Scientists are working hard to develop nuclear fusion reactor. Nuclei of heavy hydrogen , $_{1}H$ , known as deuteron and denoted by D, can be thought of as a candidate for fusion reactor , The D-D reaction is $_{1}H+_{1}H→_{2}He+n$+energy. In the core of fusion reactor , a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of $_{(1)}H$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nulear fusion to take place. Usually , the temperature in the reactors core are too high and no material wall can be used to confine the plasma . Special techniques are used which confine the plasma for a time $t_{0}$ before the particles fly away from the core. If n is the density (number/volume) of deuterons, the product $nt_{0}$ is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater than $5×10_{14}s/cm_{3}$.

If may be helpful to use the following: Boltzmann constant $k=8.6×10_{−5}eV/K,4πϵ_{0}e_{2} =1.44×10_{−9}eVm$.

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other , each with kinetic energy 1.5 kT , when the separation between them is large enough to neglect Coulomb potential energy . Also neglect any interaction from other particles in the core . The minimum temperature T required for them to reach a separation of $4×10_{−15}$ m is in the range