Question

The binding energy per nucleon of \(\alpha\)-particle (\(_2^4\text{He}\)) is 7 MeV. What is its total binding energy?

Hint:

To calculate the total binding energy of a nucleus, multiply the binding energy per nucleon by the total number of nucleons in the nucleus.

Answer 1

The binding energy per nucleon of an \(\alpha\)-particle (which is a helium-4 nucleus, \(_2^4\text{He}\)) is given as 7 MeV. An \(\alpha\)-particle consists of 2 protons and 2 neutrons, meaning it has a total of 4 nucleons. The total binding energy \(E_{\text{total}}\) of the \(\alpha\)-particle is the product of the binding energy per nucleon and the number of nucleons.

Step 1: Total Binding Energy
To find the total binding energy, we use the following equation:
\[ E_{\text{total}} = \text{Binding energy per nucleon} \times \text{Number of nucleons} \] Substitute the given values:
\[ E_{\text{total}} = 7 \, \text{MeV} \times 4 = 28 \, \text{MeV} \] Thus, the total binding energy of the \(\alpha\)-particle is \(28 \, \text{MeV}\). This is the energy required to separate all the nucleons (2 protons and 2 neutrons) from the nucleus. The binding energy is a measure of the stability of the nucleus, and a higher binding energy per nucleon indicates a more stable nucleus.