In the nuclear fusion reaction _1^2H + _1^3H | vedclass

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(A) The average kinetic energy of the molecules of a gas at temperature $T$ is given by $E = \frac{3}{2}kT$.To initiate the nuclear fusion reaction,th

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$10^9 \ K$

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(A) The average kinetic energy of the molecules of a gas at temperature $T$ is given by $E = \frac{3}{2}kT$.To initiate the nuclear fusion reaction,the kinetic energy of the nuclei must be sufficient to overcome the repulsive potential energy barrier.Equating the kinetic energy to the potential energy: $\frac{3}{2}kT = 7.7 	imes 10^{-14} \ J$.Substituting the value of Boltzmann's constant $k = 1.38 	imes 10^{-23} \ J/K$:$\frac{3}{2} 	imes (1.38 	imes 10^{-23}) 	imes T = 7.7 	imes 10^{-14}$.$2.07 	imes 10^{-23} 	imes T = 7.7 	imes 10^{-14}$.$T = \frac{7.7 	imes 10^{-14}}{2.07 	imes 10^{-23}} \approx 3.72 	imes 10^9 \ K$.Rounding to the nearest order of magnitude,the temperature is approximately $10^9 \ K$.

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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