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Question: Answered & Verified by Expert
$1 \mathrm{amu}$ is equal to
PhysicsUnits and DimensionsAP EAMCETAP EAMCET 2021 (24 Aug Shift 1)
Options:
  • A $931 \mathrm{keV}$
  • B $931 \mathrm{eV}$
  • C $931 \mathrm{MeV}$
  • D $9.31 \mathrm{MeV}$
Solution:
1174 Upvotes Verified Answer
The correct answer is: $931 \mathrm{MeV}$
Given that atomic mass $=1 \mathrm{amu}$
$=1.66 \times 10^{-27} \mathrm{~kg}$
By using Einstein's equation of mass energy relation, $E=m c^2$
where, $c=$ speed of light $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$.
$\begin{aligned}
E & =\left(1.66 \times 10^{-27}\right) \times\left(3 \times 10^8\right)^2 \mathrm{~J} \\
& =1.494 \times 10^{-11} \mathrm{~J}
\end{aligned}$
We know, $1 \mathrm{MeV}=1.6 \times 10^{-13} \mathrm{~J}$
$1 \mathrm{~J}=\frac{1}{1.6} \times 10^{13} \mathrm{MeV}$
Substituting the value, we get
$\begin{aligned}
E & =1.494 \times 10^{-11} \times \frac{1}{1.6} \times 10^{13} \mathrm{MeV} \\
& =931 \mathrm{MeV}
\end{aligned}$

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