Question

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:

• A. 0.36 MeV
• B. 0.41 MeV
• C. 0.48 MeV
• D. 1.32 MeV

Answer 1

Answer: (A)

0.36 MeV

Rest mass energy of electron = 0.54 MeV
i.e., $m_0{c}^2=0.54MeV$ ...(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))
$m{c}^2=0.9MeV$ ...(ii)
Substituting values of Eq (ii) and (i) in Eq (ii) we get
$KE=(0.9-0.54)MeV=0.36MeV$