Question

What is the mass of a photon of sodium light with a wavelength of $5890\stackrel{\circ }{A}$?$(h=6.63\times {10}^{-27}ergs,c=3\times {10}^{10}cm/s)$

• A. $7.75\times {10}^{-31}g$
• B. $3.75\times {10}^{-33}g$
• C. $7.75\times {10}^{-33}g$
• D. $7.75\times {10}^{-33}kg$

Answer 1

The correct option is B $3.75\times {10}^{-33}g$

Given: $\text{de Broglie wavelength}\left(\lambda \right)=5890\stackrel{\circ }{A}=5890\times {10}^{-8}cm$
$\text{Plank's constant}\left(h\right)=6.63\times {10}^{-27}ergs$
Let 'm' be the mass of proton.
We know that de Broglie wavelength is given by
$\lambda =\frac{h}{mc}$ Since c is the velocity of a proton
$\therefore m=\frac{h}{c\times \lambda }=\frac{6.63\times {10}^{-27}}{5890\times {10}^{-8}\times 3\times {10}^{10}}=3.75\times {10}^{-33}g$