Calculate the energy of an a-particle if in a collision of this particle with gold nucleus, the distance of closest approach is `4.95 xx 10^(-12)` m.

Explanation

To calculate the energy of an alpha particle when it collides with a gold nucleus at a distance of closest approach of \(4.95 \times 10^{-12}\) m, we can use the formula derived from electrostatics. The energy (kinetic energy) of the alpha particle can be expressed in terms of the distance of closest approach (D) and the charges involved.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The formula for the distance of closest approach \(D\) in terms of kinetic energy \(K\) is given by:
\[
D = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2e \cdot Ze}{K}
...