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. Energy conservation: K = (2Ze²/4πepsilon₀ d) . d = (2Ze²/4πepsilon₀ K) . K = 5.5 MeV = 5.5 × 1.6 × 10⁻¹³ = 8.8 × 10⁻¹³ J . d = (2 × 79 × (1.6 × 10⁻¹⁹)² × 9 × 10⁹/8.8 × 10⁻¹³) .