Question

Rest mass energy of an electron is $0.54MeV.$ If velocity of the electron is $0.8C,$ 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)

Rest mass energy of electron $=0.54MeV$
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 $KE=(0.9-0.54)MeV=0.36MeV$