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In the nuclear fusion reaction (1)^(2)...

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]`

A

`10^(7) K`

B

`10^(5) K`

C

`10^(3) K`

D

`10^(9) K`

Text Solution

Verified by Experts

The correct Answer is:
D
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`
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