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 1 MeV= 1.6×10^–13J; the masses are measured in unified atomic mass unit (u) where 1u = 1.67 × 10^–27 kg.
(a) Show that the energy equivalent of 1 u 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.

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2015-05-26T13:33:31+05:30

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E = m c²

1 u of mass unit  is equivalent to :  1.67 * 10⁻²⁷ * [2.987 * 10⁸]²    Joules
   = 1.67 * 9 * 10⁻¹¹ Joules  / [ 1.6  * 10⁻¹³  Joules/MeV ]
   = 931  MeV
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1 u * c² = 931.5 MeV ,      where c = 2.987 * 10⁸ m/s

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