### Theory:

Fissionable materials:
A fissionable material or a fissile material is a radioactive element, which undergoes fission in a sustained manner when it absorbs a neutron.
Example:
Uranium nucleus ($$U^{235}$$)

Uranium nucleus

Plutonium ($$Pu^{239}$$ and $$Pu^{241}$$)

Plutonium nucleus
When a neutron is absorbed by a uranium isotope, it is not essential for the isotope to undergo nuclear fission.

Natural uranium consists of $$99.28$$ $$\%$$ of $$_{92}U^{238}$$ and $$0.72$$ $$\%$$ of $$_{92}U^{235}$$. Out of these two, $$U^{238}$$ does not undergo fission, whereas $$U^{235}$$ undergoes fission. Hence, $$U^{235}$$ is a fissionable material, and $$U^{238}$$ is non-fissionable material.

Fertile materials:
Fertile materials are radioactive elements that are converted into fissionable materials.
Example:
Uranium ($$U^{238}$$)
Thorium ($$Th^{232}$$)
Plutonium ($$Pu^{240}$$)
Critical mass:
Generally, two to three neutrons are released in a nuclear fission process. However, not all of these neutrons may continue fission. Some of the neutrons may escape the system, causing a neutron leakage, while others may be absorbed by the non-fissionable materials in the system. As a result of these two factors, neutrons are lost.

The rate of neutron generation from nuclear fission must be greater than the rate of neutron loss to maintain the chain reaction. The reaction can be accomplished only when the size or mass of the fissionable material is maintained equal to a particular optimum value, which is known as critical mass.
The minimum mass of a fissile material required to sustain the chain reaction is called 'critical mass ($$m_c$$)'. It depends on the nature, density and size of the fissile material.

If the mass of the fissile material is less than the critical mass, it is termed as 'subcritical'. If the mass of the fissile material is more than the critical mass, it is termed as 'supercritical'.
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