Final answer:
The correct relationship for the temperature necessary for nuclear fusion to occur, where the potential energy between two nuclei equals the thermal kinetic energy, is E = kT, where E is the energy, T is the temperature, and k is the Boltzmann constant. Therefore, the correct option is A.
Step-by-step explanation:
The question pertains to the temperature necessary for nuclear fusion to occur, which relates the repulsive potential energy between two nuclear particles with the thermal kinetic energy. This thermal kinetic energy of the nuclei in a gas can be approximately described by the Boltzmann constant (k) and the temperature (T) of the system.
According to physical principles, the average kinetic energy of a particle of gas (E) is directly proportional to the temperature (T) and the Boltzmann constant (k), leading to the relationship E = kT. Thus, the correct answer to the student's question is: In the nuclear fusion reaction given that the repulsive potential energy between the two nuclei U and V is nearly E, if T is the temperature in Kelvin to which the given gases must be heated to initiate the reaction, then E = kT.