Radius of the nucleus of the atom with A=216 is (`R_0` =1.3fm)

Options

A. 7.2 fm
B. 7.8 fm
C. 280 fm
D. 19 fm

Answer

To find the radius of the nucleus of an atom with atomic mass number \( A = 216 \), we can use the formula for the radius of a nucleus:

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

where:
- \( R_0 = 1.3 \, \text{fm} \) (Fermi meter)
- \( A = 216 \)

### Step-by-step Solution:

1. **Identify the values:**
- We have \( R_0 = 1.3 \, \text{fm} \)
- We have \( A = 216 \)

2. **Substitute the values into the formula:**
\[ R = 1.3 \, \text{fm} \times (216)^{1/3} \]

3. **Calculate the cube root of 216:**
- The cube root of 216 is 6, because \( 6^3 = 216 \).
\[ (216)^{1/3} = 6 \]

4. **Now substitute back into the equation:**
\[ R = 1.3 \, \text{fm} \times 6 \]

5. **Perform the multiplication:**
\[ R = 7.8 \, \text{fm} \]

6. **Conclusion:**
- The radius of the nucleus of the atom with \( A = 216 \) is \( 7.8 \, \text{fm} \).

### Final Answer:
\[ R = 7.8 \, \text{fm} \]