Q. Rest mass energy of an electron is $0.54\ MeV$. If velocity of the electron is $0.8c$, then $K.E.$ of the electron is
A) $0.36\ MeV$
B) $0.41\ MeV$
C) $0.48\ MeV$
D) $1.32\ MeV$
Explanation
(a) $m_{0}c^{2} = 0.54\ MeV$ and K.E. $= mc^{2} - m_{0}c^{2}$
Also $m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{m_{0}}{\sqrt{1 - (0.8)^{2}}} = \frac{m_{0}}{0.6}$
$\therefore E = mc^{2} = \frac{m_{0}}{0.6}c^{2} = \frac{0.54}{0.6} = 0.9\ MeV$
$\therefore$ K.E. $= (0.9 - 0.54) = 0.36\ MeV$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.