Mass number of a nuclide is 216, its approxmiamte radius in fermi units is

Options

A. `6.0`
B. `7.0`
C. `8.0`
D. `8.4`

Answer

To find the approximate radius of a nuclide with a mass number of 216 in fermi units, we can use the formula for the radius of a nucleus:

### Step-by-Step Solution:

1. **Identify the formula for nuclear radius**:
The radius \( r \) of a nucleus can be calculated using the formula:
\[ r = r_0 \cdot A^{1/3} \]
where:
- \( r_0 \) is a constant approximately equal to 1.2 fermi,
- \( A \) is the mass number of the nuclide.

2. **Substitute the given values**:
In this case, the mass number \( A \) is given as 216. Therefore, we can substitute the values into the formula:
\[ r = 1.2 \cdot (216)^{1/3} \]

3. **Calculate the cube root of the mass number**:
First, we need to calculate \( (216)^{1/3} \):
\[ (216)^{1/3} = 6 \]
(since \( 6 \times 6 \times 6 = 216 \)).

4. **Calculate the radius**:
Now substitute the cube root back into the equation:
\[ r = 1.2 \cdot 6 \]
\[ r = 7.2 \text{ fermi} \]

5. **Round to the nearest whole number**:
Since the question asks for an approximate value, we can round 7.2 to 7 fermi.

6. **Final answer**:
Therefore, the approximate radius of the nuclide is:
\[ \text{Radius} \approx 7 \text{ fermi} \]

### Answer:
The approximate radius of the nuclide is 7 fermi.