Question

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? the speed of light is 3.00×108 m/s. express your answer numerically as a percent. view available hint(s)

Answer 1

Ans: The electron is moving at 0.732% relative to speed of light.

Explanation:
According to the de Broglie relationship:
$\lambda = \frac{h}{mv}$

So,
$v= \frac{h}{m\lambda}$
h = Planck's constant = 6.626 * 10^-34 Js
m = mass of electron = 9.11 * 10^-31 kg
λ = wavelength = 3.31 * 10^-10 m
$v= \frac{6.626 * 10^{-34}}{9.11 * 10^{-31}*3.31 * 10^{-10}}$

$v = 2.197 * 10^6$m/s

Since the electron is moving relative to the speed of light, therefore the ratio is(in %):

$\frac{v}{c} *100$% = $\frac{ 2.197 * 10^6}{3*10^8}*100$% = 0.732%