Question

The momentum of the photon of frequency $\nu$ is
A. ${\displaystyle \frac{h\nu }{c}}$
B. $h\nu c$
C. ${\displaystyle \frac{h}{c\nu }}$
D. ${\displaystyle \frac{\nu }{ch}}$

Answer 1

Hint: A photon is defined as a quantum of electromagnetic radiations. A photon is the smallest particle and also the fundamental particle of electromagnetic radiations. A photon has no mass and it also does not have any electric charge. A photon is a stable particle. .

Formula used:
The formula of the energy of a photon is given by
$E=h\nu$
Here, $E$ is the energy of a photon, $h$ is the Planck’s constant and $\nu$ is the frequency of the photon.
The energy of a photon can also be calculated by the following formula
$E=pc$
Here, $p$ is the momentum of the particle and $c$ is the speed of light.

Complete step by step answer:
A photon is defined as the bundle of electromagnetic radiations. Photons are of dual nature. A photon is an elementary particle that has zero rest mass and it moves with the speed of light.
When photons are travelling or they are in a wave motion, they possess both the energy and the momentum. The energy and the momentum depends upon the wavelength and the frequency of the electromagnetic radiations.
The formula of the energy of a photon is given by
$E=h\nu$
Also, the energy of a photon is a product of momentum and the speed of a light, which is given by
$E=pc$
Now, equating both the equations of the energy, we get
$h\nu =pc$
$\Rightarrow p={\displaystyle \frac{h\nu }{c}}$
Hence, the momentum of the photon of frequency $\nu$ is ${\displaystyle \frac{h\nu }{c}}$ .

So, the correct answer is “Option A”.

Note:
Photons can also be described as an energy packet. This is because we cannot divide the energy of a photon. Now, if the body or an atom absorbs the energy of the photon, they must absorb the whole energy of the photon. Also, photons do no obey Pauli’s exclusive principle.