Q. In the nuclear fusion reaction $_{1}^{2}H +_{1}^{3}H \rightarrow_{2}^{4}{He} + n$ 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 $k = 1.38\ \times 10^{- 23}\ JK^{- 1}$]
A) $10^{7}\ K$
B) $10^{5}\ K$
C) $10^{3}\ K$
D) $10^{9}\ K$
Explanation
(d) $\frac{3}{2}kT\ = \ 7.7\ \times \ 10^{- 14}\ J$
T = $\frac{2\ \times 7.7\ \times 10^{- 14}}{3\ \times \ 1.38\ \times 10^{- 23}} = \ 3.7\ \times \ 10^{9}\ K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.