Physics · nuclei · NEET
When a U-235 nucleus absorbs a slow neutron, it splits (fission) and releases about 2 to 3 fresh neutrons plus a lot of energy. If these new neutrons hit other U-235 nuclei, they cause more fissions, which release even more neutrons. This self-repeating process is a chain reaction. It grows step by step: 1 fission gives ~3 neutrons, which give ~9, then ~27, and so on.
Critical mass is the minimum amount (mass) of fissile fuel needed to keep a chain reaction going on its own. If the fuel piece is too small, most neutrons escape from the surface before hitting another nucleus, and the reaction dies. A big enough piece (critical mass) makes sure that on average at least one neutron from each fission causes the next fission. Below critical mass the reaction stops; at or above it, the reaction is self-sustaining.
k is the ratio of neutrons in one generation to neutrons in the previous generation. If k = 1, the reaction is steady (critical) and just sustains itself, like in a reactor. If k is greater than 1 (supercritical), neutrons grow each step and the reaction runs away, as in a bomb. If k is less than 1 (subcritical), neutrons fall each step and the reaction dies out.
Neutrons are lost in two main ways: they escape through the surface, or they are absorbed without causing fission. In a small piece, the surface is large compared to the volume, so most neutrons escape before finding another nucleus. That means fewer than one neutron per fission causes a new fission, so k is less than 1 and the reaction stops. A larger mass gives neutrons more chance to be captured inside.
In a controlled chain reaction, k is kept exactly equal to 1 using control rods that absorb extra neutrons, so energy is released steadily. This is used in nuclear reactors to make electricity. In an uncontrolled chain reaction, k is greater than 1 and neutrons multiply very fast, releasing huge energy in a fraction of a second. This is what happens in an atom bomb.
On average about 2 to 3 neutrons are released per fission of Uranium-235, along with two lighter nuclei and around 200 MeV of energy.
A reactor needs k = 1 (critical). This gives a steady, controlled release of energy. Control rods adjust neutron numbers to keep k at exactly 1.
U-235 captures slow neutrons much more easily than fast ones. Fast neutrons often escape or are not absorbed, so a moderator is used to slow them down and keep the chain reaction going.
Yes. A sphere has the least surface area for a given volume, so it loses the fewest neutrons and needs the smallest critical mass. Flat or thin shapes lose more neutrons and need more mass.
Yes. Chain reaction, critical mass, and the ideas of controlled versus uncontrolled reactions are part of the Nuclei chapter and can be asked as short conceptual questions in NEET.
