Question

Photons of frequency ‘v’ have a momentum associated with it. If ‘c’ is the velocity of light the momentum is
A. v/c
B. hvc
C. \[hv/{{c}^{2}}\]
D. hv/c

Answer 1

Hint: Photons are very tiny particles that make up the wave of Electromagnetic waves. Their energy and momentum are dependent upon the wavelength and frequency of the electromagnetic wave that they form. The energy of the photon can be given in two ways, both of them are given below.
Formula Used:
E=hv
\[E=pc\]

Complete answer:
Photons are very tiny particles that make up the wave of Electromagnetic waves. They have a dual nature. Photons have no resting mass and they travel at the speed of light.
When they are travelling or are in wave motion, they have both energy and momentum. Their energy and momentum are dependent upon the wavelength and frequency of the electromagnetic wave that they form.
The energy of the photon is given by
E=hv
Here h is a constant called the Planck’s constant and v is the frequency of the wave.
We also know that the energy of a photon is momentum time the speed of light or
\[E=pc\]
Combing the two-equation we get
\[\begin{align}
  & hv=pc \\
 & \Rightarrow p=\dfrac{hv}{c} \\
\end{align}\]
So, the momentum of a photon is given by \[\dfrac{hv}{c}\]

Therefore, Option D is our answer.

Note:
Photons are also described as energy packets. This is because the energy a photon contains cannot be divided. If a body or atom is to absorb the energy of the photon, they have to absorb the whole energy contained in that photon. For instance, in photoelectric emission, the electron absorbs the whole photon and the excess energy is transferred to the electron as kinetic energy.