Chain reactions and critical mass

Take a look at the equation for the fission of uranium-235 (U-235):

Notice that one neutron is used, but three are produced.  These three neutrons, if they encounter other U-235 atoms, can initiate other fissions, producing even more neutrons. It’s the old domino effect — or in terms of nuclear chemistry, it’s a continuing cascade of nuclear fissions called a chain reaction. Figure 1.1 shows the chain reaction of U-235.

Figure 1.1: Chain reaction.

A chain reaction depends on the release of more neutrons than are used during the nuclear reaction. If you were to write the equation for the nuclear fission of U-238, the more abundant isotope of uranium, you’d use one neutron and get only one back out. So you can’t have a chain reaction with U-238.

But isotopes that produce an excess of neutrons in their fission support a chain reaction. This type of isotope is said to be fissionable, and only two main fissionable isotopes are used during nuclear reactions: U-235 and plutonium-239 (Pu-239). Critical mass is the minimum amount of fissionable matter you need to support a self-sustaining chain reaction. That amount related to those neutrons. If the sample is small, then the neutrons are likely to shoot out of the sample before hitting a U-235 nucleus. If they don’t hit a U-235 nucleus, no extra electrons and no energy are released. The reaction just fizzles. Anything less than the critical mass is called subcritical.