Nuclear Physics And Radioactivity Question 56
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 $ ] [AIEEE 2003]
Options:
A) $ 10^{9}K $
B) $ 10^{7}K $
C) $ 10^{5}K $
D) $ 10^{3}K $
Show Answer
Answer:
Correct Answer: A
Solution:
Kinetic energy of the molecules of a gas at a temp. T is $ \frac{3}{2}kT $
$ \therefore $ To initiate the reaction $ \frac{3}{2}kT=7.7\times {{10}^{-14}}J $
$ \Rightarrow \frac{3}{2}\times 1.38\times {{10}^{-23}}T=7.7\times {{10}^{-14}}\Rightarrow T=3.7\times 10^{9}K $ .
BETA
