Atoms and Nuclei
What this domain tests
Atoms and Nuclei tests Rutherford scattering, Bohr's model, hydrogen spectra, nuclear size and density, mass defect and binding energy, radioactivity and decay laws.
Core rules
- Bohr: mvr = nh/2π; E_n = −13.6/n² eV for hydrogen; radius r_n ∝ n².
- Spectral lines: hν = E_n2 − E_n1; Lyman series ends at n = 1 (UV), Balmer at n = 2 (visible).
- Nuclear radius R = R0A^(1/3), R0 ≈ 1.2 fm; nuclear density is nearly constant.
- Mass defect Δm gives BE = Δm c²; binding energy per nucleon peaks near iron-56.
- Decay: N = N0e^(−λt); half-life T½ = 0.693/λ; activity A = λN.
- Alpha decay reduces A by 4 and Z by 2; beta-minus raises Z by 1.
Worked example
For the hydrogen transition n = 3 to n = 2: E = 13.6(1/2² − 1/3²) = 13.6(1/4 − 1/9) = 1.89 eV. The photon wavelength is λ = 1240/1.89 ≈ 656 nm, the red Hα line of the Balmer series.
Traps
- Reporting bound-state energies as positive; they are negative.
- Thinking half-life depends on sample size or temperature.
- Forgetting that gamma emission changes neither A nor Z.
- Mixing up the changes produced by alpha and beta decay.