Question
The energy equivalent of one atomic mass unit is
A.
$$1.6 \times {10^{ - 19}}J$$
B.
$$6.02 \times {10^{23}}J$$
C.
$$931\;MeV$$
D.
$$9.31\,MeV$$
Answer :
$$931\;MeV$$
Solution :
According to Einstein, mass-energy equivalence is represented by $$E = m{c^2}.$$
Taking, mass, $$m = 1\,amu = 1.66 \times {10^{ - 27}}kg,$$ and velocity of light in vacuum, $$c = 3.0 \times {10^8}m/s$$
We get, $$E = \left( {1.66 \times {{10}^{ - 27}}} \right) \times {\left( {3 \times {{10}^8}} \right)^2}J$$
$$\eqalign{
& = 1.49 \times {10^{ - 10}}J = \frac{{1.49 \times {{10}^{ - 10}}}}{{1.6 \times {{10}^{ - 13}}}}MeV\,\,\left( {\because 1\,MeV = 1.6 \times {{10}^{ - 13}}J} \right) \cr
& = 931.25\,MeV \cr} $$
Hence, $$1\,amu \simeq 931\,MeV$$