Find the mass defect and binding energy of helium nucleus, 2He4.

Solution

Theory

The mass of a nucleus is less than the sum of the masses of the same number of separate neutrons and protons when added. This difference is called the mass defect of the nucleus. This is due to the protons and neutrons binding together at the time of nucleus formation. This binding energy comes at the cost of the mass of the protons and neutrons. Also we know that

Mass of helium nucleus 2He4 is 6.6447 × 10-27 kg = m (say)

Mass of a proton = 1.6726 × 10-27 kg = mp (say)

∴, mass of 2 protons of helium = 2(1.6726 × 10-27) kg

Mass of a neutron = 1.6749 × 10-27 kg = mn (say)

∴, mass of 2 neutrons of helium = 2(1.6749 × 10-27) kg

Formula

Mass defect, Δm = (2mp + 2mn) – m     ….      (1)

Put values in formula (1) to find the mass defect.

Δm = {2(1.6726 × 10-27) + 2(1.6749 × 10-27)} – 6.6447 × 10-27

Δm = (3.3452 + 3.3498) ×10-27 – 6.6447 × 10-27 = 0.0503 × 10-27 kg     ……     (3)

Now 1.660 × 10-27 kg = 1 amu

OR     1 kg = (1/1.660) × 1027 amu = 0.602409 × 1027 amu

Multiply by the value of Δm from equation (3) on both sides.

0.0503 × 10-27 kg = 0.0503 × 0.602409 amu = 0.0303 amu

Since 1 amu = 931.5 MeV, therefore,

0.0303 amu = .0303 × 931.5 = 28.224 MeV