The binding energy of an element of `54 MeV`. If `BE//"nucleon"` is 5.4, then the number of nucleons are

Options

A. 10
B. 64
C. 16
D. 6

Answer

To find the number of nucleons in the given element, we can use the relationship between binding energy, binding energy per nucleon, and the number of nucleons.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Binding Energy (BE) = 54 MeV
- Binding Energy per Nucleon (BE/nucleon) = 5.4 MeV/nucleon

2. **Understand the Relationship:**
The binding energy per nucleon is defined as:
\[ \text{BE/nucleon} = \frac{\text{Total Binding Energy}}{\text{Number of Nucleons}} \]
Rearranging this formula gives us:
\[ \text{Number of Nucleons} = \frac{\text{Total Binding Energy}}{\text{BE/nucleon}} \]

3. **Substitute the Given Values:**
Now, substituting the known values into the rearranged formula:
\[ \text{Number of Nucleons} = \frac{54 \text{ MeV}}{5.4 \text{ MeV/nucleon}} \]

4. **Perform the Calculation:**
\[ \text{Number of Nucleons} = \frac{54}{5.4} = 10 \]

5. **Conclusion:**
Therefore, the number of nucleons in the element is 10.

### Final Answer:
The number of nucleons is **10**.

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