Question

Dynamic mass of the photon in usual notations is given by

• A. $\frac{h}{cv}$
• B. $\frac{hv}{c}$
• C. $\frac{h\lambda }{c}$
• D. $\frac{h}{c\lambda }$

Answer 1

The correct option is D

$\frac{h}{c\lambda }$

1. Photon is the quantum of electromagnetic radiation. That is photon is the smallest unit of EM radiation.
2. According to the dual nature theory of light, light possesses the characteristics of both a wave and particle
3. If the photon is assumed as a particle then by einsteins equation $E=m{c}^2$ where $E$ is the energy, $m$ is the dynamic mass, and $c$ is the speed of light.
4. If the Photon is assumed to have a wave-like behavior the equation for energy is given by $E=h\frac{c}{\lambda }$, where $E$ is the energy, $h$ is Planck's constant, $c$ is the speed of light, and is the wavelength.

Mathematical representation:

Equating both the formulae of energy, we get

$$\begin{gathered} m{c}^2=\frac{hc}{\lambda } \\ m=\frac{hc}{\lambda c^2} \\ m=\frac{h}{c\lambda } \end{gathered}$$

Thus, option D is correct.