Nuclear fission and fusion (6.4.4)
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Albert Einstein proposed that energy and mass are interchangeable and demonstrated this with his famous equation:
Where:
- is energy ,
- is mass , and
- is the speed of light in a vacuum .
The equation tells us that mass and energy are essentially the same thing and therefore equivalent, but have different forms. When we multiply mass by the speed of light squared, we get the amount of energy equivalent to that amount of mass.
An example of mass–energy equivalence is the annihilation of an electron–positron pair. When the two particles collide, they annihilate and produce two photons. The mass of the electron and positron is converted into two photons, i.e., energy.
When there is a change in the mass of an object or system, then there is an equivalent change in the amount of energy represented by Einstein’s equation:
A moving object possesses kinetic energy. Thus, the equation implies that the object’s mass when it is moving is greater than its mass while at rest (rest mass).
During radioactive decay, unstable nuclei decay by ejecting radiation in the form of particles such as alpha particles or high-energy photons in order to transition to a more stable state.
For example, during alpha decay, the initial nucleus (the parent nucleus) is unstable and emits an alpha particle (a helium nucleus) to become more stable, resulting in a more stable daughter nucleus:
The daughter nucleus recoils in the opposite direction to the alpha particle’s trajectory, so that mass, momentum and energy are conserved.
Energy is released during nuclear decay reactions. Therefore, there must also be an equivalent decrease in the total mass of the system.
This means that the total mass of the daughter nucleus and alpha particle combined must be less than the mass of the parent nucleus, i.e. the decrease in mass is equivalent to the amount of energy released from the reaction
This principle is also true for beta-minus and beta-plus decay:
In some nuclear reactions, energy may be absorbed. This occurs when there is an increase in the total mass of the system, i.e. the total mass of the products is greater than the total mass of the reactants.
This increase in mass, is equivalent to the amount of energy absorbed in the reaction, For example, this occurs in the fission of light elements and the fusion of heavy elements (heavier than iron).
Question walkthrough
Kinetic Energy Released in Alpha Decay
Calculates the total kinetic energy released when uranium-238 undergoes alpha decay, using the mass defect between the parent and daughter nuclei.
All particles have a corresponding antiparticle. They are similar in every aspect, except that they have opposite charges. When a particle and its corresponding antiparticle collide, they annihilate each other: all of the particle’s mass is converted into energy, typically in the form of photons.
An example of the process of annihilation is electron–positron annihilation:
The electron has an associated antiparticle known as the positron . The electron and the positron are similar in every aspect, except that they have the opposite charge. When an electron and positron collide, they annihilate and all their mass is transformed into energy in the form of two identical photons.
A process opposite to annihilation can occur, in which a photon transforms into a particle-antiparticle pair: this is known as pair production.
For example, a photon may create an electron–positron pair, provided the photon has an energy that is equal to at least twice the rest-mass energy of the electron i.e.
For pair production to occur, a photon must enter into the Coulomb field of a nearby atomic nucleus: it cannot happen in free space. This is because the reaction requires energy and momentum to be conserved.
In free space, the momentum of the electron and positron combined would not equal that of the photon’s initial momentum. Therefore, the nucleus absorbs some of the photon’s initial momentum, thus obeying conservation laws in the reaction.
Question walkthrough
Photon Energy from Electron-Positron Annihilation
Calculates the energy of each photon produced when an electron and positron annihilate, using E = mc² with the rest mass of an electron.
In order to split nuclei apart, we need to supply energy in order to overcome the strong attraction between the nucleons due to the strong nuclear force.
According to Einstein’s mass–energy equation, which states mass and energy are equivalent, the total mass of the split nucleons must be greater than the mass of the bound nucleus itself. This is because the energy is supplied in order to break the nucleus apart.
The definition of the mass defect of a nucleus is the difference between the mass of the separated nucleons and the mass of the bound nucleus.
The mass defect of a nucleus can be converted into a corresponding amount of energy using Einstein’s equation. This energy represents the binding energy of the nucleus.
The definition of the binding energy of a nucleus is the minimum energy required to completely separate a nucleus into its constituent protons and neutrons.
The more tightly bound a nucleus is, the harder it is to separate the nucleons and split them apart. Remember, the binding energy is what holds the nucleus together and not the entire atom.
We can measure how tightly bound a nucleus is and make comparisons with other nuclei by considering the average binding energy per nucleon.
The average binding energy per nucleon is defined as the total binding energy of a nucleus divided by the number of nucleons it contains. It represents the energy required to remove a single nucleon, on average, from the nucleus.
The greater the average binding energy per nucleon, the more tightly bound the nucleus. The more tightly bound the nucleus, the more stable it is.
Question walkthrough
Mass Defect of a Deuterium Nucleus
Calculates the mass defect of a deuterium nucleus in atomic mass units by comparing its actual mass to the combined mass of a free proton and neutron.
By plotting the average binding energy per nucleon against the atomic mass for all elements in the periodic table, we can visualise which elements have the most tightly bound nuclei and see how this changes as the size of the nucleus increases.
The binding energy per nucleon increases as the atomic mass increases up to the isotope iron-56. From iron-56 onwards, the binding energy per nucleon starts to decrease slightly. Since the curve peaks at iron-56, this means that this is the most stable (and tightly bound) nucleus in nature.
Energy is released in radioactive decay, and this can be shown using the binding energy per nucleon plot. If a nucleus spontaneously alpha-decays, the binding energy of the parent nucleus is less than the binding energy of the daughter nucleus and the alpha particle.
For example, uranium-238 alpha-decays into thorium-234. The resulting thorium-234 has a lower mass number and, according to the binding energy per nucleon against nucleon number curve, it has greater binding energy per nucleon than uranium-238. The excess energy is released in the decay in the form of kinetic energy of the thorium nucleus and the alpha particle.
We can use Einstein’s mass–energy equation to calculate the binding energy of a nucleus:
We can get a measure of how tightly bound a nucleus is by looking at the average binding energy per nucleon. The greater the average binding energy per nucleon, the more tightly bound the nucleus and the more energy that is needed to completely split the nucleus apart.
Question walkthrough
Binding Energy of a Plutonium-239 Nucleus
Calculates the binding energy of a plutonium-239 nucleus from its mass defect, using the individual masses of its constituent protons and neutrons.
Uranium is the most common fuel used in nuclear power stations. The isotope uranium-235 readily undergoes fission when absorbing a low-energy neutron. These low-energy neutrons are known as thermal neutrons.
As uranium-235 undergoes fission when absorbing a low-energy neutron, there will be a mass defect between the parent nuclei and the daughter products. This mass defect is converted to useful energy for our power stations.
Whereas, the isotope uranium-238 requires high-energy, fast neutrons to fission, which are less common in nuclear reactors. U-238 nuclei are more likely to capture a neutron to form uranium-239 because the probability of fission with low-energy thermal neutrons is low. The unstable nuclei will then quickly decay into plutonium-239 and not fission.
Both uranium-235 and uranium-238 can spontaneously undergo nuclear fission without the need for neutrons, but this process is rare. When uranium-235 absorbs a neutron, it becomes uranium-236 and has a much greater chance at spontaneously fissioning.
When the uranium-236 fissions, it releases fission products and neutrons. These products have very high kinetic energy, which is utilised in a nuclear reactor. They transfer their kinetic energy via collisions to a coolant, which increases the coolant’s temperature. The coolant is then used to heat and boil a circuit of water to create steam to drive a generator turbine, resulting in electricity. This is the basic operating principle of a nuclear power station.
Below is an example of a typical neutron-induced fission reaction of uranium-235:
The uranium-235 nucleus absorbs a thermal neutron to become uranium-236. The highly unstable uranium-236 fissions almost immediately to produce the two daughter nuclei barium-141 and krypton-92. Three fast (high energy) neutrons are also released in the reaction.
The total mass of nuclear fission products is less than the total mass of the particles before fission due to the total binding energy of the products being greater than the total binding energy of the particles before fission.
The difference in mass corresponds to the difference in binding energy , and is the energy released in the reaction.
The energy released is in the form of kinetic energy of the fission products and energy of any other particles produced, such as photons.
The three neutrons produced in a uranium-235 fission reaction are fast neutrons. If they are slowed to lower energies to become thermal neutrons, then they may go on to cause further fission of other nearby uranium-235 nuclei. This is known as a chain reaction, as shown below.
Further fissions release more neutrons, which cause further fissions and so on. After fission events, there will be neutrons, so the growth of neutrons is exponential.
Nuclear reactors are able to control this reaction to produce a steady output of power.
There are multiple designs of nuclear fission reactors, but they all contain the same key components as follows:
- Fuel rods
- Coolant
- Moderator
- Control rods
The diagram below gives an example of the main components within a typical water-cooled reactor.
Note that in the diagram above, the water in this reactor is both the coolant and the moderator, which is typical in a pressurised water reactor.
Fuel rods (nuclear reactors)
The fuel rods are evenly spaced metal pins within a steel pressure vessel (the core) that contain the nuclear fuel. The most common type of fuel is enriched uranium, consisting of uranium-238 with 2–3% uranium-235.
Coolant (nuclear reactors)
The role of the coolant in a nuclear reactor is to remove the thermal energy produced from the fission reactions. In most reactor designs, the coolant transfers this heat to a separate circuit containing water to produce steam to drive a turbine.
Common coolants are water and carbon dioxide.
Moderator (nuclear reactors)
The moderator slows down the fast neutrons produced by fission. The moderator material should be cheap and readily available and should not absorb the neutrons.
The absorption of fast neutrons produced from fission by uranium-235 nuclei is very low and so they must be slowed down to become thermal neutrons in order to induce fission. The fast neutrons lose more kinetic energy when colliding with nuclei with low atomic mass and thus are slowed down. For this reason, water is a good moderator.
In some reactors, the moderator and coolant are the same material. For example, in pressurised water reactors, water is both the coolant and moderator (see image above).
Control rods (nuclear reactors)
The control rods are made from a material that is highly absorbing of neutrons. The most common control rod materials are boron and cadmium. The level of control in the reactor is achieved by inserting and removing control rods. They are automatically adjusted to ensure a single neutron from each fission survives.
To shut the reactor down, the control rods are fully inserted into the core.
In a nuclear reactor, neutrons that have intermediate kinetic energies are absorbed by uranium-238 nuclei. The resulting uranium-239 nucleus is very unstable and quickly decays to plutonium-239:
Plutonium-239 is a very toxic and radioactive isotope, with a half-life of 24 000 years. Plutonium-239 also undergoes neutron-induced fission and produces radioactive daughter nuclei. The radioactive nuclei produced in nuclear reactors present a challenge when dealing with this radioactive waste.
Radioactive waste cannot be disposed of in the same manner as normal waste. Therefore, its storage presents a challenge from both an ethical and a practical point of view.
High-level radioactive waste, such as spent fuel rods, has to be stored deep underground for many centuries due to the very long half-lives of the isotopes and to prevent them from contaminating the water and food supply. The locations for these underground disposal sites need to be geologically stable, safe, and secure.
Generating electricity using a nuclear power station has several advantages and disadvantages compared to a fossil fuel power station and renewables. These inform the decision-making process regarding whether to build a new nuclear power station.
| Advantages of nuclear power | Disadvantages of nuclear power |
|---|---|
| Nuclear fuel yields significantly more energy per unit mass compared to fossil fuels. | Nuclear power stations have substantially higher initial construction and decommissioning costs. |
| Nuclear reactors do not emit greenhouse gases. | Due to the long half-lives of daughter products, spent nuclear fuel remains radioactive for millennia, necessitating secure disposal. |
| Less fuel is needed, so transport and storage of fuel are easier. | Nuclear power plant accidents pose the risk of radioactive material release into the environment. (For example, Fukushima and Chernobyl disasters) |
| Reduces dependence on fossil fuels, helping with energy security. | Mining and refining fissile nuclear fuel can still harm the environment and require energy. |
| Nuclear power stations can produce electricity continuously, unlike some renewables. | Nuclear power stations take a comparatively long time to build. |
Several ethical concerns must be considered when deciding whether to build a new nuclear power station.
When deciding on whether to build a new nuclear power station, science is used to inform decision-making.
Science
- The decision-making process involves evaluating the latest scientific research on nuclear power plant technology, including safety systems, waste disposal methods and the potential impact of exposure to radiation.
- Governments and regulatory bodies use studies and assessments to set safety standards and assess the viability of new nuclear power plants.
- Governments must consider the public opinion and address public concerns regarding safety, environmental impacts and economic viability.
- Society uses science to compare nuclear power to alternatives such as renewables, evaluating factors such as energy output, carbon emissions and costs.
Nuclear fusion is the process of combining small nuclei into larger nuclei, releasing several of energy per reaction. This process is what occurs in the cores of stars.
In order for nuclei to fuse, they have to be brought very close together within a few femtometres, At these short distances, the strong nuclear force takes effect and overcomes the electrostatic repulsion between the protons created by the Coulomb force.
Fusion requires very high temperatures in order for the nuclei to have enough kinetic energy to get close enough for the strong nuclear force to take effect. The conditions in stars are ideal for fusion due to the very high temperatures and their very high density.
There are multiple fusion reactions that can occur and are often sequential reactions. For example, the production of helium-3 in stars results from the proton–proton chain:
The cycle is repeated again with the two protons produced at the end. Each reaction releases energy.
Currently, there are no power stations utilising nuclear fusion. There are challenges with maintaining the very high temperatures for sufficient periods of time and confining the hot fuel in the reactor. The first controlled nuclear fusion reaction that produced more energy than it took to sustain only occurred in 2022, but it was still far from being economical.
Future fusion devices, such as ITER in Europe, will use deuterium and tritium nuclei as fuel. The fuel will be heated to temperatures above 150 million kelvin, where it becomes a plasma. In ITER, powerful magnetic fields will be used to confine the plasma to a doughnut shape to prevent it from touching the vessel walls and losing energy.
The fusion of tritium and deuterium nuclei produces a helium nucleus and a free neutron.
This reaction releases of energy in the form of kinetic energy of the products. The neutron possesses 80% of the energy and will be absorbed by a lithium blanket surrounding the fusion reactor. This interaction of the neutron with lithium breeds more tritium to be used as fuel.
When balancing nuclear transformation equations, it is important to remember to conserve the following quantities on either side of the equation:
- Mass number,
- Atomic number,
Question walkthrough
Balancing a Deuterium-Tritium Fusion Reaction
Shows that a deuterium-tritium fusion reaction is balanced by checking that mass number and atomic number are conserved on both sides.