The probability of nuclear fusion is greatly enhanced when the appropriate nuclei are brought close together, but their mutual coulomb repulsion must be overcome. This can be done using the kinetic energy of high temperature gas ions or by accelerating the nuclei toward one another. Required:
a. Calculate the potential energy of two singly charged nuclei separated by 1.00×10^−12m
b. At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?

a

b

Explanation:

From the question we are told that

      The distance of separation is  

Generally the electric potential energy can be mathematically represented as

Given that in a nuclei the only charged particle is the proton who charge is

Hence

And k is the coulomb constant with values  

      So we have that

The relationship between the electrical potential energy and the temperature is mathematically represented as

Here  k is  the Boltzmann's constant with value  

   making T the subject

substituting values