Question

The dynamic mass of a photon having a wavelength of 10 nm is:

• A. $2.21\times {10}^{-35}kg$
• B. $2.21\times {10}^{-34}kg$
• C. $2.21\times {10}^{-33}kg$
• D. $2.21\times {10}^{-32}kg$

Answer 1

The correct option is B $2.21\times {10}^{-34}kg$

According to de-Broglie hypothesis,
$\lambda =\frac{h}{p}$
where,
$h$ = Planck's constant
$p$ = momentum of photon
So p = $\frac{h}{\lambda }$ = $\frac{6.626\times {10}^{-34}}{10\times {10}^{-9}}$ = $6.626\times {10}^{-26}$ $\frac{kg.m}{s}$
Since photon travels at the speed of light, $v=c$
Hence, p = mc
where, $c=3\times {10}^{8}m/s$
So, dynamic mass m = $\frac{6.626\times {10}^{-26}\frac{kg.m}{s}}{3\times {10}^{8}m/s}$
$\approx 2.21\times {10}^{-34}kg$