Question

Find the energy equivalent of one atomic mass unit in joules and in $MeV$.

• A. $ 1.66 \times 10^{-10} J , 93.15 \: Me V . $
• B. $ 2.5 \times 10^{-10} J , 931.5 \: Me V . $
• C. $ 1.5 \times 10^{-10} J , 931.5 \: Me V . $
• D. $3 \times 10^{-10} J , 9.315 \: Me V . $

Answer 1

Answer: (C)

Here, $m = 1 \, u = 1.6605 \times 10^{-27} \, kg$
According to Einstein's mass-energy equivalence relation
$E = mc^2$
$ \, \, \, = (1.6605 \times 10^{-27} \, kg)(2.9979 \times 10^8 \, m \, s^{-1})^2$
$= 1.4924 \times 10^{-10} J = 1.5 \times 10^{-10} J$
$ E = \frac{ 1.4924 \times 10^{-10}}{1.602 \times 10^{-19}} eV$
$= 0.9315 \times 10^9 eV = 931.5 \times 10^6 \: eV = 931.5\: MeV$