## Nuclear Fission

Subject: Physics

#### Overview

According to Einstein’s mass-energy relation, the difference in mass (Δm) is converted into energy as ΔE = Δmc2 which is released during the reaction. The energy released is called nuclear energy. This note provides us an information on nuclear fission.

### Nuclear Fission and Fusion

When a heavy nucleus like 92U235 is bombarded by a neutron, the total mass of nuclei is not equal to the sum of the masses of the heavy nucleus and the neutron. Similarly, when two light nuclei like 1H2 fused together to form a heavier and stable nucleus, the mass of the product are not equal to the sum of masses of the initial lighter nuclei. This shows that there is always a difference in mass, called mass defect, in a nuclear reaction. According to Einstein’s mass-energy relation, the difference in mass (Δm) is converted into energy as ΔE = Δmc2 which is released during the reaction. The energy released is called nuclear energy.

#### Nuclear Fission

The subdivision of a heavy atomic nucleus, such as that of uranium or plutonium, into two fragments of roughly equal mass, is called the nuclear fission. For example: When uranium, 92U235 is bombarded with a slow neutron, the uranium nucleus captures the neutron, and a compound nucleus is formed. The new nucleus becomes unstable and almost immediately, splits into two or more fragments with some additional neutrons. The fission reaction is

$$_0n^1 + _{92}U^{235} \rightarrow [_{92}U^{235}] \rightarrow _{56} Ba^{141} + _{36}Ba^{141} + _{36} Kr^{92} + 3_0n^1 + \text {Energy}$$

##### Energy released in Fission

The energy released in the process is due to the difference in mass of the initial nucleus and its products. The initial mass is greater than the sum of masses of the products and difference in mass (Δm) s converted into energy according to Einstein’s mass-energy relation ΔE = Δmc2.

##### Bohr wheeler Theory of Nuclear Fission

According to Bohr and wheeler, the nucleus behaves like a liquid drop whose shape of drop depends upon the balance between the surface tension force and columbic repulsion force. When uranium nucleus captures a bombarding neutron it sets an oscillation within the drop. This excitation energy tends to distort the nucleus into an ellipsoidal shape. If the surface tension force is more, it tends to return the nucleus into its original shape and if the excitation energy is more the drop is further repelled and finally gets split into two or more or less equal fragments. If however the excitation energy is not sufficiently high, the nucleus returns to its original shape with the release of excess excitation energy in the form of γ-rays photon. The process is radiation capture but no fission.

##### Chain Reaction

A chain reaction is a self-propagating process in which a number of neutrons go on multiplying rapidly almost in geometrical propagation during fission till all the fissionable material is disintegrated. There are two types of chain reaction:

1. Controlled chain reaction:
In this reaction number of neutron and hence energy is controlled to a desired level. This principle is used in a nuclear reactor.
2. Uncontrolled chain reaction:
In this reaction, the neutrons are allowed to multiply indefinitely. This entire energy is released all at a time. This principle of an atom bomb.
##### Multiplication Factor

The ratio of secondary neutrons produced to the initial number of neutrons is called multiplication factor. It is denoted by k.

\begin{align*} K = \frac {\text { Number of neutrons in any generation}} {\text { Number of neutrons in previous generation}} \\ \text {If} \: K = 1, \: \text {the reaction is steady or critical} \\ \text {If} \: K > 1, \: \text {the reaction is building up or super-critical} \\ \text {If} \: K < 1, \: \text {the reaction is dying down or sub-critical} \\ \end{align*}

##### Critical Size for Maintenance of Chain Reaction

The critical size of a system containing fissile material is defined as the minimum size for which the number of neutrons produced in the fission process just balance those lost by leakage and non fission capture. Corresponding mass of fissionable material is called critical mass. If the size is less than the critical size, a chain is not possible.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

##### Things to remember

According to Einstein’s mass-energy relation, the difference in mass (Δm) is converted into energy as ΔE = Δmc2 which is released during the reaction. The energy released is called nuclear energy.

The subdivision of a heavy atomic nucleus, such as that of uranium or plutonium, into two fragments of roughly equal mass, is called the nuclear fission.

According to Bohr and wheeler, the nucleus behaves like a liquid drop whose shape of drop depends upon the balance between the surface tension force and columbic repulsion force.

A chain reaction is a self-propagating process in which a number of neutrons go on multiplying rapidly almost in geometrical propagation during fission till all the fissionable material is disintegrated.

The ratio of secondary neutrons produced to the initial number of neutrons is called multiplication factor.

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