Question

In the nuclear fusion reaction,

${}_1{\text{H}}^2{+}_1{\text{H}}^3{\to }_2{\text{He}}^4{+}_0{n}^1$

The repulsive potential energy between the two fusing nuclei is $7.7\times {10}^{-14}\text{J}$. The temperature to which the gas must be heated is nearly
$(\text{Boltzmen constant}K=1.38\times {10}^{-23}{\text{JK}}^{-1})$

• A. ${10}^3\text{K}$
• B. $3.7\times {10}^5\text{K}$
• C. ${10}^7\text{K}$
• D. $3.7\times {10}^9\text{K}$

Answer 1

The correct option is D $3.7\times {10}^9\text{K}$

The thermal kinetic energy of the nuclei is utilized to overcome the repulsive potential energy,

$\Rightarrow K.E_T=P.E$

We know that, $K.E_T=\frac{3}{2}KT$

$\Rightarrow \frac{3}{2}\times 1.38\times {10}^{-23}T=7.7\times {10}^{-14}$

$\Rightarrow T=\frac{2\times 7.7}{3\times 1.38}\times {10}^9\text{K}$

$T=3.7\times {10}^9\text{K}$

Hence, option $\left(D\right)$ is correct.

Why this question? To know the temperature range at which the fusion reaction takes places.