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In the nuclear fusion reaction $_1^2H + _1^3H \to _2^4He + n,$ 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 $k = 1.38 \times {10^{ - 23}}J/K$ ]

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${10^9}K$

${10^7}K$

${10^5}K$

${10^3}K$

answer is A.

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Detailed Solution

Kinetic energy of the molecules of a gas at a temp. $T\,\,is\,\,\frac{3}{2}kT$

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

$\Rightarrow \frac{3}{2} \times 1.38 \times {10^{ - 23}}T = 7.7 \times {10^{ - 14}} \Rightarrow T = 3.7 \times {10^9}K$

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