Question

The mass of a photon having wavelength 1 nm is:

• A. $2.21\times {10}^{-35}kg$
• B. $2.21\times {10}^{-33}g$
• C. $2.21\times {10}^{-33}kg$
• D. $2.21\times {10}^{-26}kg$

Answer 1

The correct option is C $2.21\times {10}^{-33}kg$

According to de-Broglie hypothesis,
$\lambda =\frac{h}{mv}$
where,
$h$ = Planck's constant
$m$ = mass of particle
$v$ = velocity of particle

Since photon travels at the speed of light, $v=c$
Hence the formula becomes $\lambda =\frac{h}{mc}$
where, $h=6.626\times {10}^{-34}Js$
$c=3\times {10}^{8}m/s$
Substituting the values, we get
$m=\frac{h}{c\lambda }=\frac{6.626\times {10}^{-34}}{3\times {10}^8\times {10}^{-9}}$
$\approx 2.21\times {10}^{-33}kg$