Question 339: Atoms & Nuclei

Question

In the nuclear fusion reaction 
$$${}_1^2H + {}_1^3H 	o {}_2^4He + n$$$
given that the repulsive potential energy between the two nuclei is $$ \sim 7.7 	imes {10^{ - 14}}J$$, the temperature at which the gases must be heated to initiate the reaction is nearly 
[ Boltzmann's Constant $$k = 1.38 	imes {10^{ - 23}}\,J/K$$ ]

Accepted Answer

The average kinetic energy per molecule $$ = {3 \over 2}kT$$
This kinetic energy should be able to provide the repulsive potential energy
$$	herefore$$ $${3 \over 2}kT = 7.7 	imes {10^{ - 14}}$$
$$ \Rightarrow T = {{2 	imes 7.7 	imes {{10}^{ - 14}}} \over {3 	imes 1.38 	imes {{10}^{ - 23}}}} = 3.7 	imes {10^9}$$

Answer

$${10^7}\,\,K$$

Answer

$${10^5}\,\,K$$

Answer

$${10^3}\,\,K$$

Answer

$${10^9}\,\,K$$

Atoms & Nuclei

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