In the nuclear fusion reaction `""_(1)^(2)H+""_(1)^(3)Hto""_(2)^(4)He+""_(0)^(1)n`, given that the repulsive potential energy between the two nuclei is `-7.7xx10^(14)J`. The temperature at which the gases must be heated to initiate the reaction is nearly, [Boltzmann's constant, `k=1.38xx10^(23)J//K`]

Options

A. `10^(7) K`
B. `10^(5) K`
C. `10^(3) K`
D. `10^(9) K`

Answer

D

Explanation

In order to fuse two nuclei against repulsion, the repulsive potential energy has to be supplied by kinetic energy i.e.,
`PE = KE rArr 7.7 xx 10^(-14) = (3)/(2) kT`
`rArr 7.7 xx 10^(-14) = (3)/(2) xx 1.38 xx 10^(-23)T`
`rArr T = 3.7 xx 10^(9) k`