The mass number of atom whose nucleus has a radium of 5.6 Fermi `(R_0=1.40xx10^(-13)cm)` is

Options

A. 61
B. 37
C. 27
D. 64

Answer

To find the mass number of an atom whose nucleus has a radius of 5.6 Fermi, we can follow these steps:

### Step-by-Step Solution:

1. **Convert the Radius from Fermi to Centimeters**:
- Given that 1 Fermi (Fm) = \(10^{-13}\) cm, we can convert the radius:
\[ r = 5.6 \text{ Fermi} = 5.6 \times 10^{-13} \text{ cm} \]

2. **Use the Given Value of \(R_0\)**:
- The value of \(R_0\) is given as \(1.40 \times 10^{-13}\) cm.

3. **Understand the Relationship Between Radius and Mass Number**:
- The radius of the nucleus is related to the mass number \(A\) by the formula:
\[ r = R_0 \cdot A^{1/3} \]
- Rearranging this gives:
\[ A^{1/3} = \frac{r}{R_0} \]

4. **Substitute the Values into the Equation**:
- Substitute \(r\) and \(R_0\) into the equation:
\[ A^{1/3} = \frac{5.6 \times 10^{-13}}{1.40 \times 10^{-13}} \]

5. **Calculate the Ratio**:
- Calculate the ratio:
\[ A^{1/3} = \frac{5.6}{1.40} = 4 \]

6. **Cube Both Sides to Find \(A\)**:
- To find \(A\), cube both sides:
\[ A = 4^3 = 64 \]

7. **Conclusion**:
- The mass number \(A\) of the atom is 64.

### Final Answer:
The mass number of the atom is **64**.