find binding energy

Question

Find the binding energy (in MeV) for lithium ₃Li⁹ (atomic mass = 9.026789 u).

Answer 1

As we know, the total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons. The difference between them is called mass defect. When it is destroyed, it is converted to the so-called binding energy of the nucleus. It means that to find binding energy we need:

1.    Find the total mass of all neutrons and protons in a nucleus.

2.    Subtract from it the mass of a stable nucleus.

3.    Express this difference in units of energy.

₃Li⁹ has 3 protons and 6 (9 – 3) neutrons.

The mass of the proton in atomic mass units m_p = 1.00728 u, mass of the neutron m_n= 1.008665 u.

The mass of all protons is 3 x 1.00728 u = 3.02184 u.

The mass of all neutrons is 6 x 1.008665 u = 6.05199 u.

Then the total mass of all particles in Li nucleus is 3.02184 u + 6.05199 u = 9.07383 u.

 Now we subtract from this mass the mass of the Li nucleus 9.026789 u.

The difference will be Δm = 9.07383 u – 9.026789 u = 0.047041 u.

And finally, knowing that if the mass is changing by 1 u the released energy is 931.5 Mev, we find that the binding energy for lithium is 43.81869 Mev.