Question

The momentum of a photon with energy $20$ eV is ?

• A. $10.66\times {10}^{-27}$ Kg m sec${}^{-1}$
• B. $10.55\times {10}^{-27}$ Kg m sec${}^{-1}$
• C. $10.60\times {10}^{-27}$ Kg m sec${}^{-1}$
• D. $10.80\times {10}^{-27}$ Kg m sec${}^{-1}$

Answer 1

The correct option is A $10.66\times {10}^{-27}$ Kg m sec${}^{-1}$

$E=hv=\frac{hc}{\lambda }$

$\lambda =\frac{hc}{E}=\frac{h}{mv}=\frac{h}{p}$

$\text{momentum}=p=\frac{E}{c}$

But $E=20$ eV $=20\times 1.6\times {10}^{-19}$ J $=32\times {10}^{-19}$ J

$p=\frac{32\times {10}^{-19}}{3\times {10}^8}=10.66\times {10}^{-27}$ Kg m sec${}^{-1}$

Hence, the correct option is $\text{A}$