Introduction

Nuclear fission is a fundamental nuclear process where a heavy atomic nucleus splits into lighter nuclei, releasing significant energy. This process forms the basis for both nuclear power generation and nuclear weapons, depending on how the reaction is controlled.

The Physics of Nuclear Fission

Nuclear fission occurs when a heavy nucleus splits into smaller nuclei, typically releasing neutrons and energy in the process. The most common example is the fission of uranium-235 ($^{235}\text{U}$). When a neutron strikes a uranium-235 nucleus, it forms an unstable uranium-236 nucleus that quickly splits into two smaller nuclei.

The energy released during fission can be calculated using Einstein's mass-energy equivalence equation:

$E = mc^2$

where:

Chain Reactions

A nuclear chain reaction occurs when neutrons released from fission trigger additional fission events. There are two types of chain reactions:

1. Critical Reactions

A critical reaction maintains a constant rate, where each fission event triggers exactly one subsequent fission. The amount of fissile material needed to sustain this reaction is called the critical mass.

2. Uncontrolled Chain Reactions

In an uncontrolled chain reaction, each fission event triggers multiple subsequent fissions, leading to an exponential increase in energy release. This type of reaction is used in nuclear weapons. The rate of fission follows:

$\text{Rate} \propto e^{kt}$

where $k$ is the growth constant and $t$ is time.

Controlled Chain Reactions and Nuclear Reactors

Nuclear power plants use controlled chain reactions to generate electricity. Key components include:

Essential Components:

Safety and Control

Nuclear reactor safety relies on maintaining controlled chain reactions through:

The power output ($P$) of a reactor can be controlled using:

$P = P_0e^{(\rho - \beta)t/\Lambda}$

where: