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(Understanding the fission process) Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into two or more smaller nuclei, along with the release of a large amount of energy and several neutrons. This process is triggered when the nucleus of a fissionable material, such as uranium-235 or plutonium-239, absorbs a neutron, which causes it to become unstable and split.

(Understanding neutron multiplication and chain reactions) During the fission process, several neutrons are released, each of which has the potential to be absorbed by another fissionable nucleus and cause it to undergo fission, releasing even more neutrons. This is known as neutron multiplication. If the number of neutrons released in each fission event is enough to induce fission in at least one other nucleus, a chain reaction can occur, leading to a self-sustained release of energy as long as there are enough fissionable nuclei present.

(Explaining the concept of critical mass) The term "critical mass" refers to the minimum amount of fissionable material that must be present in a sample for a nuclear chain reaction to be self-sustaining. This value depends on the shape and density of the material, as well as the presence of any neutron reflectors or absorbers. The critical mass is the point at which the loss of neutrons due to various mechanisms, such as escape from the sample or non-fission absorption, is equal to the number of neutrons produced through fission events, allowing the chain reaction to continue indefinitely.

(Can a chain reaction occur when a sample has less than the critical mass?) When the amount of fissionable material in a sample is less than the critical mass, it is considered "subcritical". In a subcritical mass, the number of neutrons produced through fission events is not sufficient to replace the losses and sustain a continuous chain reaction. While individual fission events may still occur, the reaction will not self-sustain and will eventually die out due to a lack of sufficient neutrons. In conclusion, fissionable material possesses a critical mass when there is enough material present to sustain a nuclear chain reaction. A chain reaction can not occur when a sample has less than the critical mass, as the number of neutrons produced will not be sufficient to keep the reaction going indefinitely.