The mass of an electron is 9.11×10−31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m, how fast is the electron moving relative to the speed of light?

Answer 1

de Broglie's equation: λ = h/mv constants: h = 6.626 x 10^-34 J-s 1J = 1 kg-m²/s²

v = h/mλ = (6.626 x 10^-34 )J-s / [(9.11 x 10^-31) kg x 3.31 x 10^-10m] x 1.0 kg-m²/ 1.0 J = 2.20 x 10⁶ m/s

(2.20 x 10⁶) m/s / 3.0 x 10⁸ m/s = 0.0073 x 100 = 0.73 % the speed of light = 3.0 x 10⁸ m/s

The electron is moving 0.73 % less fast than the speed of light.