Calculate the energy of an `alpha`-particle whose distance of closest approach with the gold nucleus is 29.5 fermi.

Explanation

To calculate the energy of an alpha particle whose distance of closest approach with the gold nucleus is 29.5 fermi, we can follow these steps:

### Step 1: Understand the Concept of Closest Approach
The distance of closest approach is the point at which the kinetic energy of the alpha particle is converted entirely into potential energy due to electrostatic repulsion from the gold nucleus.

### Step 2: Identify the Charges Involved
- The charge of the alpha particle (which consists of 2 protons) is \( Q_{\alpha} = 2e \).
- The charge of the gold nucleus (which has an atomic number of 79) is \( Q_{Au} = Ze = 79e \).
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