Practice question

**De Broglie wavelength calculations** for electron moving at 2×10⁶ m/s λ= h/(m v)=6.63×10⁻³⁴/(9.11×10⁻³¹×2×10⁶)=3.64×10⁻¹⁰ m=0.364 nm, for mass 5×10⁻³⁰ kg v=2×10⁵ m/s λ=6.63×10⁻³⁴/(1×10⁻²⁴)=6.63×10⁻¹⁰ m, showing λ decreases with increasing m v. p = (h/λ) = (6.63 × 10⁻³⁴/0.5 × 10⁻⁹) = 1.326 × 10⁻²⁴ kg m/s . v = (p/m) = (1.326 × 10⁻²⁴/2.5 × 10⁻²⁹) = 5.304 × 10⁴ m/s . Applying E = h f = h c/λ, p = h/λ, K_max = h f - Φ, Φ = h f₀ = h c/λ₀, λ = h/√(2 m e V) and f_max = e V/h, result 5.304 × 10⁴ m/s follows, reflecting photoelectric and de Broglie relations.