Obtain the Binding energy of MeV of a helium nucleus. Mass of Helium = 4.00263 u.

To find the binding energy of a helium nucleus, we first need to understand what binding energy is. Binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It can also be thought of as the energy released when a nucleus is formed from its constituent particles. For helium, which consists of two protons and two neutrons, we can calculate the binding energy using the mass defect and Einstein's mass-energy equivalence principle, E=mc².

Step-by-Step Calculation

1. Determine the Mass Defect

The mass defect is the difference between the mass of the individual nucleons (protons and neutrons) and the actual mass of the helium nucleus. The masses of the individual nucleons are approximately:

• Proton mass = 1.007276 u
• Neutron mass = 1.008665 u

For helium, which has 2 protons and 2 neutrons, the total mass of the individual nucleons is:

Total mass of nucleons = (2 × 1.007276 u) + (2 × 1.008665 u)

Calculating this gives:

Total mass of nucleons = 2.014552 u + 2.01733 u = 4.031882 u

2. Calculate the Mass Defect

Now, we can find the mass defect by subtracting the actual mass of the helium nucleus from the total mass of the nucleons:

Mass defect = Total mass of nucleons - Mass of Helium

Mass defect = 4.031882 u - 4.00263 u = 0.029252 u

3. Convert Mass Defect to Energy

Next, we convert the mass defect into energy using Einstein's equation, E=mc². We need to convert atomic mass units (u) to MeV. The conversion factor is:

1 u = 931.5 MeV

Now, we can calculate the binding energy:

Binding Energy = Mass defect × 931.5 MeV/u

Binding Energy = 0.029252 u × 931.5 MeV/u ≈ 27.27 MeV

Final Result

The binding energy of a helium nucleus is approximately 27.27 MeV. This value indicates how tightly the nucleons are held together in the nucleus, reflecting the stability of helium as an element.

Understanding the Significance

This binding energy is significant because it helps explain why helium is a common product of nuclear fusion in stars. The energy released during fusion reactions is a result of the binding energy of the resulting nuclei being greater than that of the original nucleons, which is a fundamental principle in nuclear physics.