In a Geiger- Marsden experiment, calculate the distance of closest approach to the nucleus of Z=80, when an `alpha` particle of 8 Me V energy impinges on it before it comes momentarily to rest and reverses its direction.
How will the distance of closest approach be affected when the kinetic energy of the `alpha-` particle is doubled ?

Explanation

To solve the problem of calculating the distance of closest approach to the nucleus in a Geiger-Marsden experiment, we can follow these steps:

### Step 1: Understand the Concept
The distance of closest approach \( R_0 \) occurs when the kinetic energy of the alpha particle is completely converted into electrostatic potential energy due to the repulsion from the nucleus.

### Step 2: Write the Formula
The relationship between kinetic energy \( K \) and potential energy \( U \) at the closest approach can be expressed as:
\[
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