Question

Calculate the binding energy and binding energy per nucleon (in MeV) of a Nitrogen nucleus ${}^{7}N_{14}$ from the following data: Mass of proton = 1.00783 u, Mass of neutron = 1.00867 u, Mass of Nitrogen nucleus = 14.00307 u.

Answer 1

Step 1: Determination of the total number of nucleons.
In ${}^{7}N_{14}$,
Number of protons = 7
Number of neutrons = 7
Total number of nucleons = 7 +7
Total number of nucleons = 14.

Step 2: Calculation of mass defect
Mass defect (ΔM) = 7 (mass of proton) + 7(mass of neuton) – mass of Nitrogen nucleus
ΔM =7(1.00783) +7(1.00867) −14.00307 amu
ΔM = 0.11243 amu.

Step 3: Calculaion of binding energy
Binding energy (E) = ΔM × 931.5 MeV
Binding energy = 0.11243 × 931.5
Binding energy = 104.73 MeV.

Step 4: Calculation of binding energy per nucleon
Binding energy per nucleon =$\frac{104.73}{14}$
Binding energy per nucleon = 7.48 MeV

Therefore, the binding energy is 104.73 MeV, and the binding energy per nucleon is 7.48 MeV.