Q. Rest mass energy of an electron is $0.51\ MeV.$ If this electron is moving with a velocity $0.8\ c$ (where $c$ is velocity of light in vacuum), then kinetic energy of the electron should be
A) $0.28\ MeV$
B) $0.34\ MeV$
C) $0.39\ MeV$
D) $0.46\ MeV$
Explanation
(b) Given $m_{0}c^{2} = 0.51\ MeV\ $and $v = 0.8\ c$
$K.E.$ of the electron $= mc^{2} - m_{0}c^{2}$
$But\ m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{m_{0}}{\sqrt{1 - \left( \frac{0.8c}{c} \right)^{2}}} = \frac{m_{0}}{\sqrt{0.36}} = \frac{m_{0}}{0.6}$
Now,$\ mc^{2} = \frac{0.51}{0.6}MeV = 0.85\ MeV$
$\therefore K.E.\ = (0.85 - 0.51)MeV = 0.34\ MeV$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.