JEE Main & Advanced Physics Nuclear Physics And Radioactivity Difficulties in Chain Reaction          

In chain reaction following difficulties are observed

(1) Absorption of neutrons by \[{{U}^{238}}\]: the major part in natural uranium is the isotope \[{{U}^{238}}\] (99.3%), the isotope \[{{U}^{235}}\] is very little (0.7%). It is found that \[{{U}^{238}}\] is fissionable with fast neutrons, whereas \[{{U}^{235}}\]is fissionable with slow neutrons. Due to the large percentage of \[{{U}^{238}},\] there is more possibility of collision of neutrons with \[{{U}^{238}}\]. It is found that the neutrons get slowed on coliding with \[{{U}^{238}},\] as a result of it further fission of \[{{U}^{238}}\] is not possible (Because they are slow and they are absorbed by \[{{U}^{238}}\]). This stops the chain reaction.

Removal : (i) To sustain chain reaction \[_{92}{{U}^{235}}\] is separated from the ordinary uranium. Uranium so obtained \[\left( _{92}{{U}^{235}} \right)\] is known as enriched uranium, which is fissionable with the fast and slow neutrons and hence chain reaction can be sustained.

(ii) If neutrons are slowed down by any method to an energy of about 0.3 eV, then the probability of their absorption by \[{{U}^{238}}\] becomes very low, while the probability of their fissioning \[{{U}^{235}}\] becomes high. This job is done by moderators. Which reduce the speed of neutron rapidly graphite and heavy water are the example of moderators.

(2) Critical size : The neutrons emitted during fission are very fast and they travel a large distance before being slowed down. If the size of the fissionable material is small, the neutrons emitted will escape the fissionable material before they are slowed down. Hence chain reaction cannot be sustained.

Removal : The size of the fissionable material should be large than a critical size.

The chain reaction once started will remain steady, accelerate or retard depending upon, a factor called neutron reproduction factor (k). It is defined as follows.

\[k=\frac{\text{Rate of production of neutrons}}{\text{Rate of loss of neutrons}}\]

If k = 1, the chain reaction will be steady. The size of the fissionable material used is said to be the critical size and it's mass, the critical mass.

If \[k>1\], the chain reaction accelerates, resulting in an explosion. The size of the material in this case is super critical. (Atom bomb)  

If \[k<1\], the chain reaction gradually comes to a halt. The size of the material used us said to be sub-critical.  

Types of chain reaction