### Nuclear Chain Reaction and Critical Mass

A nucleus in the middle emits a neutron in a random direction, if it hits another nucleus it is absorbed, that hit nucleus emits two neutrons and dies.

A full chain reaction, involving essentially all the nuclei, is much more likely to occur with a bigger piece of material. In real life, with trillions of trillions of nuclei (at least) there is a precise critical size (for a given shape) at which the reaction "goes critical" and explodes.

With our far smaller grids the random fluctuations are large, so we can just get the general idea. For the smallest grid, you'll find most times not much happens. For the largest grid, almost all the nuclei will explode. (The number of exploded nuclei is the black number at bottom left of the grid picture, the red number is survivors.) Try it a few times with different grid sizes! The initial neutron has random direction, so you'll get different results each time, even for the same grid, but the general trend with grid size is clear.

Hint: You'll get a clearer picture of what's going on if you activate "Trace Paths".

The mean free path is how far the neutron gets on average before hitting another nucleus. Roughly it's the inverse of the ratio of the nuclear size (the 'cross section") to the atom size (meaning distance between nuclei). This is how many rows of atoms the neutron will get through, on average, before it hits a nucleus. For a real neutron in uranium, for example, the cross section of the nucleus is (now two-dimensional) about a billionth the size of the atom, so the neutron can go through a billion rows (actually planes, in 3D) or so of atoms, and the distance between planes is of order one-third of a nanometer, so the mean free path is of order tens of centimeters. This gives the scale of size needed for a successful chain reaction. Many more details in Wikipedia at Critical Mass.

Code by Atallah Hezbor