In Rutherford scattering experiment, if a proton is taken instead of an alpha particle, then for same distance of closest approach, how much K.E. in comparison to K.E. of a particle will be required?

Explanation

To solve the problem, we need to analyze the relationship between the kinetic energy (K.E.) of alpha particles and protons in the context of Rutherford's scattering experiment, particularly focusing on the distance of closest approach.

### Step 1: Understand the Charges Involved
- The charge of an alpha particle is \(2E\) (since it consists of 2 protons).
- The charge of a proton is \(E\).

### Step 2: Write the Formula for Distance of Closest Approach
The distance of closest approach \(R\) for a charged particle can be derived from the electrostatic force and the kinetic energy. The formula for the distance of closest approach \(R_0\) for an alpha particle is given by:
...