Atomic number of Iodine is 53 and its mass number is 125. Radius of iodine is approximately. `(R_0 = 1.2 xx 10^(-15) m)`

Options

A. `6xx10^(-5)` m
B. `6xx10^(-11)` m
C. `6xx10^(-15)` m
D. `6xx10^(-18)` m

Answer

To find the radius of iodine given its atomic number (Z = 53) and mass number (A = 125), we can use the formula for the radius of a nucleus:

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

where \( R_0 \) is a constant approximately equal to \( 1.2 \times 10^{-15} \) m, and \( A \) is the mass number.

### Step-by-Step Solution:

1. **Identify the mass number (A)**:
- From the problem, the mass number of iodine is given as \( A = 125 \).

2. **Use the formula for nuclear radius**:
- The formula for the radius of a nucleus is:
\[ R = R_0 A^{1/3} \]

3. **Substitute the values into the formula**:
- We know \( R_0 = 1.2 \times 10^{-15} \) m and \( A = 125 \).
- Substitute these values into the formula:
\[ R = 1.2 \times 10^{-15} \times (125)^{1/3} \]

4. **Calculate the cube root of 125**:
- The cube root of 125 is \( 5 \) (since \( 5^3 = 125 \)).
- Therefore, we can simplify the equation:
\[ R = 1.2 \times 10^{-15} \times 5 \]

5. **Perform the multiplication**:
- Now, calculate \( 1.2 \times 5 = 6.0 \).
- Thus, we have:
\[ R = 6.0 \times 10^{-15} \text{ m} \]

6. **Final Result**:
- The approximate radius of iodine is:
\[ R \approx 6.0 \times 10^{-15} \text{ m} \]

### Conclusion:
The radius of iodine is approximately \( 6.0 \times 10^{-15} \) meters.

---