Atomic and nuclear physics: atomic structure, spectra, radioactive decay, nuclear reactions, mass-energy
What this domain tests
Atomic and nuclear physics covers atomic structure and spectra, radioactive decay, nuclear reactions and the mass–energy relation. Tasks range from reading a decay curve to calculating a Q-value and judging whether a proposed reactor or stellar reaction can run at all.
Atomic structure and spectra
- Rutherford scattering shows a small, massive, positive nucleus.
- Line spectra arise from transitions between discrete levels: h·f = E_m − E_n; absorption lines lie at the same wavelengths as the corresponding emission lines.
- Characteristic X-rays shift to higher energies for heavier nuclei.
Radioactive decay
- N(t) = N₀·e^(−λt); half-life T₁/₂ = ln2/λ.
- Activity A = λ·N, unit becquerel (1 Bq = 1 decay per second).
- α decay lowers Z by 2 and A by 4; β⁻ turns a neutron into a proton, an electron and an antineutrino; γ is a de-excitation and changes neither Z nor A.
- α radiation is strongly ionising with a short range; γ penetrates deeply.
Nuclear reactions and mass–energy
- Charge and nucleon number are conserved in every reaction.
- Mass defect: E = Δm·c², with 1 u = 1.66·10⁻²⁷ kg ≙ 931.5 MeV.
- Binding energy per nucleon peaks near iron-56, so fission of heavy nuclei and fusion of light ones both release energy.
Worked example
²²⁶Ra → ²²²Rn + ⁴He. Using atomic masses (226.02541 u, 222.01758 u, 4.00260 u): Δm = 226.02541 − (222.01758 + 4.00260) = 0.00523 u. Then Q = 0.00523 · 931.5 MeV/u ≈ 4.87 MeV. The energy appears as kinetic energy of the α particle and of the recoiling nucleus; momentum conservation gives the heavy nucleus only a tiny share.
Traps
- Confusing the decay constant λ with the half-life, or using t instead of ln2.
- Confusing activity in Bq with the number of nuclei present.
- Forgetting the antineutrino in β⁻ decay and the neutrino in β⁺ decay.
- Mixing nuclear and atomic masses - for α decay atomic masses are fine because the electron numbers cancel.
- Claiming mass disappears; it is converted into energy.