What is a nuclear chain reaction? Explain the difficulties and their removal for its successful operation.

(N/A) nuclear chain reaction is a process where neutrons released from the fission of one nucleus trigger further fission events in other nuclei,leading to a self-sustaining series of reactions.
On average,$2.5$ neutrons are released per fission of a ${ }_{92}^{235} U$ nucleus. These extra neutrons can initiate further fission processes.
If the chain reaction is uncontrolled,it leads to an explosive energy release,as in a nuclear bomb. If controlled,the energy can be harnessed for power generation in a nuclear reactor.
Difficulties and their removal:
$(i)$ Fast neutrons are less likely to cause fission in ${ }_{92}^{235} U$ and tend to escape the reactor. To solve this,a moderator is used to slow down the neutrons. Materials like water,heavy water $(D_2O)$,and graphite are used as moderators. They slow down fast neutrons through elastic scattering,making them more effective at inducing fission.
$(ii)$ The multiplication factor $K$ (ratio of fissions in one generation to the preceding one) must be maintained at $K=1$ for a steady,critical state. If $K > 1$,the reactor becomes supercritical,leading to an exponential power increase. If $K < 1$,the reaction dies out. Control rods (e.g.,cadmium or boron) are used to absorb excess neutrons and maintain $K=1$.