Atoms and Nuclei
Atoms and nuclei tests Rutherford scattering, Bohr model, hydrogen spectra, nuclear size, mass defect and binding energy, radioactivity, half-life, fission, and fusion. The exam expects energy-level arithmetic and conservation laws in nuclear reactions.
Core rules and concepts
- Bohr energy for hydrogen: E_n = -13.6/n^2 eV. Radius grows as n^2. Ionisation energy from ground state is 13.6 eV.
- Spectral lines obey h nu = E_upper - E_lower. The shortest wavelength in a series comes from the highest upper level.
- Nuclear radius R = R0 A^(1/3), with R0 about 1.2 fm. Density is roughly independent of mass number.
- Mass defect Delta m gives binding energy BE = Delta m c^2. Binding energy per nucleon peaks near iron, explaining fission of heavy nuclei and fusion of light nuclei.
- Radioactive decay N = N0 e^(-lambda t); half-life T1/2 = ln2/lambda. Activity A = lambda N.
- Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1; gamma emission changes neither A nor Z.
Worked example
For hydrogen transition n = 3 to n = 2, E3 = -13.6/9 = -1.51 eV and E2 = -13.6/4 = -3.40 eV. Energy difference is 1.89 eV. Wavelength is 1240/1.89, about 656 nm, the red H-alpha line.
Traps that cost marks
- Treating bound-state energies as positive.
- Using n = 1 to n = infinity incorrectly for ionisation.
- Forgetting that beta decay changes the element.
- Assuming half-life means half the sample disappears in every equal time regardless of amount; it is exponential.
- Confusing binding energy with total rest energy.