Question

Calculate the mass of a photon of sodium light having wavelength 600 nm and velocity $3\times {10}^{8}m{s}^{-1}$.

• A. $3.68\times {10}^{-36}kg$
• B. $2.68\times {10}^{-36}kg$
• C. $5.68\times {10}^{-36}kg$
• D. $7.68\times {10}^{-36}kg$

Answer 1

The correct option is A $3.68\times {10}^{-36}kg$

Here, we know,
E=hv [planck's quantum theory]
& $E=m{c}^2$ [Enstein's equation]
Now,
$hv=m{c}^2$
$\Rightarrow m=\frac{hv}{c^2}\Rightarrow m=\frac{hc}{c^2\lambda }$
$\Rightarrow m=\frac{h}{c\lambda }$
Now,
Velocity of photon(v)=$3\times {10}^{8}m{s}^{-1}$
Using relationship
$m=\frac{h}{c\lambda }$
We get
Mass of photon=$\frac{6.626\times {10}^{-34}Js}{3\times {10}^{8}m{s}^{-1}\times 6.0\times {10}^{-7}m}$
$=3.68\times {10}^{-36}kg$