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Physics Question on Nuclei

Find the energy equivalent of one atomic mass unit in joules and in MeVMeV.

A

1.66×10−10J,93.15 MeV.1.66 \times 10^{-10} J , 93.15 \: Me V .

B

2.5×10−10J,931.5 MeV.2.5 \times 10^{-10} J , 931.5 \: Me V .

C

1.5×10−10J,931.5 MeV.1.5 \times 10^{-10} J , 931.5 \: Me V .

D

3×10−10J,9.315 MeV.3 \times 10^{-10} J , 9.315 \: Me V .

Answer

1.5×10−10J,931.5 MeV.1.5 \times 10^{-10} J , 931.5 \: Me V .

Explanation

Solution

Here, m=1 u=1.6605×10−27 kgm = 1 \, u = 1.6605 \times 10^{-27} \, kg
According to Einstein's mass-energy equivalence relation
E=mc2E = mc^2
   =(1.6605×10−27 kg)(2.9979×108 m s−1)2\, \, \, = (1.6605 \times 10^{-27} \, kg)(2.9979 \times 10^8 \, m \, s^{-1})^2
=1.4924×10−10J=1.5×10−10J= 1.4924 \times 10^{-10} J = 1.5 \times 10^{-10} J
E=1.4924×10−101.602×10−19eVE = \frac{ 1.4924 \times 10^{-10}}{1.602 \times 10^{-19}} eV
=0.9315×109eV=931.5×106 eV=931.5 MeV= 0.9315 \times 10^9 eV = 931.5 \times 10^6 \: eV = 931.5\: MeV