92U²³⁵ + ₀n¹ ® [₉₂U²³⁶]* ® ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3₀n¹

The  reaction  shown above is one of the many reactions  that  take place in fission reaction involving U²³⁵. In any such fission reaction the  total  mass  of  fission products  is less than that of the reactants.  The energy equivalent of this mass difference appears as  kinetic energy (KE)  of  the fragments and the neutrons. Release of g rays, b - particles  and  neutrinos  also takes place. The neutron which are produced, alongwith the reaction (within~ 10-14 s) are called prompt  neutrons. Their kinetic energy goes upto 15 MeV, with most probable value near 1 MeV.The mass ratio of fission fragments is approximately 1.5.

The  fragments  produced  are  generally  unstable, being neutron rich. They undergo further decay producing delayed neutrons (0.05 s to 56 s after the reaction).

Approximately  200 MeV  is  produced  in a complete fission reaction. The average number of neutrons is 2.5 out of which < 1% neutrons are delayed neutrons.

Bohr  and  Wheeler  have  given a theory of nuclear fission, based on the liquid drop model*. The stable nucleus is analogous with  a  charged spherical drop of an incompressible liquid. The nucleus  is  in  equilibrium  as a  result  of  balance between attractive  strong nuclear forces and the Coulomb repulsive forces between  the protons.  The  capture  of  neutrons by the nucleus produces  mechanical  vibrations which  causes distortion in its shape, as  a result of which the nucleus breaks. The theory gives the  values of minimum energy, Ed required to induce fission. Ed for U²³⁵ is 5.4 MeV. The binding energy released when U²³⁵ absorbs a  neutron is 6.2 MeV. Therefore fission is induced in U²³⁵ with neutrons having  very  small  kinetic energy  (~ 0.04 eV, known  as  thermal neutron). In case of U²³⁸, the value of E_d is 5.9 MeV. The binding energy  of  a  neutron  in  U²³⁹  formed  from  U²³⁸  is 5.2 MeV. Therefore the incident neutron must have at least 0.7 MeV in order to induce fission in U²³⁸. It is observed experimentally that fast neutron > 1.2 MeV have high probability of inducing fission in U238.

Chain  reaction  :The promt neutrons produced in a fission reaction can induce further fission in a mass of uranium. The atoms of U²³⁸ are 140 times more numerous than that of U²³⁵ in natural uranium. It may be possible for a self sustained chain reaction to occur as soon as one fission takes place. However only few neutrons cause further fission out of the neutrons initially above the U²³⁸ threshhold; most of them lose energy quickly through inelastic scattering process. As the neutrons approach thermal energies, fission of U²³⁵ assumes importance. At energy of 6.7 eV, U²³⁸ nuclei absorb neutrons forming U²³⁹. This resonant absorption process depletes the number of neutrons preventing the continuation of chain reaction. The escape of neutrons from the surface is another important cause of neutron loss.

The following steps are necessary to have a self sustaining chain reaction.

(i) The material must be enriched in U²³⁵. This process is carried out by converting uranium to uranium hexafluoride, a  gas.This  is  allowed to diffuse through a pourous membrane. Hexaflouride of U²³⁵ will diffuse faster      because  of its lighter mass. This has be done several times  over because  the  mass difference between U²³⁵ and U²³⁸ is only 3 parts in 238.

(ii) The surface loss is to be minimized by increasing the size. The  number of fissile nuclei increase as r3 (being proportional to  volume) while surface loss increases as r2. Beyond a critical size the chain reaction will be sustainable.

In  an  atom  bomb  the  chain reaction is uncontrolled. Two masses of uranium highly enriched in U²³⁵, and less than the critical  size  are brought rapidly together. Within very short time chain reaction builds up producing violent explosion.

The  nuclear reactor : In a nuclear reactor the chain reaction is sustained  in  a controlled manner, and the heat produced is used to  drive generators.  As  a biproduct radioactive nuclides are obtained  which  find applications  in medicine, agriculture and industry.

The  condition  that  must be satisfied in a sustained chain reaction  is that  on an average, at least one neutron produced from   a   fission  should induce  another  fission.  We  define reproduction factor, k as the ratio of number of neutrons in any one generation to the number of neutrons in the immediate preceding generation. The value of k must be maintained slightly greater than unity.

The  reactor fuel is natural uranium (consisting of U²³⁵ and U²³⁸) or or slightly enriched uranium. The losses due to non fission capture of fast neutrons (kinetic energy 2 MeV), by U²³⁸ is reduced by use of moderator, a material composed of light nuclei. Collision of fast neutrons with light nuclei brings down their kinetic energy most effectively (see discussion under elastic collision). Deuterium in the form of heavy water (D₂O) is widely used as moderator in the present day reactors. The lightest nuclei , that of hydrgen is a gas at normal temperatures, and therefore is not suitable. Hydrgen in the form of water is also not suitable as it has a large capture cross section for neutrons. Carbon in the form of graphite is also used but it should be extremely pure to avoid neutron capture by contaminants. From the point of view of fire hazards, heavy water has natural advantage.

The  reactor  design  must  also ensure that at no stage the chain reaction  should become  uncontrollable  (over critical). Strips  or  rods  of cadmium called control rods are inserted in suitable  places  as  a  safety measure. Cadmium has a very high absorption  cross section for slow neutrons. The control rods are carefully withdrawn in order to make the reactor critical i.e. to have sustained and controlled chain reaction.