Answer to Question #202403 in Astronomy | Astrophysics for Pranali Patil

Question

The most common isotope of gold is gold-197 with a measured mass of 196.966569u.

1. Determine the mass defect;
2. Determine the binding energy;
3. Determine the binding energy per nucleon.

Answer 1

1.

m(proton) = 1.007276 u

m(neutron) = 1.008665 u

Cu-63 has 79 protons and 118 neutrons.

m(defect) = -(196.966569 - 1.007276$\times$79 - 1.008665$\times$118) = 1.630705 u

2.

1.630705 u = 2.707849$\times$10^-27 kg

E(per atom) = mc² = 2.707849$\times$10^-27 $\times$ 299,792,458² = 2.433693$\times$10^-10 J

3.

E(per nuclon) = $\frac{2.433693×10^{-10} J }{197} = 1.235377\times 10^{-12} J$