Question

The mass of an electron is 9.11×10−31 kg9.11×10−31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m3.31×10−10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00×108 m/s3.00×108 m/s. Express your answer numerically as a percent.

Answer 1

Answer:

The speed of electron is 0.73 % of the speed of light.

Explanation:

Given that,

Mass of the electron, $m=9.1\times 10^{-31}\ kg$

De- Broglie wavelength of the electron, $\lambda=3.31\times 10^{-10}\ m$

Speed of light, $c=3\times 10^8\ m/s$

The De Broglie wavelength of the electron is given by the formula as follows :

$\lambda=\dfrac{h}{mv}\\\\v=\dfrac{h}{m\lambda}\\\\v=\dfrac{6.63\times 10^{-34}}{9.11\times 10^{-31}\times 3.31\times 10^{-10}}\\\\v=2.19\times 10^6\ m/s$

The electron moving relative to the speed of light is calculated as :

$=\dfrac{v}{c}\times 100\\\\=\dfrac{2.19\times 10^6}{3\times 10^8}\times 100\\\\=0.73$

So, the speed of electron is 0.73 % of the speed of light. Hence, this is the required solution.