Practice question

**Hydrogen atom radius** r_n = n² a₀, a₀=5.3×10⁻¹¹ m first Bohr radius, r₂=4a₀=2.12×10⁻¹⁰ m, ratio r₄/r₂ =16/4=4, r₃=9a₀, circumference 2πr_n =2π n² a₀, for n=3 circumference=2π×9×5.3×10⁻¹¹=3×10⁻⁹ m. Orbital period T =2πr/v, v_n = v₁/n, v₁=2.2×10⁶ m/s, T₂=2πr₂/v₂, v₂=1.1×10⁶ m/s, T₂≈1.21×10⁻¹⁵ s. d = (2Ze²/4πepsilon₀ K) . K = 6.0 × 1.6 × 10⁻¹³ = 9.6 × 10⁻¹³ J . d = (2 × 79 × (1.6 × 10⁻¹⁹)² × 9 × 10⁹/9.6 × 10⁻¹³) . d = (3.641 × 10⁻²⁸/9.6 × 10⁻¹³) ≈ 3.79 × 10⁻¹⁴ m ≈ 38 fm . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R