The rest-mass energy of an electron is \( \left(m_e=9.1\times10^{-31}\,\mathrm{kg},\ c=3\times10^{8}\,\mathrm{m\,s^{-1}},\ 1\,\mathrm{MeV}=1.6\times10^{-13}\,\mathrm{J}\right) \)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 510 keV
By Einstein’s mass-energy relation \( E=mc^{2} \), a particle of rest mass \( m \) has an energy equivalent \( mc^{2} \). For the electron:
\( \begin{aligned} E &= m_ec^{2} \\ &= 9.1\times10^{-31}\,\mathrm{kg}\times(3\times10^{8}\,\mathrm{m\,s^{-1}})^{2} \\ &= 8.19\times10^{-14}\,\mathrm{J} \end{aligned} \)
Converting to MeV with \( 1\,\mathrm{MeV}=1.6\times10^{-13}\,\mathrm{J} \):
\( \begin{aligned} E &= \frac{8.19\times10^{-14}}{1.6\times10^{-13}}\,\mathrm{MeV} \\ &\approx 0.51\,\mathrm{MeV} \\ &= 510\,\mathrm{keV} \end{aligned} \)