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Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of 6.40×10^{-14} J . What temperature is needed? (answer in ×10^{9} K)

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boffeemadrid

Answer:

[tex]3.09\times 10^{9}\ K[/tex]

Explanation:

K = Kinetic energy of the fusion experiment = [tex]6.40\times 10^{-14}\ J[/tex]

k = Boltzmann constant = [tex]1.38\times 10^{-23}\ J/K[/tex]

T = Temperature of gas

Kinetic energy of a gas molecule is given by

[tex]K=\frac{3}{2}kT\\\Rightarrow T=\frac{2K}{3k}\\\Rightarrow t=\frac{2\times 6.40\times 10^{-14}}{3\times 1.38\times 10^{-23}}\\\Rightarrow T=3091787439.61352=3.09\times 10^{9}\ K[/tex]

The temperature which is needed is [tex]3.09\times 10^{9}\ K[/tex]

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