When two nuclei (with A=8) join to form a heavier nucleus , the binding energy (B.E) per nucleon of the heavier nuclei is

Answer

To solve the problem of determining the binding energy per nucleon of a heavier nucleus formed by the fusion of two nuclei with atomic mass \( A = 8 \), we can follow these steps:

### Step 1: Understand the concept of binding energy
Binding energy is the energy required to separate a nucleus into its constituent nucleons. The binding energy per nucleon is the total binding energy divided by the number of nucleons in the nucleus. Higher binding energy per nucleon indicates a more stable nucleus.

**Hint**: Recall that binding energy is a measure of the stability of a nucleus.

### Step 2: Identify the initial nuclei
We have two nuclei, each with an atomic mass \( A = 8 \). Therefore, the total mass of the two nuclei before fusion is:
\[ \text{Total mass} = 8 + 8 = 16 \]

**Hint**: Remember that when two nuclei fuse, their masses combine.

### Step 3: Consider the fusion process
When these two nuclei fuse, they form a heavier nucleus. The mass of the resulting nucleus will be slightly less than the total mass of the two original nuclei due to the mass-energy equivalence principle (some mass is converted into energy).

**Hint**: Think about the mass defect that occurs during fusion.

### Step 4: Calculate the binding energy of the resulting nucleus
The binding energy of a nucleus can be calculated using the semi-empirical mass formula or by using known values for binding energies of specific nuclei. For a nucleus with \( A = 16 \), we can look up or calculate the binding energy.

For example, the binding energy of \( ^{16}O \) (oxygen-16) is approximately 127.62 MeV.

**Hint**: Use known binding energy values for common isotopes to find the total binding energy.

### Step 5: Calculate the binding energy per nucleon
To find the binding energy per nucleon of the heavier nucleus formed, we divide the total binding energy by the number of nucleons:
\[ \text{Binding Energy per Nucleon} = \frac{\text{Total Binding Energy}}{\text{Number of Nucleons}} = \frac{127.62 \text{ MeV}}{16} \approx 7.98 \text{ MeV} \]

**Hint**: Remember to divide the total binding energy by the total number of nucleons to find the per nucleon value.

### Final Answer
The binding energy per nucleon of the heavier nucleus formed by the fusion of two nuclei with \( A = 8 \) is approximately \( 7.98 \) MeV.

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