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

Answer

A

Explanation

(a) Kinetic energy of the molecules of a gas at a temp. `T` is.
So, to initiate the reaction, `(3)/(2) kT = 7.7 xx 10^-14 J`
`rArr (3)/(2) xx 1.38 xx 10^-23 T = 7.7 xx 10^-14 rArr T = 3.7 xx 10^9 K`.