The radius of a spherical nucleus as measured by electron scattering is 3.6 fm. What is the mass number of the nucleus most likely to be ?

Options

A. 27
B. 40
C. 56
D. 120

Explanation

To find the mass number of a nucleus given its radius, we can use the formula for the radius of a spherical nucleus:

\[ R = R_0 A^{1/3} \]

Where:
- \( R \) is the radius of the nucleus,
- \( R_0 \) is a constant (approximately \( 1.2 \, \text{fm} \)),
- \( A \) is the mass number of the nucleus.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius of the nucleus, \( R = 3.6 \, \text{fm} \)
- Constant, \( R_0 = 1.2 \, \text{fm} \)

2. **Substitute the values into the formula**:
\[ R = R_0 A^{1/3} \]
Substituting the known values:
\[ 3.6 = 1.2 A^{1/3} \]

3. **Solve for \( A^{1/3} \)**:
To isolate \( A^{1/3} \), divide both sides by \( 1.2 \):
\[ A^{1/3} = \frac{3.6}{1.2} \]
Calculate the right side:
\[ A^{1/3} = 3 \]

4. **Cube both sides to find \( A \)**:
\[ A = (A^{1/3})^3 = 3^3 = 27 \]

5. **Conclusion**:
The mass number \( A \) of the nucleus is \( 27 \).

### Final Answer:
The mass number of the nucleus is **27**.

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