ABSTRACT
(a) The existence of a critical mass below which a self-sustaining chain reaction is not possible is an example of the 'square-cube law'. The fraction of fission neutrons which escape across the surface of a lump of fissionable material can be reduced by increasing the size of the lump since the rate of production is proportional to the volume (R3) whilst the rate of escape is proportional to the area (R2). At the critical mass on average each fission gives rise to an extra fission which is the condition for a self-sustaining chain reaction. A spherical lump minimises the critical mass as a sphere minimises the surface area to volume ratio.
