Nuclear Fusion and Fission

Elements lighter than iron(Fe) will undergo fusion to become more stable by increasing their binding energy.

For light nuclei, increasing the number of nucleons increases the strong nuclear force, as the number of protons is relatively low, so the electrostatic force of repulsion is not dominant.

For fusion to happen, nuclei must have very high kinetic energy - they need to be moving extremely fast - to overcome the electrostatic repulsion between their positive charges and get close enough to fuse.

Fusion occurs when two light nuclei join together to form a heavier nucleus, thereby increasing their binding energy and becoming more stable. Fusion occurs in stars as the extremely high temperatures there provide the nuclei with enough kinetic energy to fuse. In the Sun, two lighter hydrogen nuclei fuse to form a heavier helium nucleus, releasing a vast amount of energy.

Research into fusion reactors began in the 1940s, but no design has produced positive net energy. There are several challenges in building a net energy-positive fusion reactor:

• A significant amount of energy is required to heat the material to a superhot plasma state so the kinetic energies of the nuclei are high. This requires very high electric currents.

• The plasma must be contained by a powerful magnetic field so that it does not come into contact with the reactor walls (if it did, the plasma would cool, transferring heat to the container and thus losing kinetic energy, which would stop the reaction).

Elements heavier than iron nuclei are less stable, as the large number of protons increases the electrostatic repulsion force within the nucleus, and the strong nuclear force has less of an effect due to the larger nucleus. Therefore, the binding energy per nucleon decreases, as less energy is needed to remove a nucleon from the larger nucleus.

Large nuclei, therefore, undergo fission to become more stable, to increase their binding energy per nucleon. The large nucleus breaks into two smaller nuclei that have a higher binding energy.

We can induce fission by firing a neutron at a Uranium-235 nuclei. The neutron is absorbed, causing the nucleus to split into two lighter nuclei, releasing energy and more neutrons.

The emitted neutrons can go on to cause further fission events in other Uranium nuclei, which can lead to an uncontrolled reaction and potentially an explosion. Nuclear reactors operate at or slightly above critical mass - the smallest amount of fissile material needed to sustain a self-sustaining nuclear chain reaction, where the number of neutrons produced = the number of neutrons lost.

Spontaneous fission occurs when the nucleus splits without a neutron being absorbed. This is rare.

To calculate the energy released in fission, we need to calculate the difference in binding energies.

Uranium-236 undergoes nuclear fission to produce barium-144, krypton-89 and three free neutrons.

The binding energies per nucleon are given here, so we need to multiply by the total nucleon number/mass number to calculate the total binding energy per nucleus first in order to find the differences.

We do not need to include the three neutrons here, as neutrons have zero binding energy.

To find the change in binding energies, we subtract the total binding energy of the parent nuclei from the total binding energy of the products, as the two daughter nuclei have a higher binding energy per nucleon, as fission always occurs to increase the binding energy per nucleon.

This change in energy is the energy released. The energy comes from the change in mass as the total mass of the products is always less than that of the reactants. This difference in mass is converted to energy, . The products have a higher binding energy as they are more stable; more energy would be required to break these nuclei up into their individual nucleons.