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Question

(A) To initiate a nuclear fusion reaction, the kinetic energy of the nuclei must be sufficient to overcome the repulsive electrostatic potential energ

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$10^9 \,K$

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(A) To initiate a nuclear fusion reaction, the kinetic energy of the nuclei must be sufficient to overcome the repulsive electrostatic potential energy barrier.According to the kinetic theory of gases, the average kinetic energy of a particle at temperature $T$ is given by $E = \frac{3}{2} kT$, where $k$ is the Boltzmann constant.Equating the kinetic energy to the potential energy barrier $U = 2.07 	imes 10^{-14} \,J$:$\frac{3}{2} kT = U$$T = \frac{2U}{3k}$Substituting the given values:$T = \frac{2 	imes 2.07 	imes 10^{-14}}{3 	imes 1.38 	imes 10^{-23}}$$T = \frac{4.14 	imes 10^{-14}}{4.14 	imes 10^{-23}}$$T = 10^9 \,K$Therefore, the required temperature is $10^9 \,K$.

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