(A) Find the radius of nucleus of an atom having atomic mass number equal to `125. ("Take" R_(0)=1.3xx10^(-15) m)`

Explanation

To find the radius of the nucleus of an atom with an atomic mass number of 125, we can use the formula for the radius of a nucleus:

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

where:
- \( R \) is the radius of the nucleus,
- \( R_0 \) is a constant (given as \( 1.3 \times 10^{-15} \) m),
- \( A \) is the atomic mass number (given as 125).

### Step-by-Step Solution:

1. **Identify the given values**:
- Atomic mass number \( A = 125 \)
- Constant \( R_0 = 1.3 \times 10^{-15} \) m

2. **Substitute the values into the formula**:
\[ R = 1.3 \times 10^{-15} \cdot (125)^{1/3} \]

3. **Calculate \( (125)^{1/3} \)**:
- To find the cube root of 125, we can recognize that \( 125 = 5^3 \).
- Therefore, \( (125)^{1/3} = 5 \).

4. **Substitute back into the equation**:
\[ R = 1.3 \times 10^{-15} \cdot 5 \]

5. **Perform the multiplication**:
\[ R = 6.5 \times 10^{-15} \text{ m} \]

6. **Final answer**:
The radius of the nucleus of the atom is:
\[ R = 6.5 \times 10^{-15} \text{ m} \]