Atoms And Nuclei Question 347
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- $ \sim 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 $ ]
Options:
A) $ 10^{7}K $
B) $ 10^{5}K $
C) $ 10^{3}K $
D) $ 10^{9}K $
Show Answer
Answer:
Correct Answer: D
Solution:
- average kinetic energy per molecule
$ =\frac{3}{2}kT $
This kinetic energy should be able to provide the repulsive potential energy
$ \therefore \frac{3}{2}kT=7.7\times {{10}^{-14}} $
$ \Rightarrow ,T=\frac{2\times 7.7\times {{10}^{-14}}}{3\times 1.38\times {{10}^{-23}}}=3.7\times 10^{9}K $
