# Calculate the momentum of electron moving with $\large\frac{1}{3}$rd velocity of light

$\begin{array}{1 1}(a)\;9.69\times 10^{-18}gcm/s&(b)\;9.89\times 10^{-11}gcm/s\\(c)\;8.32\times 10^{-18}gcm/s&(d)\;8.98\times 10^{-11}gcm/s\end{array}$

momentum of electron =$m'u$
m' is the mass of electron in motion$=\large\frac{m}{\sqrt{1-(\Large\frac{u}{c})^2}}$
Also $u=\large\frac{c}{3}$
Momentum $=\large\frac{9.108\times 10^{-28}}{\sqrt{1-\big(\Large\frac{c}{3\times c}\big)^2}}\times \frac{3\times 10^{10}}{3}$
$\Rightarrow \large\frac{9.108\times 10^{-28}\times 3\times 10^{10}}{0.94\times 3}$
$\Rightarrow 9.69\times 10^{-18}gcm/s$
Hence (a) is the correct answer.