Question

The dynamic mass of a photon of wavelength $\lambda$ is

• A. Zero
• B. $\frac{h}{c\lambda }$
• C. $\frac{h}{\lambda }$
• D. $\frac{hc}{\lambda }$

Answer 1

The correct option is B

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

Step 1: Given

The wavelength of the photon $=\lambda$

Step 2: Formula used

1. From de-Broglie equation $\lambda =\frac{h}{P}$, where $P$ is the momentum of the photon and $h$ is Planck's constant.
2. The momentum of the photon, $P=mc,where\left[c=Thespeedofthelight\right]$ and $m$ is the mass of the photon.

Step 3: Solution

Let the mass of the photon be $m$ and the momentum of the photon be $P$.

The momentum of the photon, $P=mc\left[c=Thespeedofthelight\right]$

From the de-Broglie equation

$$\begin{gathered} \lambda =\frac{h}{P}\left[\because h=Planck\text{'}scons\tan t\right] \\ \Rightarrow \lambda =\frac{h}{mc} \\ \Rightarrow m=\frac{h}{c\lambda } \end{gathered}$$

Hence, the correct option is $B$.