Question

In the nuclear fusion reaction, ${}_1^{2}H{+}_1^{3}H{\to }_2^{4}He$ $+n$ given that the repulsive potential energy between the two nuclei is $7.7\times {10}^{-14}J$, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann's constant $k=1.38\times {10}^{-23}J/K$]

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

Answer 1

The correct option is D ${10}^{9}K$

To initiate the reaction, the energy of the gas molecules must be equal to the repulsive potential energy.

We know that the kinetic energy of translation per molecules is given by:

$K.E.=\frac{3}{2}kT$

In order to initiate the fusion reaction,

$\frac{3}{2}kT=7.7\times {10}^{-14}J$

$⟹T=\frac{2\times 7.7\times {10}^{-14}}{3\times 1.38\times {10}^{-23}}\approx 3.7\times {10}^{9}K$