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.

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 × 10^{8}
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.

**
**