is the minimum amount of a substance
that is needed to sustain a reaction
. This amount can vary based on how it is shape
and the density
of the substance. When a reaction
occurs it emit
that are capable of producing more reactions but only if they collide
with more atoms. Higher probability
of a collision means more collisions
which is a more efficient
When a reaction starts an atom
is split and neutrons are emitted. Optimally, all neutrons hit other atoms because if they do not then the overall reaction is less efficient because time
emphasizes these errors as shown in the second table. If an atom is completely surrounded by other atoms when it gets split then its neutrons have a 100% chance
of hitting more atoms. A 100% chance means no waste, at least for that particular atom. If an atom is on the surface
of the mass
then its neutrons have a chance to go away from the mass and not produce another reaction. If it is within the mass they are forced to react with more atoms because no matter what direction they go in they cannot avoid splitting an atom. This means that we want to minimize the mass's surface area and maximize its volume which is controlled by the shape of the mass.
Some shapes have excellent surface area to volume
ratios. Here are calculations for the surface area of various shapes given 1000 volume:
As you can see a sphere is by far the best, only about 1% of the volume is exposed to the surface. This is because spheres only have one surface and no corners. Also consider that a sphere cannot be tangent to a plane at more than one point, plane
s being the worst for SA:V ratios. Sphere
s produce better reactions because they have the smallest surface area to volume ratio.
The last factor
that controls critical mass is density
. When the density of the mass is increased, the neutrons cannot go as far without colliding so it makes the chain reaction faster. Critical mass is just enough mass to make the reaction continue
happening. If the best shape and highest density is used then the quantity of mass required for a sustained reaction or the critical mass is lessened.
Here is a table illustrating how fast the total reaction is going with different quantities of successful (colliding) neutrons:
2 3 4
1| 2 3 4
2| 4 9 16
3| 8 27 64
4| 16 81 256
5| 32 243 1024
The smaller the number of successful reactions the more dramatic
the results are later on. In practice
since it is determined by probability whether or not a collision fails to occur it is not this bad unless the probability is very low. The chain increases in total reactions exponentially
over time so the longer it has been going the worse the effect of a miss.
In summary, critical mass is the quantity of a substance needed to sustain a chain reaction and it is directly dependent upon the shape and density, and when these factors are manipulated correctly (spheres and high density) critical mass is lessened.