Atoms and Nuclei
Atoms and nuclei questions cover Bohr’s hydrogen model, spectral lines, nuclear composition, mass defect, binding energy and radioactive decay. Expect energy-level arithmetic and decay-law calculations.
Core rules and concepts
- Rutherford’s alpha-scattering experiment showed a small, dense, positively charged nucleus.
- Bohr postulates: electrons occupy stationary orbits without radiating; angular momentum is nh/2π; radiation occurs on transition between levels.
- Hydrogen energy levels: E_n = −13.6/n² eV. Transition energy = E_initial − E_final; photon wavelength follows E = hc/λ.
- Nucleus contains Z protons and A − Z neutrons. Mass defect Δm = [Z m_p + (A − Z)m_n − M_nucleus]; binding energy = Δm c².
- Radioactive decay: N = N0e^(−λt); half-life T½ = 0.693/λ. Alpha decay reduces A by 4 and Z by 2; beta-minus increases Z by 1.
Worked example
Find the photon energy and wavelength for the hydrogen transition n = 3 to n = 2. E3 = −13.6/9 = −1.51 eV; E2 = −13.6/4 = −3.40 eV. ΔE = 3.40 − 1.51 = 1.89 eV. λ = 1240/1.89 ≈ 656 nm, the red H-alpha line.
Traps
- Bohr’s formula applies to hydrogen-like one-electron species; use Z² for He⁺ etc.
- Energy levels are negative; a transition to a lower n releases a photon.
- Half-life is statistical; it is not the time for every nucleus to decay.
- Binding energy per nucleon peaks near iron-56; fusion powers light nuclei, fission powers heavy nuclei.
- Balance both A and Z in every nuclear equation.