Question

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
  

Answer 1

The correct option is B 0.34 MeV

Given $m_0{c}^2=0.51MeV$ and $v=0.8c$
K.E. of the electron = $m{c}^2-m_0{c}^2$
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, $m{c}^2=\frac{0.51}{0.6}MeV=0.85MeV$
$\therefore K.E.=(0.85-0.51)MeV=0.34MeV$.