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

The electron moves less fast than light

Explanation:

The complete question is written below:

The mass of an electron is . If the de Broglie wavelength for an electron in a hydrogen atom is , how fast is the electron moving relative to the speed of light? The speed of light is .

The De Broglie wavelength equation is:

(1)

Where:  

is the de broglie wavelength for an electron

is the Planck constant

is the momentum of the electron

On the other hand, the momentum of the electron is given by:

(2)

Where:

is the mass of the electron

is the velocity of the electron

Substituting (2) in (1):

(3)

Isolating :

(4)

Finally:

This is the velocity of the electron

Calculating the ratio between the velocity of the electron and the velocity of a photon:

Therefore, the electron moves less fast than the photon (light).