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

Answer 1

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

Kinetic energy of molecules of a gas at a temperature T is $\frac{3}{2}kT$
$\therefore$ To initiate the reaction $\frac{3}{2}kT=7.7\times {10}^{-14}J\Rightarrow T=3.7\times {10}^{9}K$.