For an element, mass of nucleus is 7.05 u, the mass of protons is 3.023475 u and the mass of neutrons is 4.034660 u. If 1 u = 931.5 MeV/c2, the binding energy of the nucleus is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ~7.58 MeV
The binding energy is the mass defect (mass of the separate nucleons minus the mass of the nucleus) converted into energy using 1 u = 931.5 MeV/c2.
\( \text{Mass of nucleons} = 3.023475\,\mathrm{u} + 4.034660\,\mathrm{u} = 7.058135\,\mathrm{u} \)
\( \displaystyle \Delta m = 7.058135\,\mathrm{u} - 7.05\,\mathrm{u} = 0.008135\,\mathrm{u} \)
\( \displaystyle E_b = \Delta m \times 931.5\,\mathrm{MeV\,u^{-1}} \)
\( \displaystyle E_b = 0.008135 \times 931.5\,\mathrm{MeV} \)
\( \displaystyle E_b \approx 7.58\,\mathrm{MeV} \)