Atomic and Nuclear Physics: Atomic Structure, Radioactivity, Nuclear Reactions, Mass-Energy Equivalence
This domain concentrates on decay laws, mass defect and the binding-energy curve. Typical tasks ask for a decay constant from a logarithmic plot or for the energy released in a fusion or fission step.
Atomic structure
Rutherford scattering revealed a small, dense, positive nucleus; the shell model explains line spectra through discrete energy levels. The Franck-Hertz experiment and ionisation energies support quantised atomic energies.
Radioactivity
N(t) = N₀·e^(−λt); T½ = ln2/λ; activity A = λ·N in becquerel (1 Bq = 1 decay per second). Alpha decay: A − 4, Z − 2. Beta-minus: A unchanged, Z + 1 (a neutron becomes a proton, an electron and an antineutrino). Gamma: no change in A or Z, only de-excitation. Penetrating power increases from alpha to gamma; ionising power decreases in the same order.
Mass–energy equivalence
Δm = Z·m_p + N·m_n − m_nucleus; E = Δm·c²; 1 u = 1.6605×10⁻²⁷ kg corresponds to 931.5 MeV. Binding energy per nucleon peaks near Fe-56, so fission of heavy nuclei and fusion of light nuclei both release energy.
Worked example
A source with T½ = 8.0 d and A₀ = 400 kBq is measured after 20 d. Then 20/8.0 = 2.5 half-lives have elapsed: A = 400 kBq · 2^(−2.5) = 400 · 0.177 = 71 kBq. Equivalently λ = ln2/8.0 d = 0.0866 d⁻¹ and A = 400·e^(−0.0866·20) = 71 kBq. Note that the activity never reaches zero; it halves repeatedly.
Traps
- Rounding t/T½ to whole half-lives instead of using the exponent.
- Confusing activity with count rate: detector efficiency and background must be corrected.
- Forgetting that beta-minus decay leaves A unchanged.
- Mixing atomic and nuclear masses inconsistently in the mass defect.
- Reading a decay curve as linear - only ln A against t is a straight line with slope −λ.