Atoms and Nuclei
What this domain tests
Bohr radii and energy levels, spectral series, and nuclear physics: mass defect and binding energy, radioactive decay law, half-life and activity, fission and fusion.
Core rules
- Bohr model: angular momentum is nh/2π; r_n = 0.529 n²/Z Å; E_n = −13.6 Z²/n² eV; hydrogen ionisation energy is 13.6 eV.
- Transitions: hν = E_upper − E_lower; Rydberg 1/λ = R(1/n₁² − 1/n₂²), R = 1.097×10⁷ m⁻¹; Lyman series ends at n₁ = 1 (ultraviolet), Balmer at n₁ = 2 (visible).
- Mass defect Δm = [Z m_p + (A−Z)m_n] − M; binding energy = Δm × 931.5 MeV with Δm in atomic mass units.
- Decay: N = N₀e^(−λt); half-life t½ = 0.693/λ; activity A = λN in becquerel.
- Fission of heavy nuclei and fusion of light ones both release energy because binding energy per nucleon rises towards A ≈ 56.
Worked example
Find the photon wavelength for the n = 3 to n = 2 transition in hydrogen. E = 13.6(1/4 − 1/9) = 13.6(0.1389) = 1.89 eV. Then λ = 1240/1.89 ≈ 656 nm - the red H-alpha line. Subtract the smaller (n = 2) from the larger (n = 3) so the photon energy comes out positive.
Traps that cost marks
- Interchanging the two levels so the photon energy is negative.
- Confusing half-life with mean life τ = 1/λ.
- Reporting binding energy per nucleon when total binding energy is asked.
- Believing that after one half-life the whole sample has decayed.