Chapter-Wise Summary: Atoms & Nuclei

Section A: Rutherford's Nuclear Model

Geiger and Marsden's 1909–1911 experiment, directed by Rutherford, fired alpha particles at a thin gold foil and detected them using a zinc sulfide screen. Results: most alphas (>95%) passed undeflected; about 1 in 8000 deflected at large angles; very rarely (~1 in 20,000) bounced back nearly 180°. Conclusions: the atom is mostly empty space; a tiny dense positively charged nucleus (~10^{-15} m) exists; electrons orbit at ~10^{-10} m. The distance of closest approach formula d = 2k$Ze^{2}$/KE_α provides an upper limit on nuclear size. For a 5 MeV alpha on gold (Z=79), d ≈ 45.5 fm — far larger than the actual nuclear radius (≈7 fm for gold), so the alpha never reaches the nucleus.

Section B: Bohr's Atomic Model

Bohr's 1913 model applied quantum ideas to Rutherford's nuclear atom. Three postulates: stationary orbits without radiation; quantized angular momentum L = nℏ; photon emission/absorption during transitions E = hν. Results for hydrogen-like atoms: r_n = 0.529$n^{2}$/Z Å (radius), v_n = $2.18 \times 10^{6}$ Z/n m/s (velocity), E_n = −13.6$Z^{2}$/$n^{2}$ eV (energy). Energy relations: KE = −E (positive), PE = 2E (negative), total E = KE + PE. For H ground state: KE = +13.6 eV, PE = −27.2 eV, E = −13.6 eV. Limitations: valid only for one-electron systems; does not explain multi-electron atoms, fine structure, or Zeeman effect.

Section C: Hydrogen Spectrum

Spectral lines arise when electrons transition between levels. Rydberg formula: 1/λ = R(1/n_{1}^{2} − 1/n_{2}^{2}) for hydrogen. R = $1.097 \times 10^{7}$ $m^{-1}$. The five named series: Lyman (UV, n_{1}=1, first line 121.6 nm), Balmer (visible, n_{1}=2, H-α=656.3 nm red, H-β=486 nm blue-green, H-γ=434 nm violet), Paschen (IR, n_{1}=3, first line 1875 nm), Brackett (far IR, n_{1}=4), Pfund (far IR, n_{1}=5). Only the Balmer series is visible — the most NEET-tested fact. Number of spectral lines from level n: N = n(n−1)/2 (e.g., from n=5: N = 10 lines).

Section D: Nuclear Structure and Binding Energy

Nuclei contain Z protons and (A−Z) neutrons. Nuclear radius R = $R_{0}A$^(1/3) with $R_{0}$ = 1.2 fm implies constant nuclear density (~$2.3 \times 10^{17}$ kg/$m^{3}$, far greater than atomic matter). Mass defect $\Delta m$ = [Zm_p + (A−Z)m_n] − M (actual mass < constituent masses). Binding energy BE = $\Delta m$ × 931.5 MeV. BE/A peaks at Fe-56 (~8.75 MeV/nucleon). For lighter nuclei, fusion releases energy (increases BE/A); for heavier nuclei, fission releases energy (also increases BE/A towards Fe-56). Example: each U-235 fission releases ~200 MeV; D-T fusion releases 17.6 MeV.

Section E: Radioactive Decay

Unstable nuclei decay following N = $N_{0}$e^(−λt). Half-life t_{1}/{2} = 0.693/λ is the characteristic time constant. After n half-lives: N = $N_{0}$/2ⁿ. Mean life τ = 1/λ = 1.443 t{1}/{2} (> t{1}/{2}). Activity A = λN is measured in becquerel (SI) or curie. Three types: alpha decay (He-4 emitted: $\Delta A$ = −4, $\Delta Z$ = −2), beta-minus decay (n→p+$e^{-}$+ν̄: $\Delta A$ = 0, $\Delta Z$ = +1), gamma decay (photon emitted: $\Delta A$ = 0, $\Delta Z$ = 0). Applications: radiocarbon dating (^{14}C, t{1}/_{2}=5730 y), nuclear medicine, power generation.

NEET Weightage Distribution:

• Bohr model calculations: ~1 question/year
• Spectral series: ~1 question/year
• Radioactive decay (half-life): ~1 question/year
• Nuclear decay equations/binding energy: ~0–1 question/year