Question

The rest energy of an electron is $0.511\, MeV$. The electron is accelerated from rest to a velocity $0.5\, c$. The change in its energy will be

• A. 0.026 MeV
• B. 0.051 MeV
• C. 0.079 MeV
• D. 0.105 MeV

Answer 1

Answer: (C)

According to Einstein's equation relation between rest energy and moving energy is
$E =E_{0}\left(1-\frac{v^{2}}{c^{2}}\right)^{-1 / 2}$
Given, $v=0.5\, c$
$\therefore E=E_{0}\left(1-\frac{(0.5\, c)^{2}}{c^{2}}\right)^{-1 / 2}$
$E =E_{0}(1-0.25)^{-1 / 2}$
$=\frac{E_{0}}{\sqrt{0.75}}$
Change in energy $\Delta E=E-E_{0}$
$=\frac{E_{0}}{\sqrt{0.75}}-E_{0}$
$=E_{0}\left(\frac{1}{\sqrt{0.75}}-1\right)$
$=0.511\left(\frac{1}{\sqrt{0.75}}-1\right)$
$=0.079\, MeV$