Compare the radii of two nuclei with mass number 1 and 8 respectively.

Options

A. 1/2
B. 1/3
C. 2/1
D. 2/3

Explanation

To compare the radii of two nuclei with mass numbers 1 and 8, we can use the formula for the radius of a nucleus:

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

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

### Step-by-Step Solution:

1. **Identify the Mass Numbers**:
- Let \( A_1 = 1 \) (for the nucleus with mass number 1).
- Let \( A_2 = 8 \) (for the nucleus with mass number 8).

2. **Write the Formula for the Radii**:
- The radii of the two nuclei can be expressed as:
\[ R_1 = R_0 A_1^{1/3} \]
\[ R_2 = R_0 A_2^{1/3} \]

3. **Calculate the Ratio of the Radii**:
- To find the ratio of the radii \( \frac{R_1}{R_2} \):
\[ \frac{R_1}{R_2} = \frac{R_0 A_1^{1/3}}{R_0 A_2^{1/3}} \]
- The \( R_0 \) terms cancel out:
\[ \frac{R_1}{R_2} = \frac{A_1^{1/3}}{A_2^{1/3}} \]

4. **Substitute the Values of Mass Numbers**:
- Substitute \( A_1 = 1 \) and \( A_2 = 8 \):
\[ \frac{R_1}{R_2} = \frac{1^{1/3}}{8^{1/3}} = \frac{1}{2} \]

5. **Conclusion**:
- The ratio of the radii of the two nuclei is:
\[ \frac{R_1}{R_2} = \frac{1}{2} \]
- This means that the radius of the nucleus with mass number 1 is half that of the nucleus with mass number 8.

### Final Answer:
The ratio of the radii of the two nuclei with mass numbers 1 and 8 is \( \frac{1}{2} \).

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