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 $6.40\times 10^{-14}\text{ J}$. What temperature is needed?

Video Transcript

This is College Physics Answers with Shaun Dychko. This question gives us a sense of why nuclear fusion is a difficult technology to use in a electricity generation plant because the temperatures are so crazy high. If you want average kinetic energy of your hydrogen atoms to be 6.4 times 10 to the minus 14 joules, the temperature required will be given by this formula which says the average kinetic energy is three over two times Boltzmann's constant times the absolute temperature in Kelvin then we can solve for T by multiplying both sides by two over three times K. And we get that the temperature is two times the kinetic energy divided by three times the Boltzmann's constant. So that's two times 6.4 times 10 to the minus 14 joules divided by three times 1.38 times 10 to the minus 23 joules per gallon which is the temperature of 3.09 billion Kelvin.