Induced Fission (AQA A Level Physics): Revision Note

Induced Fission

• 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

• One of the many decay reactions uranium-235 can undergo is shown below:

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

Thermal Neutrons

• 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 $\frac{3}{2}kT$

  • Where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature

• Typically, the average kinetic energy of a thermal neutron is:

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

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

• Typically, a thermal neutron has a speed of:

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

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

Chain Reactions

• 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

Critical Mass

• 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

• 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

Subcritical, critical and supercritical mass