Consider two deuterons moving towards each other with equal speeds in a deuteron gas. What should be their kinetic energies (when they are widely separated) so that the closest separation between them becomes `2 fm?` Assume that the nuclear force is not effective for separations greater than `2 fm`. At what temperature will the deuterons have this kinetic energy on an average?

Explanation

To solve the problem, we need to determine the kinetic energy of two deuterons moving towards each other such that their closest separation is \(2 \, \text{fm}\). We will also find the temperature corresponding to this kinetic energy.

### Step 1: Understanding the Problem
We have two deuterons, each with charge \(e\), moving towards each other. The closest separation they can reach is \(2 \, \text{fm}\). At this point, the kinetic energy will be converted into potential energy due to the Coulomb repulsion between the two positively charged deuterons.

### Step 2: Coulomb Potential Energy Calculation
The potential energy \(U\) at the closest separation can be calculated using the formula for Coulomb's law:
\[
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