Practice question

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. E₃ = -1.51 eV , E₂ = -3.4 eV . Δ E = 1.89 eV = 1.89 × 1.6 × 10⁻¹⁹ = 3.024 × 10⁻¹⁹ J . λ = (hc/Δ E) = (6.6 × 10⁻³⁴ × 3 × 10⁸/3.024 × 10⁻¹⁹) ≈ 6.56 ×