Class 12 > Unit # 27: Nuclear Physics > Nuclear Fission

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Nuclear Fission & Fission Chain Reaction

Nuclear Fission

Definition: The splitting of a heavy nucleus ($A > 230$) into two medium-mass nuclei in a nuclear reaction with the release of a huge amount of energy due to mass defect is called nuclear fission.

Figure: Splitting of a Uranium-235 nucleus into two fission fragments and neutrons upon bombardment by a thermal neutron.

Example: When a uranium nucleus ($\text{U-235}$) is bombarded by a slow-moving neutron (called a thermal neutron), the $\text{U-235}$ nucleus splits into two medium-mass nuclei with the release of a huge amount of energy. This fission reaction is given by:

$_{0}^{1}\text{n} + {}^{235}_{\ 92}\text{U} \to {}^{236*}_{\ 92}\text{U} \to \text{Fission Fragments} + (2 \text{ to } 3)_{0}^{1}\text{n} + \text{Energy}$

Where the asterisk (*) on $\text{U}^*$ represents that $\text{U-236}$ is in an excited state. Two things are worth noting in this fission reaction:

1. A huge amount of energy (about $200 \text{ MeV}$ per $\text{U-235}$ nucleus) is released in the process.
2. On average, 2 to 3 neutrons are released in the process. The released neutrons can further cause splitting of $_{92}\text{U}^{235}$ nuclei and lead to self-sustaining nuclear fission.

When nuclear fission takes place, it is found that the sum of the masses of fission products is very slightly less than the sum of the masses of reactant products. As a result, there occurs a mass defect ($\Delta m$) in nuclear fission. This mass defect is converted into energy according to the relation $E = mc^2$.

Calculation of Energy Released in Fission

The energy released in the fission can be determined from the mass defect that occurs in the process:

Total Mass Before Fission:

• Mass of $\text{U-235} = 235.043933 \text{ a.m.u}$
• Mass of neutron $= 1.008665 \text{ a.m.u}$
• Sum of masses before fission $= 236.052598 \text{ a.m.u}$

Total Mass After Fission:

• Mass of two fragments $= 232.812000 \text{ a.m.u}$
• Mass of 3 neutrons $= 3.025995 \text{ a.m.u}$
• Sum of masses after fission $= 235.837995 \text{ a.m.u}$

$\Delta m = 236.052598 - 235.837995 = 0.214603 \text{ a.m.u}$

Therefore, energy released per fission of $\text{U-235}$:

$E = 0.214603 \times 931.5 \text{ MeV} \approx 200 \text{ MeV}$

Fission Chain Reaction

Definition: The nuclear fission which once started continues till all the atoms of the fissionable material are disintegrated is called a chain reaction.

Figure: Self-sustaining chain reaction showing multiple generations of neutron multiplication and uranium nucleus splits.

When a single neutron initially causes the fission of a uranium nucleus, 3 neutrons in turn cause three more nuclei to split, thereby proceeding very quickly. In a very short time, it liberates a total of 9 neutrons and so on.

For the fission to be self-sustaining, the number of emitted fission neutrons should be more than the incident ones. Under such conditions, the fission neutrons keep on increasing, thus maintaining the chain reaction.

This is evaluated using the neutron multiplication factor ($k$):

$k = \frac{\text{Number of neutrons present in any particular generation}}{\text{Number of neutrons present in the preceding generation}}$

Obviously, for a chain reaction to be self-sustaining, the value of $k$ must be greater than 1 ($k > 1$), which means that neutrons increase or multiply with time.

Types of Fission Chain Reactions

Based on the neutron multiplication factor ($k$), chain reactions are classified into two types:

1. Controlled Chain Reaction ($k \ge 1$):

   A controlled chain reaction is a chain reaction in which the number of neutrons produced can be controlled. This allows for a sustained release of energy, which can be used for beneficial purposes, such as generating electricity. A chain reaction can be controlled by systematically removing some of the fission neutrons from the reaction vessel. The apparatus in which a controlled chain reaction takes place is called a nuclear reactor.

2. Uncontrolled Chain Reaction ($k > 1$ rapidly):

   An uncontrolled chain reaction is a chain reaction in which the number of neutrons produced cannot be controlled. This results in a sudden and rapid release of energy, which can be destructive. A prominent example of this is the atomic bomb.

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