# What is the binding energy in kJ/mol per nucleons for the formation of gallium-69? The number of protons are 31 and that of neutrons is 38. The required masses (g/mol) are: proton = 1.00783;...

What is the binding energy in kJ/mol per nucleons for the formation of gallium-69? The number of protons are 31 and that of neutrons is 38. The required masses (g/mol) are: proton = 1.00783; neutron = 1.00867; gallium-69 = 68.92570.

Expert Answers
gsenviro | Certified Educator

Binding energy is the amount of energy generated when the protons and neutrons form a nucleus. It can also be thought of as the energy needed to break the nucleus into these individual sub-atomic particles. This is calculated by using Einstein's mass-energy equivalency relationship, E = mc^2

where, m is the mass defect and c is the velocity of light.

Mass defect, m = actual mass of nucleons - actual mass of nucleus

= number of protons x mass of protons + number of neutrons x mass of neutrons - mass of nucleus

= 31 x 1.00783 + 38 x 1.00867 - 68.9257 = 0.6465 g/mol

And thus, the binding energy = 0.6465 g/mol x (3 x 10^8 m/s)^2

= 5.8184 x 10^12 kg m^2/s^2/mol = 58.184 x 10^9 kJ/mol

In terms of per nucleon, we can simply divide the binding energy by the number of nucleons (which is 69).

Thus, binding energy = 58.184 x 10^9 kJ/mol / 69

= 8.43 x 10^8 kJ/mol/nucleon.

Hope this helps.

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