Calculation of Binding Energy per Nucleon of nucleus 20Ca40

1. Introduction:
The binding energy per nucleon of a nucleus represents the energy required to separate all the nucleons in the nucleus. It is a measure of the stability of the nucleus.

2. Formula:
The binding energy per nucleon (BE/A) can be calculated using the formula:

BE/A = (Z*mp + (A-Z)*mn - mN) / A

where:
- BE/A is the binding energy per nucleon
- Z is the atomic number (number of protons)
- mp is the mass of a proton
- A is the mass number (number of protons + neutrons)
- mn is the mass of a neutron
- mN is the mass of the nucleus

3. Given Data:
- mn = 1.008665 u (atomic mass units)
- mp = 1.007825 u
- mN (20Ca40) = 39.962589 u

4. Calculation:
Let's calculate the binding energy per nucleon of nucleus 20Ca40.

We plug the given values into the formula:

BE/A = (Z*mp + (A-Z)*mn - mN) / A

For 20Ca40:
- Z = 20
- A = 40

BE/A = (20*1.007825 + (40-20)*1.008665 - 39.962589) / 40

Simplifying the equation:

BE/A = (20.1565 + 20.1733 - 39.962589) / 40

BE/A = 0.367146025

5. Result:
The binding energy per nucleon (BE/A) of nucleus 20Ca40 is approximately 0.367146025 u.

Explanation:
The binding energy per nucleon represents the average amount of energy required to remove one nucleon from the nucleus. Higher values of BE/A indicate greater stability of the nucleus. In the case of 20Ca40, the calculated BE/A value of 0.367146025 u indicates that the nucleus is relatively stable.