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  • 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.

Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass (m) to energy (E) as E = mc2, 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 \times 10^{-13}J, the masses are measured in unified equivalent of 1u is 931.5 MeV.

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.

Answers (1)

(a) Given :

m=1

u=1.67\times10^{-27}kg

c=3\times10^{8}m/s

By the formula E=mc^{2}

E=1.67\times10^{-27}\times3\times10^{8}\times3\times10^{8}

      =1.67\times10^{-27+16}\times9J

      =\frac{(1.67)(9)(10^{-11})}{(1.6)(10^{-13})}MeV

     =939.4\; Mev

   \cong 931.5\; Mev

(b) 1 u mass converted into total energy will be released by 931.5 MeV.

However, 1 amu = 931.5 MeV is dimensionally incorrect.

E=mc^{2}\rightarrow 1uc^{2}\cong 931.5\; Mev, will be dimensionally correct.

 

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infoexpert22

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