Atoms and Nuclei
What this domain tests
Atoms and Nuclei tests Rutherford scattering, Bohr model, hydrogen spectra, nuclear size, mass defect, binding energy, radioactivity, decay law, fission and fusion. Expect energy-level and half-life calculations.
Core rules
- Bohr model: angular momentum mvr = nh/2π; radius r_n = n²r1; energy E_n = -13.6/n² eV for hydrogen. Transitions: hf = E_initial - E_final.
- Spectral series: Lyman to n=1 (ultraviolet), Balmer to n=2 (visible), Paschen to n=3 (infrared).
- Nuclear radius R ≈ R0 A^(1/3), R0 ≈ 1.2 fm. Mass defect Δm = Zm_p + (A-Z)m_n - M_nucleus.
- Binding energy = Δm c². 1 u = 931.5 MeV.
- Radioactive decay: N = N0 e^(-λt); half-life T½ = 0.693/λ. Activity A = λN.
Worked example
Find the energy of the photon emitted when hydrogen falls from n=3 to n=2. E3 = -13.6/9 = -1.51 eV; E2 = -13.6/4 = -3.40 eV. Photon energy = E3 - E2 = -1.51 - (-3.40) = 1.89 eV. This is the first Balmer line, in the visible region. The reasoning subtracts final minus initial with signs, then takes magnitude for the photon.
Traps
Do not use E = +13.6/n²; bound-state energies are negative. Do not confuse half-life with mean life. In decay, the number of nuclei decreases exponentially, not linearly. Binding energy per nucleon peaks near iron, so both fission of heavy nuclei and fusion of light nuclei can release energy.