a. What role does a neutron serve in starting a nuclear chain reaction and in keeping it going? b. Why must neutrons in a chain reaction be controlled? c. Why must there be a minimum mass of material in order to sustain a chain reaction?

Neutrons are fundamental particles that do not possess an electric charge, making them key players in the process of nuclear fission. Their neutrality allows them to penetrate the nuclei of certain atoms without being repelled, as they would be if they carried a charge. In a nuclear chain reaction, a neutron initiates the fission process when it collides with a fissile atom, such as Uranium-235 or Plutonium-239. Upon impact, the nucleus of the fissile atom captures the neutron and becomes unstable, leading it to split into two smaller atoms known as fission fragments.

This fission also releases a tremendous amount of energy and, crucially, additional neutrons. These newly-released neutrons can then collide with other fissile atoms, causing further fission events. It is this sequence of rapidly occurring fissions that constitutes a chain reaction. The neutron's role in both starting and perpetuating the nuclear chain reaction is why its behavior is a subject of such intense study and careful control in nuclear physics and reactor design.

While the propagation of a chain reaction is what makes nuclear reactors possible, this process must be closely regulated to avoid an exponential increase in fission events, which could lead to overheating, radiation release, or in the worst case, a nuclear explosion. This regulation is known as neutron control and is a critical aspect of nuclear reactor safety.

To achieve neutron control, nuclear reactors use materials called control rods. These rods, made from elements like boron, cadmium, or hafnium, are capable of absorbing excess neutrons without undergoing fission themselves. By adjusting the insertion depth of control rods into the nuclear reactor core, operators can control the number of free neutrons that are available to continue the chain reaction, thus regulating the power output. The careful balancing act of absorbing just enough neutrons to keep the reaction steady is what keeps a nuclear reactor in a 'critical' state, as opposed to 'subcritical' which would shut the reaction down, or 'supercritical' which would make it uncontrollable.

The existence of a 'critical mass' is essential for a sustained nuclear chain reaction to occur. Essentially, critical mass is the smallest amount of fissile material needed to maintain a chain reaction at a constant rate. If the amount of material is less than the critical mass, the reaction will not be self-sustaining, as too many of the free neutrons will escape into the surrounding environment without contributing to further fission events.

The critical mass depends on several factors, including the shape and density of the material, and the presence of a neutron reflector which can bounce escaping neutrons back into the fissile material. The concept of critical mass is why nuclear reactors and weapons have precise engineering specifications to ensure that the mass and arrangement of fissile material can sustain a controlled or, for weapons, a rapidly uncontrollable chain reaction.