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)Jthe 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.

Einstein's mass-energy relation emerging out of his famous theory of r

1.	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)Jthe 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.
Answer» Solution :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`