A level Physics

Nuclear Physics: Reactors

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Uranium is a fairly common element on Earth, incorporated into the planet during the planet's formation. Uranium is originally formed in stars. Old massive stars exploded, and the dust from these shattered stars aggregated together to form our planet.

Uranium-238 (U-238) has an extremely long half-life> (4.5 billion years), and therefore is still present in fairly large quantities.

Uranium-235 has an interesting property that makes it useful for both nuclear power production and for nuclear bomb production:

In order for there to be enough fissioning U-235 nuclei to sustain a civilian power generation plant, a sample of uranium (which contains a mixture of the various uranium isotopes) must be enriched so that it contains 3% more uranium-235 than it would in the natural state. Three-percent enrichment is sufficient for use in a civilian nuclear reactor used for power generation. Weapons-grade uraniumis enriched substantially more: is composed of at least 10% U-235.


Controlled Fission

A nuclear reactor operates through the controlled fission of 235U. Fission is made to occur at a slow steady rate, rather than in a fraction of a second as in a nuclear bomb. Fission produces heat, which in turn is used to generate electricity - in the same way that the heat of burning oil or coal generates electricity in a conventional power plant.

Continuous operation depends on each fission of a nucleus producing neutrons for the next fissions. But we do not use the multiplying effect of a chain reaction. Instead, we allow on average only one of the neutrons produced as a result of each fission to carry on and initiate a further fission. In this way the reaction continues at a constant rate rather than growing rapidly.


Some reactors, like the UK's Magnox reactors, operate with natural uranium (which contains 0.7% 235U). On the other hand some, like the UK's Advanced Gas-Coolled Reactors, use slightly enriched uranium (which contains about 3% 235U). The uranium used in reactors cannot be diverted to weapons use, because weapons need about 90% 235U

Slow Neutrons

The presence of large amounts of 238U in the reactor imposes important constraints on the reactor's design. As neutrons collide with the 238U nuclei there is a growing chance of them being absorbed (producing 239U). There will eventually be so much absorption, that not enough neutrons will remain to initiate further fissions, and to maintain the reactor in operation. When neutrons strike a 235U nucleus, there is a high probability that they will be absorbed, and produce the unstable 236U, which then fissions. This probability is greater if the neutron is moving relatively slowly. (Slowing the neutrons down - from a typical speed of 1/10 of the speed of light just after fission to a speed 10,000 times less - greatly increases the probability of absorption of these neutrons by the Uranium-235 nuclei, which then become unstable and undergo a fission themselves.)

The Moderator

Thus, reactors are designed to operate with a moderator. This is a substance, spread throughout the reaction space, containing light nuclei that do not absorb neutrons. In collision with a light nucleus (such as hydrogen or carbon), the neutron scatters, and as result loses a considerable fraction of its energy. After a few such scatterings, its energy gets down to the level where it has a high probability of absorption by 235U. The moderator in most American reactors is water.

Fuel Rods; Water

The reactor consists of a large pool of water. Immersed in this pool are a large number of fuel rods. These are narrow cylinders that contain small pea-sized pellets of uranium. Neutrons released in one fission will usually travel out of one of the fuel rods, and have to pass through some water before they encounter uranium in another fuel rod. The effect of the water, primarily its hydrogen nuclei, is to slow the neutrons, and allow them to initiate further fissions. Without the moderator fission probability is too low and the reactor stops.

Control Rods

The third major element in the reactor (beyond the fuel and the moderator) is the control rods. To keep the reactor running at a constant rate there are cylinders in the pool made of material that readily absorbs neutrons. One example is boron. The 105B readily undergoes a neutron absorption reaction to form 115B. If the reactor's fission rate begins to increase, the control rods are moved a little deeper into the pool. They absorb more neutrons, there are fewer fissions, and the reactor slows down. If the reactor runs too slowly, the control rods are withdraw slightly from the pool.

Energy Production

The fission fragments fly apart with a lot of kinetic energy. Temperature is a measure of the energies of the atomic particles, so the reactor core is at a high temperature.

Pressurized Water

The water in the reactor is not stationary. Cool water is constantly flowing into the reactor and getting heated by contact with the fuel rods. Then, at high temperature, it flows out. Here is another important part of reactor technology: The temperature reached in a nuclear reactor is in the range of 300 degrees Celsius. This is higher than the usual boiling point of water, 100 degrees. But the boiling point of water is not always 100 degrees. It can be increased if the water is kept under high pressure (higher than the usual atmospheric pressure of about 76 cm or 30 inches as measured by a mercury barometer).

[This is a general property of the phases of matter: solid, liquid and gas. The temperature at which a phase change occurs can be quite different at different pressures.]

This pressurized hot water is what produces electricity. Outside of the nuclear reactor swimming pool, the water is allowed to vaporize, forming steam under high pressure. The steam causes the rotation of coils of wire that turn in the space between the poles of a magnet. That "electrodynamic" effect causes the flow of electric current.

Functions of Water

Water in the reactor is thus a heat transfer device, a cooling system (to keep the fuel from getting too hot), and the moderator.

In some reactors the moderator is heavy water, water in which the hydrogen isotopes are 2H instead of 1H. In other reactors the moderator is carbon in the form of graphite. The very first reactor, built by Enrico Fermi in 1943, used a graphite moderator.

Nuclear Fear


Nuclear science has been part of public knowledge for a full century now, and nuclear reactors have been known for more than half a century. Nonetheless, the public still retains a certain fear of nuclear technology which far exceeds its fear of other technologies (e.g. electricity, or the internal combustion engine). To some this fear is irrational, and holds back important progress; to others this fear is justified. One focus of nuclear fear is the possibility of nuclear accidents in a reactor: runaway production of energy (as in a bomb), or a release of radioactivity to the environment. We have seen that reactor design precludes a runaway nuclear explosion, but a chemical explosion did occur in the accident at Chernobyl in Ukraine, as well as a serious release of radioactivity. This event, however, was by far the worst nuclear accident, and the Chernobyl design was faulty.

Nuclear Waste

A second focus of nuclear fear is the consequences of long-term storage of nuclear waste.

New Technologies

The design of today's nuclear reactors had its beginning in the years immediately after World War II. The reactor was originally planned as a small unit to be used to power nuclear submarines. It was then modified, and enlarged, for large-scale generation of civilian electricity. Thus, the questions of long-term safety and environmental protection that concern people today were never considered in the early years when nuclear power was being introduced. In anticipation of a continuing and expanding need for nuclear power, both in the U.S. and elsewhere, many scientists and engineers today -- with the support of the federal government -- are working on new designs for reactors, still using the fission of heavy elements as the basic source of energy.

Why Nuclear Energy?

No new nuclear power plants have been built in the U.S. since the 1979 Three-Mile Island accident. The main reason is that nuclear plants are much less competitive than was anticipated. This is largely because the price of oil has stayed low, and because coal has come into wider use for generating electricity. Still, nuclear power is an important part of the energy scene. 17% of all electricity worldwide is generated by nuclear power. In France, about 80% of the electricity is nuclear-generated.

Supporters of nuclear energy argue that it is unwise to rely as heavily as we do on fossil fuel sources (oil, coal, natural gas), for four reasons: (1) supplies of these are limited (although estimating how much there is in the earth is not as reliable as we would like); (2) oil comes from politically unstable parts of the globe; (3) burning fossil fuels produces air pollution (toxic gases such as carbon monoxide and sulfur oxides); (4) the possibility of global warming due to increased levels of carbon dioxide.

Supporters also claim that new designs will make nuclear plants safer and cheaper. One of the reasons for the increased cost of these plants is the need to add safety devices to a design that goes back to the 1950s, a time when safety was not a paramount consideration.

Alternative Fuels

Opponents of nuclear energy look to the development of renewable energy sources (direct use of sunlight, wind, biomass fuels). A recent study, sponsored by a group that strongly favors renewables, concludes that renewables could supply half of America's energy needs within about 40 years. This leaves the problem of what to do during the next few decades. Fusion energy is also not likely to be practicable until 40 or 50 years from now. Thus, some see nuclear energy as a stopgap measure, to supply energy for the next few decades, until something else is ready.


Critics also point to the increased risk of the proliferation of nuclear weapons if reactors are built more widely around the world, and nuclear materials are generally more available.


  • Use natural or low-enriched uranium.
  • Slow neutrons: The moderator
  • "Swimming pool" layout
  • Control rods; absorb neutrons
  • Water as moderator, coolant, heat transfer device
  • Pressurized water
  • Arguments against nuclear energy:
    • Accidents
    • Waste
    • Expense
  • Arguments for nuclear energy:
    • Pollution from fossil fuels
    • Political instability in oil-rich areas
    • Does not contribute to global warming.
  • Renewables: Cannot supply all energy needs for several decades.


Nuclear Waste.

Fission fragments, trans-uranics, and 238U

After a reactor has been operating for about 18 months, it is shut down for a period of time and the fuel rods are replaced. What remains of the old fuel rods is called nuclear waste. This waste is the product of a very large number of different nuclear processes and contains many different isotopes. Most of these isotopes are radioactive. They comprise:

  • fission fragments - elements like barium and krypton;
  • trans-uranic elements - produced when neutrons are absorbed by the 238U in the fuel rods, the 238U then being transmuted to these elements.

Unless a chemical separation of useful material from the non-useful and dangerous material takes place - something that is not ordinarily done - the entire fuel rod material is treated as nuclear waste, i.e. it is stored and subsequently disposed of. A large part of the discarded fuel rods is 238U, which has not itself been invoved in any nuclear reactions and is itself only very slightly radioactive.


The Test-ban Treaty

As an example of what happens to fission fragments, consider the 9035Br nucleus. It undergoes three quick beta decays and ends up as 9038Sr. This strontium-90 has a half-life of 29 years, so it hangs around for a while. Strontium is chemically very similar to calcium, so if it is in the environment it can appear in the same places that calcium appears, such as in milk. When nuclear weapons were being tested in the atmosphere in the 1950s, strontium-90 was one of the components of the radioactive "fallout". Its presence in milk and other foods meant that it would be incorporated into children's bones and teeth. This undesirable effect eventually led to a ban on testing in the atmosphere, signed in 1963.

Relation between half-life and intensity

In dealing with the question of nuclear waste, the half-lives are an important factor. In general there is an inverse relation between the half-life and the intensity of radioactivity of an isotope. Isotopes with a long half-life decay very slowly, and so produce fewer radioactive decays per second; their intensity is less. Istopes with shorter half-lives are more intense.

In nuclear waste, isotopes with very short half-lives, say a few days or even a few weeks, are not the major concern. They will decay to negligible amounts within a year or two.

Isotopes with very long half-lives, more than 1000 years, are likely to be less intense. But one has to plan storage and protection for the public on a time-scale of thousands of years. We cannot be very confidant about guaranteeing this protection reliably. Some trans-uranics are in this category.

Isotopes with intermediate half-lives (say from 10 to 100 years), need only be secured on a time-scale of a few hundred years. Although they are likely to be more intense storage is still a serious problem. Isotopes with intermediate half-lives typically are fission fragments. After 90Sr, the most important isotope is 13755Cs (cesium). Its half-life is 30 years. It is chemically similar to potassium, which is taken up by the body for use in various fluids and in the nervous system.

Long-term Storage

The problem of radioactive waste is finding a way to keep it isolated, over a long period of time, from the biosphere - particularly from underground water sources.

It cannot simply be placed in ordinary containers. The radiation itself tends to damage materials like steel and other metals. Furthermore, a large quantity of radioactive matter tends to get very hot, and this also weakens containers.

One important approach is to incorporate waste in certain kinds of glass and ceramic materials that are very resistant to being dissolved in water, or to any chemical reaction with the environment. Certain kinds of natural underground sites are effective in preventing the flow of chemicals, and thus can keep the waste isolated.

Yucca Mountain

The US is thinking of burying its waste under Yucca Mountain, a barren area in Nevada.


  • Waste consists of fission fragments, trans-uranics, and 238U
  • Inverse relation between half-life and intensity
  • Strontium-90 and atmospheric test ban
  • Storage of waste underground; protection of water sources; ceramic materials
  • Yucca Mountain

There are three main types of reactor that are used around the world:

Diagram of Advanced Gass Cooled Reactor
Advanced Gas-cooled Reactor, enclosed in concrete pressure vessel.

The Advanced Gas-Cooled Reactor (AGR) is the one that is focussed on in the UK. It uses graphite as the neutron moderator and high-pressure carbon dioxide as the coolant. The fuel is uranium oxide pellets, enriched to about 3%%, in stainless steel tubes. The carbon dioxide circulates through the core, reaching 640°C and then passes through steam generator assemblies outside the core but still within the steel lined, reinforced concrete pressure vessel. Control rods penetrate the moderator. One kind of secondary shutdown mechanism involves releasing boron ball devices.

 Cerenkov  radiation produced in the core of a nuclear reactor
Cerenkov radiation produced in the core of a pressurised-water nuclear reactor.

The Pressurised Water Reactor (PWR) is the reactor of choice in North America. It uses high-pressure water to transfer heat from the core to the secondary coolant system. The main difference between the Advanced Gas Cooled reactor and the Pressurised Water Reactor is that the water in the Pressurised Water Reactor is also the moderator. This makes the reactor simpler. It still has all of the safety features that the Advanced Gas Cooled Reactor has.

The Fast Breeder Reactor (FBR) is a fast neutron reactor designed to breed fuel by producing more fissile material than it consumes - about 20% more. The most common breeding reaction is that of plutonium-239 from non-fissionable uranium-238. After its initial fuel charge of plutonium, a fast breeder reactor requires only natural (or even depleted) uranium feedstock as input to its fuel cycle. France has made the largest implementation of breeder reactors.



There are two ways to release nuclear energy: fission, breaking apart a large nucleus into two smaller parts, and fusion, combining two small nuclei to make a larger one.

The hydrogen isotope 21H is often called deuterium or heavy hydrogen and a single nucleus is called a deuteron. Water in which one of the hydrogen atoms is deuterium is called heavy water.

The isotope 31H is referred to as tritium and a sngle nucleus is called a triton.

Fusion Reactions

The simplest fusion process one might imagine would be combining a proton and a neutron to form a deuteron:

This is not practical as an energy source because free neutrons are not found in nature. One might also consider combining two protons:

But helium-2 does not exist. (That is to say, two protons do not hold together. A neutron and a proton do hold together, but two protons don't. Why? Also, bearing in mind the fact that there is an attractive nuclear force, think about the following question: Why is it that 3He holds together, but 2He does not?)

Most fusion reactions are not really "complete" fusion, where two nuclei combine to one. Rather, you have a reaction in which you end up with some larger combinations than you had at the beginning. Two examples:

These are called deuterium-deuterium (or D-D) reactions. When two deuterons come close together they may just bounce off each other (as a result of mutual electrical repulson), or they may undergo a change such as (3) or (4). There is a certain probability for each of these processes to occur. (3) and (4) can be viewed as transfer reactions. (What is transferred?)

Release of Energy

Note that in order for these reactions to occur, the two deuterons must move towards each other fast enough to overcome their electrical repulsion (as in most nuclear reactions). The two deuterons have a certain amount of kinetic energy. After their collision, the two reaction products move apart with more kinetic energy than there was before. This is because of binding energy: There is less mass on the right side of these reactions than on the left side, so the mass difference has been converted to kinetic energy, represented by the equation
ΔE = Δmc2.

The Plasma

The D-T Reaction
Fusion of deuterium & tritium nuclei
In a terrestrial fusion reactor, the fuel would be deuterium and tritium – types of hydrogen atom. This fuel would be heated to about 100 million K. They would then fuse to produce helium and high speed neutrons.

If we want energy production from a human-sized sample of ordinary hydrogen (11H), we must raise the hydrogen to very high temperature (say 50 million degrees). Under such conditions, the electrons will be stripped away from the nuclei, producing matter with no atoms as such - just bare nuclei and free electrons. This is called a plasma. The nuclei and electrons will be moving randomly and very rapidly . If the plasma is hot enough, nuclei overcome the electrical repulsion barrier, undergo reactions (3) and (4), and produce more energy, increasing the plasma's temperature even further. To create energy by fusion we have to first put in energy, and then hope that we will gain more than was put in at the start. (It's like using a match to start a wood fire. The burning wood produces much more heat energy than the match, but the match is needed to start the wood burning.)

It turns out that if you start with 21H and 31H you don't need to reach quite so high a temperature to initiate fusion. This is why much of the attention in fusion research centres on the deuterium-tritium (D-T) reaction:

Controlled Fusion
Diagram of thermonuclear (fusion) reactor
The International Thermonuclear Experimental Reactor (Iter) is a collaboration between the EU, US, Japan, Russia, China and South Korea. The aim is to design and build a fusion reactor in about a decade at a cost of five billion euros.A commercial fusion power station would use the heat generated by the energetic neutrons to drive turbines.

Since the invention of the hydrogen bomb, scientists have sought to carry out fusion reactions in a controlled way. The object is to gradually heat a system of hydrogen fuel until it reaches the point of fusion. Then the fusion reaction proceeds itself, heating the hydrogen further. This heat would then be used as in an ordinary power plant, to generate electricity.

The problem is that the very hot plasma cannot be kept in a container, because any solid container -- steel, for example -- would be vaporized at temperatures of millions of degrees. If the plasma is not contained, then as it is heated it will just dissipate, like cigarette smoke into a room. There are two approaches to containing the plasma:

(1) Magnetic Confinement

(2) Inertial Confinement

In magnetic confinement, the trajectories of fast-moving electrically charged particles are bent in a magnetic field. Plasma physicists have devised very complex arrangements of magnets, so that the electrons and ions are kept within a finite volume; when a particle approaches the edge of the volume, it feels a magnetic force that turns it back into the volume.

In inertial confinement, a small pellet of solid hydrogen fuel is hit on all sides by many laser beams. This compresses the pellet and heats it to fusion temperature. The pellet is quickly vaporized and begins to dissipate, but it may stay together long enough so that fusion can generate additional heat.


The object in each of these techniques is to keep the plasma confined long enough so that fusion can generate more heat energy than was used to trigger the fusion. This will be the "break-even" point. Neither confinement method has quite reached break-even, but there has been steady progress over the past 20 years or so. Estimates are that fusion might be practical in 40 or 50 years.


Although deuterons make up just over one ten-thousandth of all the hydrogen nuclei on earth, there is so much hydrogen in the water of the oceans that there would be enough hydrogen fuel for us to use fusion energy for thousands of years. The D-T reaction is easier to deal with than the D-D one. Hydrogen bombs all use the D-T reaction.

Making tritium

The problem with the D-T process is that tritium is not found naturally on earth. It has to be manufactured in a nuclear laboratory. One method is to use the lithium isotope, 63Li, and the following reaction:

Here the neutron would have to be produced in some prior nuclear reaction. Lithium-6, however, is rare. So if we had to rely on 6Li to obtain tritium fuel, the D-T reaction would not be a very long-term solution to the energy problem.

The outlook

Although fusion energy will not be available in the near future, it seems worthwhile to continue research into it, because:

  1. fusion fuel is effectively unlimited;
  2. there is virtually no problem with radioactive waste. There are no fission fragments and no trans-uranic elements produced. The only radioactivity problem is that reaction (4) produces a triton, 3H, which is beta-active with a half-life of 12 years. One would have to guard against the release of this isotope to the environment, but only for a period of a few half-lives, less than a century. In contrast, nuclear fission produces plutonium, which has a half-life of 24,000 years.


  • D-D and D-T reactions
  • High temperatures needed: plasma
  • Fuel unlimited: 2H in seawater
  • Little radioactive waste
  • Containment
    • Magnetic
    • Inertial
  • Not available for several decades