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

The average kinetic energy per molecule = `(3)/(2)` kT
This kinetic energy should be able to provide the repulsive potential energy
`therefore (3)/(2) kT = 7.7 xx 10^(-14)`
`implies T = (2 xx 7.7 xx 10^(-14))/(3 xx 1.38 xx 10^(-23)) = 3.7 xx 10^(9)`