Thank you for reporting, we will resolve it shortly
Q.
Rest mass energy of an electron is $0.54\, MeV.$ If velocity of the electron is $0.8\, C,$ then its kinetic energy will be
Bihar CECEBihar CECE 2012Nuclei
Solution:
Rest mass energy of electron $=0.54\,MeV$
i.e., $m_{0} c^{2}=0.54\, MeV$ ...(i)
But the kinetic energy of electron
$=m c^{2}-m_{0} c^{2}$ ...(ii)
Also,
$m=\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$
$=\frac{m_{0}}{\sqrt{1-(0.8)^{2}}}=\frac{m_{0}}{0.6}$
So, $m c^{2} =\frac{m_{0} c^{2}}{0.6}$
$=\frac{0.54}{0.6} MeV$ [From Eq (i)]
$m c^{2}=0.9\, MeV$ ...(ii)
Substituting values of Eq (ii) and (i) in Eq (ii),
we get $KE =(0.9-0.54) MeV =0.36\, MeV$