An `alpha`- particle moving with initial kinetic energy K towards a nucleus of atomic number z approaches a distance 'd' at which it reverse its direction. Obtain the expression for the distance of closest approach 'd' in terms of the kinetic energy of ` alpha`- particle K.

Explanation

To find the distance of closest approach \( d \) for an alpha particle moving towards a nucleus of atomic number \( z \) with initial kinetic energy \( K \), we can use the conservation of energy principle. Here’s a step-by-step solution:

### Step 1: Understand the System
An alpha particle has a charge of \( +2e \) and is approaching a nucleus with charge \( +Ze \) (where \( Z \) is the atomic number of the nucleus). As the alpha particle approaches the nucleus, it experiences a repulsive electrostatic force due to the positive charges.

### Step 2: Initial Conditions
At a large distance (effectively at infinity), the potential energy is zero, and the kinetic energy of the alpha particle is \( K \):
\[
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