Einstein’s mass-energy equation describes how mass and energy are interchangeable quantities.
Conservation of mass-energy can also be used to explain radioactivity phenomena: when energy is released in the KE of an alpha or beta particle (or the energy of a gamma photon), there is a decrease in mass. So the mass of an alpha particle and the daughter nucleus is less than the mass of the parent nucleus. Energy is released or absorbed in simple nuclear reactions.
Whenever a particle and antiparticle meet they annihilate, converting mass into energy and producing two photons to conserve momentum. Equivalently, a single photon of energy can be converted into a particle-antiparticle pair. You should also take into account the KE of the interacting particles.
The mass defect of a nucleus is the difference between the mass of the completely separated nucleons and the mass of the nucleus. You do work to separate them, so the mass of the separated nucleons is greater than the mass of the nucleus.
This mass can also be expressed in terms of energy: the binding energy of a nucleus is the minimum energy to completely separate a nucleus into its constituent protons and neutrons.
The average binding energy per nucleon is a measure of how much work must be done to separate the nucleons, and therefore how stable the nucleus is. This informs whether nuclear fission or fusion takes place.
- If < 56, fusion occurs
- If > 56, fission occurs
In both cases, the BE of the daughter nuclei is greater than that of the parent nuclei. More work needs to be done to separate the nucleons, so energy has been released.
Equally, radioactive decay increases the BE of the daughter nuclei. Consequently, energy is released (as the KE of the products).
Induced nuclear fission can be used to release energy for generation of electricity.
- Enriched uranium, with a higher proportion of U-235, is used as a fuel
- U-235 absorbs a slow (thermal) neutron, forming U-236
- U-236 is unstable so undergoes fission: 23692U → 14156Ba + 3692Kr + 310 Other decay products are possible.
- The total mass of the particles after the fission process is less than the total mass of the particles before, so energy is released. Equivalently, the total binding energies has increased.
- The fast-moving neutron is slowed down and absorbed by another U-235 nucleus, initiating a chain reaction.
Structure of a fission reactor:
- Fuel rods are evenly spaced within a steel-concrete vessel, the reactor core
- A coolant is used to remove the thermal energy produced from the fission reactors within the fissile fuel
- The fuel rods are surrounded by the moderator. This slows down the fast neutrons produced in fission reactions, allowing a chain reaction. Water or carbon are typically used (comparable mass so big loss in neutrons’ KE)
- Control rods are made of a material whose nuclei readily absorb neutrons, e.g. boron or cadmium. The position of the control rods is adjusted to ensure than one slow neutron survives per fission reaction. To slow down or stop the fission, the rods are pushed further into the reactor core.
Nuclear waste has a significant environmental impact.
- Neutrons of intermediate kinetic energies are absorbed by U-238 nuclei within fuel rods. These decay into nuclei of plutonium-239 by beta-minus decay.
23892U + 10n → 23992U → 23993Np → 23994Pu
- Plutonium-239 is extremely toxic as well as radioactive, with a half-life of 24,000 years. The daughter nuclei produced by its fission reactions are also radioactive.
- High-level radioactive waste (including spent fuel rods) is buried deep underground in locations which are geologically stable, secure from attack and designed for safety. Isotopes with long half-lives must not enter our water and food supplies.
Nuclear fusion reactions can also be used to release energy and generate electricity. For this to happen, nuclei must get within a few femtometres of each other so the strong nuclear force can overcome their mutual electrostatic repulsion. This requires enormous temperatures – around 1.4 × 107K. One cycle of fusion that occurs in stars proceeds as follows:
- Protons fuse to produce a deuterium nucleus, a positron and a neutrino. 11p + 11p → 21H + +01e + . This releases about
2.2MeV of energy.
- Deuterium nucleus fuses with a proton, forming a helium-3 nucleus and releasing 5.5MeV of energy. 21H + 11p → 32He
- Helium-3 nucleus combines with another helium-3 nucleus, forming a helium-4 nucleus, 2 protons and 12.9MeV of energy. 32He + 32He → 42He + 211
- The cycle is repeated with the 2 protons. This is called the hydrogen burning cycle, or the proton-proton cycle.
Power stations for fusion do not yet exist on Earth. The main problems centre on maintaining high temperatures for long enough to sustain fusion and confining the extremely hot fuel in the reactor.