Induced Fission (AQA A Level Physics)

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8 November 2024

Induced nuclear fission occurs when:
A stable nucleus splits into small nuclei due to the absorption of a slow-moving neutron
For example, when a nucleus of uranium-235 absorbs a neutron, it becomes uranium-236
A uranium-236 nucleus is highly unstable and will decay into two smaller nuclei almost immediately
- This is why it is not usually shown in nuclear decay equations

When a uranium-235 nucleus absorbs a neutron it may decay into two smaller daughter nuclei

Neutrons involved in induced fission are known as thermal neutrons, meaning:
- They have low kinetic energy
- They are slow-moving

Only slow-moving neutrons can be absorbed by uranium-235 nuclei and induce fission
If a fast-moving neutron is incident on a uranium-235 nucleus it will rebound from it

A thermal neutron is defined as:
A neutron which is in thermal equilibrium with its surroundings
In a nuclear reactor, neutrons are slowed until they are in thermal equilibrium with the moderator
- This corresponds to a core reactor temperature of about 300 K

Thermal neutrons have kinetic energies associated with $\frac{3}{2} k T$
- Where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature

$E = \frac{3}{2} \times (1.38 \times 10^{- 23}) \times 300 = 6.21 \times 10^{- 21}$ J

$E = \frac{6.21 \times 10^{- 21}}{1.6 \times 10^{- 19}} = 0.04$ eV

$E = \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{\frac{2 E}{m}}$

$v = \sqrt{\frac{2 \times (6.21 \times 10^{- 21})}{1.67 \times 10^{- 27}}} = 2700$ m s⁻¹

The products of fission are two daughter nuclei and two or three neutrons
The neutrons released during fission go on to cause more fission reactions leading to a chain reaction, where each fission goes on to cause at least one more fission

Only one thermal neutron is used to create another fission reaction in a controlled chain reaction

Nuclear reactions are designed to be self-sustaining yet very controlled
This can be achieved by using a precise amount of uranium fuel, known as the critical mass
The critical mass is defined as:
The minimum mass of fuel required to maintain a steady chain reaction
Using exactly the critical mass of fuel will mean that a single fission reaction follows the last
- Using less than the critical mass (subcritical mass) would lead the reaction to eventually stop
- Using more than the critical mass (supercritical mass) would lead to a runaway reaction and eventually an explosion