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 based on its radius, we can use the formula for the radius of a nucleus:

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

Where:
- \( R \) is the radius of the nucleus,
- \( R_0 \) is a constant (approximately \( 1.2 \, \text{fm} \) or \( 1.2 \times 10^{-15} \, \text{m} \)),
- \( A \) is the mass number of the nucleus.

### Step 1: Rearrange the formula to solve for \( A \)

We can rearrange the formula to express \( A \) in terms of \( R \):

\[ A = \left( \frac{R}{R_0} \right)^3 \]

### Step 2: Substitute the values

Given:
- \( R = 3.6 \, \text{fm} = 3.6 \times 10^{-15} \, \text{m} \)
- \( R_0 = 1.2 \times 10^{-15} \, \text{m} \)

Now, substitute these values into the equation:

\[ A = \left( \frac{3.6 \times 10^{-15}}{1.2 \times 10^{-15}} \right)^3 \]

### Step 3: Simplify the fraction

Calculate the fraction:

\[ \frac{3.6}{1.2} = 3 \]

### Step 4: Cube the result

Now cube the result:

\[ A = 3^3 = 27 \]

### Conclusion

The mass number \( A \) of the nucleus is most likely to be 27.

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

---