A-level Physics (Advancing Physics)/Fusion

Nuclear fusion is the joining together of atomic nuclei to form a larger nucleus, and possibly some other products, including energy. It occurs naturally in stars, where hydrogen is fused together into larger isotopes of hydrogen and then into helium, releasing energy along the way.

Forces

Nuclei repel each other due to the electromagnetic force since they have the same charge. However, at a range of between 1 and 3 femtometers, the strong force causes nucleons to be attracted to one another, with the magnitude of this force being far greater than that of electromagnetic repulsion. Therefore in order for two nuclei to fuse, they must be sufficiently close enough together that the attractive force between the baryons due to the strong nuclear force is greater than the repulsive force due to the electromagnetic force. If this is the case, then the two nuclei will become a new, larger, nucleus.

Uses

Nuclear fusion was used by humans for the first time in the hydrogen bomb, whereby a nuclear fission reaction would occur, releasing enough thermal energy so that nuclear fusion could occur, which would release free neutrons allowing the nuclear fission reaction to being more efficient, with more of the unstable isotope undergoing fission as well as a modest amount of energy being released during the fusion process. At the time of writing (2020), commercially viable fusion power has not yet been achieved. However, research is underway, specifically at the Culham Centre for Fusion Energy, to bring a fusion reaction under control so that it can be used to generate electricity. This would have the advantage of minimal nuclear waste, since the main product would be non-radioactive helium, with some tritium, which has a relatively short 12-year half-life.

Binding Energy

The fusion of nuclei smaller than Iron-56 releases energy. This is because, if we were to take all the baryons of both the nuclei apart, and then stick them all back together as one, we would do less work that would be required to stick them together as the two separate nuclei. The difference in binding energy is the energy that is released by a fusion reaction. This energy might be given to the 'real' particles which are given off, or to a 'virtual' particle such as a photon.

Questions

c = 3 x 10⁸ ms⁻¹

1. In the Sun, two tritium nuclei ( $_{1}^{3}H$ ) are fused to produce helium-4 ( $_{2}^{4}He$ ). What else is produced, apart from energy?

2. In larger stars, carbon-12 ( $_{6}^{12}C$ ) is fused with protium ( $_{1}^{1}H$ ). What single nucleus does this produce?

3. In this reaction, 1.95MeV of energy is released. What difference in binding energy does this correspond to?

4. If all this energy was emitted as a photon, what would its frequency be?

5. In order to contain a fusion reaction, electromagnetism may be used. What other force could be used? Why is this not being used for fusion reactors on Earth?

Worked Solutions