Question

If the momentum of a photon is p, then its frequency is
A. \[\dfrac{{ph}}{c}\]
B. \[\dfrac{{pc}}{h}\]
C. \[\dfrac{{mh}}{c}\]
D. \[\dfrac{{mc}}{h}\]

Answer 1

Hint:The rest mass of a photon is zero. The photon is a quantization of the energy of an electromagnetic wave. The momentum of a particle is the characteristic of motion. When an electromagnetic wave travels then it carries energy in the form of energy packets called photons.

Formula used:
\[p = \dfrac{h}{\lambda }\]
Here p is the momentum of a photon with wavelength \[\lambda \]and $h$ is called the Plank’s constant.
\[c = \nu \lambda \]
Here c is the speed of light, \[\nu \]is the frequency of the light and \[\lambda \]is the wavelength of the light.

Complete step by step solution:
The energy of the light (electromagnetic wave) comprises energy packets called photons. It can be absorbed by the atom or can be emitted. When an electron in an excited state moves to the ground state then it releases energy in the form of photons and when an electron absorbs energy in the form of photons then jumps to an excited state.

The wavelength of the wave is the horizontal distance of a full wave. It is given that the momentum of the given photon is \[\nu \]. Using the relation of the characteristics of the wave, i.e. the speed, frequency and wavelength,
\[\lambda = \dfrac{c}{\nu } \ldots \left( i \right)\]
From the relation of momentum,
\[p = \dfrac{h}{\lambda }\]

On replacing the wavelength from 1st equation, we get
\[p = \dfrac{h}{{\left( {\dfrac{c}{\nu }} \right)}}\]
\[\Rightarrow p = \dfrac{{h\nu }}{c}\]
\[\therefore \nu = \dfrac{{pc}}{h}\]
Hence, the frequency of the photon is \[\dfrac{{pc}}{h}\].

Therefore, the correct option is B.

Note: The momentum of the photon is the reason the light can exert force on the area of incidence. But the magnitude of the force exerted by the photon is insignificant. The Newtonian laws of motion have limited the motion where speed is very less compared to the speed of light. As the photon moves with a speed which is equal to the speed of light, so we can’t use the Newtonian laws of motion to calculate the momentum, otherwise, it will be zero because as per Newtonian laws of motion the momentum of the particle is the product of the mass and the velocity. As the rest mass of the photon is zero, it will be zero.