy rather than binding energy per nucleon.