Compare the radii of two nuclei with mass number 1 and 27 respectively.

Explanation

To compare the radii of two nuclei with mass numbers 1 and 27, we can use the formula for the radius of a nucleus, which is given by:

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

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 Mass Numbers**:
- For the first nucleus, the mass number \( A_1 = 1 \).
- For the second nucleus, the mass number \( A_2 = 27 \).

2. **Calculate the Radius of the First Nucleus \( R_1 \)**:
\[ R_1 = R_0 A_1^{1/3} = R_0 \cdot 1^{1/3} = R_0 \cdot 1 = R_0 \]

3. **Calculate the Radius of the Second Nucleus \( R_2 \)**:
\[ R_2 = R_0 A_2^{1/3} = R_0 \cdot 27^{1/3} \]
Since \( 27 = 3^3 \), we have:
\[ 27^{1/3} = 3 \]
Therefore:
\[ R_2 = R_0 \cdot 3 = 3R_0 \]

4. **Compare the Radii**:
- Now we have:
- \( R_1 = R_0 \)
- \( R_2 = 3R_0 \)

5. **Find the Ratio of the Radii**:
\[ \frac{R_1}{R_2} = \frac{R_0}{3R_0} = \frac{1}{3} \]
This implies:
\[ R_2 = 3R_1 \]

### Conclusion:
The radius of the nucleus with mass number 27 is three times the radius of the nucleus with mass number 1.