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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
The temperature T to which gases must be heated should provided energy sufficient to overcome the repulsive potential energy between the two nuclei.
As K.E. of translation/molecule=`3/2kT`
`:. 3/2kT+3/2kT`=repulsive P.E.
`3kT=7.7xx10^(-14)`
`T=(7.7xx10^(-14))/(3k)=(7.7xx10^(-14))/(3xx1.38xx10^(-23))`
`T=1.85xx10^(9)K~=10^(9)K`
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