The mass number of He is `4` and that for suphur is `32`. The radius of sulphur nuclei is larger than that of helium by

Options

A. `sqrt(8)`
B. `4`
C. `2`
D. `8`

Answer

To solve the problem of finding how much larger the radius of the sulfur nucleus is compared to that of the helium nucleus, we can follow these steps:

### Step 1: Understand the formula for nuclear radius
The radius of a nucleus can be approximated using the formula:
\[ R = R_0 A^{1/3} \]
where \( R_0 \) is a constant (approximately \( 1.2 \, \text{fm} \)), and \( A \) is the mass number of the nucleus.

### Step 2: Calculate the radius of the sulfur nucleus
For sulfur (mass number \( A_s = 32 \)):
\[ R_s = R_0 A_s^{1/3} = R_0 (32)^{1/3} \]

### Step 3: Calculate the radius of the helium nucleus
For helium (mass number \( A_{he} = 4 \)):
\[ R_{he} = R_0 A_{he}^{1/3} = R_0 (4)^{1/3} \]

### Step 4: Find the ratio of the radii
To find how much larger the radius of sulfur is compared to helium, we can take the ratio of the two radii:
\[ \frac{R_s}{R_{he}} = \frac{R_0 (32)^{1/3}}{R_0 (4)^{1/3}} \]

### Step 5: Simplify the ratio
The \( R_0 \) cancels out:
\[ \frac{R_s}{R_{he}} = \frac{(32)^{1/3}}{(4)^{1/3}} = \left(\frac{32}{4}\right)^{1/3} = (8)^{1/3} = 2 \]

### Step 6: Conclusion
Thus, the radius of the sulfur nucleus is 2 times larger than that of the helium nucleus.

### Final Answer
The radius of sulfur nuclei is larger than that of helium by a factor of 2.

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