In the nuclear fusion reaction
`_(1)^(2)H + _(1)^(3)H rarr _(2)^(4)He + n `
given that the repulsive potential energy between the two nuclei is `- 7.7 xx 10^(-14) J` , the temperature at which the gases must be heated the reaction is nearly
[Boltzmann's constant `k = 1.38 xx 10^(-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`