The mass equivalent of 931 MeV of energy is

The correct answer is Option (1) → \( 1.66\times10^{-27}\,\mathrm{kg} \)

By Einstein’s mass–energy equivalence \( E=mc^{2} \), the mass equivalent of an energy \( E \) is \( m=E/c^{2} \). Take \( 1\,\mathrm{MeV}=1.6\times10^{-13}\,\mathrm{J} \) and \( c=3\times10^{8}\,\mathrm{m\,s^{-1}} \).

The energy in joules is:

    \( \begin{aligned} E &= 931\,\mathrm{MeV} \\ &= 931\times1.6\times10^{-13}\,\mathrm{J} \\ &\approx 1.49\times10^{-10}\,\mathrm{J} \end{aligned} \)

The mass equivalent is then:

    \( \begin{aligned} m &= \frac{E}{c^{2}} \\ &= \frac{1.49\times10^{-10}\,\mathrm{J}}{(3\times10^{8}\,\mathrm{m\,s^{-1}})^{2}} \\ &\approx 1.66\times10^{-27}\,\mathrm{kg} \end{aligned} \)

This is the mass of one atomic mass unit, since \( 1\,\mathrm{u}\approx931.5\,\mathrm{MeV}/c^{2} \).