IIT JEE Nuclear Fission 

Nuclear fission is the process in which the nucleus of an atom breaks into smaller nuclei. These smaller nuclei are termed as fission products and when the fission reaction takes place some by products are also released. Fission may be termed as a form of elemental transmutation because the resulting element is not the same as the original element. Most fissions are binary fissions (producing two charged fragments), but occasionally (2 to 4 times per 1000 events), three positively charged fragments are produced, in a ternary fission. The smallest of these fragments in ternary processes ranges in size from a proton to an argon nucleus.

The by-products produced in the fission reaction may include free neutrons or photons in the form of gamma rays and other nuclear fragments such as beta or alpha particles. The process of fission of heavy elements is primarily an exothermic reaction which releases huge amount of useful energy. The released energy may be in the form of either gamma rays or kinetic energy. The energy released by nuclear fission may be used for nuclear power or to drive explosion of nuclear weapons.
The most typical fission reaction occurs when slow moving neutrons strike ₉₂U²³⁵. The following nuclear reaction takes place.

Nuclear Chain Reaction

If more than one of the neutrons produced in the above fission reaction is capable of inducing a fission reaction (provided U²³⁵ is available), then the number of fissions taking place at successive stages goes increasing at a very brisk rate and this generates a series of fissions. 

This is known as a nuclear chain reaction. The chain reaction takes place only if the size of the fissionable material (U²³⁵) is greater than a certain size called the critical size. 
₉₂U²³⁵ + ₀n¹ ——> ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3 ₀n¹ + 200 MeV
If the number of fission in a given interval of time goes on increasing continuously, then a condition of explosion is created. In such cases, the chain reaction is known as uncontrolled chain reaction. This forms the basis of atomic bomb.In a chain reaction, the fast moving neutrons are absorbed by certain substances known as moderators (like heavy water), then the number of fissions can be controlled and the chain reaction is such cases is known as controlled chain reaction. This forms the basis of a nuclear reactor.

Watch this Video for more reference
 

Neutron Cross – Section

The neutron cross- section for a particular reaction describes the probability of the occurrence of a neutron involved reaction like that of fission. The cross-section is basically an area that surrounds the nucleus and if the reaction is to occur, then the incoming neutron must pass through this area. As the velocity of the neutron reduces from around 20,000 km/s to 2 km/s, the fission and the related cross sections tend to increase. In nuclei with an odd-number of neutrons, such as U²³⁵, the fission cross-section becomes very large at the thermal energies of slow neutrons.

Problem 1:

When a beta particle is emitted from a nucleus the effect on its neutron-proton ratio is

(a) increased                   (b) decreased
(c) remains same             (d) first (1) then (2)

Solution:-

Since a beta particle is emitted from the nucleus, so we have, 

_ZX^A ——> _Z+1Y^A + _–1e⁰ (β) + v

₀n^t ——> ₁P¹ + _–1e⁰ (β) + v   

Hence, N_n / N_p i.e. the neutron-proton ratio is decreased.    

Problem 2:

In which sequence, the radioactive radiations are emitted in the following nuclear reactions?

_ZX^A —> _Z+1Y^A —> _Z–1K^A–4 —> _Z–1K^A–4

(a) β, α and γ                    (b) β, γ and α
(c) α, β and γ                    (d) γ, α and β

Solution:-

We know that on emission of a α-particle from the nucleus, atomic number reduces by 2 and mass number reduces by 4. And on emission of β-particle from the nucleus, the atomic number increases by 1. Similarly on emission of γ-particle from the nucleus, there is no change in the atomic number or the mass number. Using these concepts we note that in the first part of the sequence, there is an increase in the atomic number by 1. So it has to be a beta particle. Then there is a decrease in atomic number by 2 and reduction in mass number by 4. So it is an alpha-particle. Then there is no change and hence it is gamma particle. So the answer is (A). 

Question 1:

In fission reactor heavy water is used as a:

(a) coolant                    (b) moderator

(c) heat exchanger        (d) controller of reaction rate

Question 2:

Energy in the sun is produced as a result of :

(a) fission                   (b) thermo-nuclear reaction

(c) explosion              (d) combustion

Question 3:

In a spontaneous fission:

(a) nuclear stability is always achieved

(b) the fragments are never radioactive

(c) the nucleus splits into 2 or 3 fragments

(d) the nucleus is unchanged