Question

An electron and a photon each have a wavelength of 1.00 nm. Find

(a) their momenta,

(b) the energy of the photon, and

(c) the kinetic energy of electron.

Answer 1

Wavelength of an electron

= 1 × 10⁻⁹ m

Planck’s constant, h = 6.63 × 10⁻³⁴ Js

(a) The momentum of an elementary particle is given by de Broglie relation:

It is clear that momentum depends only on the wavelength of the particle. Since the wavelengths of an electron and a photon are equal, both have an equal momentum.

(b) The energy of a photon is given by the relation:

Where,

Speed of light, c = 3 × 10⁸ m/s

Therefore, the energy of the photon is 1.243 keV.

(c) The kinetic energy (K) of an electron having momentum p,is given by the relation:

Where,

m = Mass of the electron = 9.1 × 10⁻³¹ kg

p = 6.63 × 10⁻²⁵ kg m s⁻¹

Hence, the kinetic energy of the electron is 1.51 eV.