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 vary small. The energy at nuclear level is usually measured in MeV, where `1 MeV = 1.6 xx 10^(-13) J ,` the masses are measured in unified mass unit (u) where `1 u = 1.67xx10^(-27)kg.` (a) Show that the energy equivalent of 1u is 931.5 MeV. (b) A student writes the relation as 1 u = 931.5 MeV. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

Explanation

(a) We know that
`1 " amu"=1u=1.67xx10^(-27)kg`
`"Applying " E=mc^(2)`
`"Energy "= E=(1.67xx10^(-27))(3xx10^(8))^(2)J`
`=1.67xx9xx10^(-11)J`
`E=(1.67xx9xx10^(-11))/(1.6xx10^(-13))"MeV = 939.4 MeV "approx" 931.5 MeV"`
(b) The dimensionally correct relation is
`1" amu"xxc^(2)=1"u"xxc^(2)=931.5 " MeV"`