Einstein's mass-energy relation emerging out of his famous theory of relativity relates mass (m) to energy (E) as `E = mc^(2)` where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV, where `I MeV = 1.6 xx 10^(-13)J` the masses are measured in unified atomic mass unit (u) where, `1u = 1.67 xx 10^(-27) kg`
. (a) Show that the energy equivalent of luis 931.5 MeV. (b) A student writes the relation as lu = 931.5 MeV.
The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

Explanation

We know that,
1 amu=`1u=1.67xx10^(-27)kg`
Energy `=E=(1.67xx10^(-27))(3xx10^(8))^(2)J`
`=1.67xx9xx10^(-11)J`
`E=(1.67xx9xx10^(-11))/(1.6xx10^(-13))MeV`
`=939.4 MeV~~931.5 MeV`
(b) The dimensionally correct relation is ,
1 amu `xx c^(2)=1uxxc^(2)=931.5 MeV`