Question

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 $k = 1.38 \times 10^{- 23}J ⥂ / ⥂ K$]

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

Answer 1

Answer: (A)

$10^{9}K$

Answer 2

Kinetic energy of molecules of a gas at a temperature T is 3/2 kT

∴ To initiate the reaction $\frac{3}{2}kT = 7.7 \times 10^{- 14}J$

⇒ T = 3.7 × 10⁹ K.