A solid sphere of a fissile isotope is assembled in a laboratory glove-box under standard atmospheric conditions. Engineers can vary the sphere’s radius while keeping the density of the material constant.
In all of the following parts, assume no external neutron absorbers are present and that temperature effects on density are negligible.
(a) Describe qualitatively what is meant by the term "critical mass" for the sphere and explain how it relates to the concept of a self-sustaining chain reaction.
(b) As the radius of the sphere increases, explain how the relative importance of neutron leakage through the surface versus neutron production inside the volume changes. Your answer should reference geometric considerations without the use of numerical calculations.
(c) Using your reasoning from part (b), predict whether doubling the radius of the sphere would more than double, exactly double, or less than double the likelihood that the sphere becomes critical. Justify your prediction.
(d) An engineer proposes compressing the sphere so that its density increases while its mass remains constant. Explain qualitatively how this compression could move the assembly from a sub-critical to a critical state.