Elementary Nuclear Physics

Relevant Very Elementary Physics, Mostly Nuclear.

 by John McCarthy

(John McCarthy wrote this over 17 years ago. We are using it because Elementary Physics has not changed. His 2002 update of the last item shows that little has changed in the politics of nuclear energy. The United States is still trying to decide what to do with high level nuclear waste.)

Unless one takes some rather complex facts on authority, which may be good enough depending on the authority, forming an opinion on nuclear energy requires just a little bit of physics. Let me assure the reader that nothing in what follows is controversial. Many readers will find nothing they don’t already know. Here are some facts.

  1. Energy is an additive quantitative entity. Thus if you use 50 kilowatt-hours of energy for one purpose and 40 kilowatt-hours for another purpose, then you will have to pay for 90 kilowatt-hours at the end of the month. The United States generated 2.572 trillion kilowatt-hours of electricity in 1987. A kilowatt-hour cost approximately between $.02 and $.10 in 1987 depending on the customer and the utility.
  2. Power is measured in watts or kilowatts (1,000 watts) or megawatts (one million watts. An electric generator is rated in watts. A large nuclear power plant has a power of 1,000 megawatts (or one gigawatt). If a one kilowatt generator runs for an hour, it produces a kilowatt-hour of electric energy.
  3. The amount of energy handled by humanity is still small compared to the amount of energy in the sunlight that strikes the earth. It’s about one part in 50,000.
  4. Energy is conserved. It can be transformed among various forms, (e.g. mechanical, electrical, chemical, heat) but the total remains the same. In each transformation, some of the energy becomes unusable, usually in the form of heat.
  5. All matter is composed of elements. The important elements for our discussion of nuclear energy are uranium, plutonium, carbon and hydrogen. Uranium and plutonium are involved in nuclear energy production, and carbon and hydrogen are the main elements in conventional fuels like coal, oil and natural gas.
  6. An atom of an element consists of a nucleus surrounded by electrons. What element it is, is determined by the number of protons in the nucleus, but the elements come in various isotopes, and the isotope is defined by the number of neutrons in the nucleus.
  7. Matter takes part in two kinds of reactions involving atoms of different kinds – chemical reactions and nuclear reactions. Chemical reactions are common and re-arrange how the atoms are combined into molecules but never change what element an atom is – or even what isotope it is. The reactions involved in the production and use of non-nuclear fuels are all chemical reactions.

Nuclear reactions can change what element an atom is, occur on earth only under special conditions and involve something like ten million times the energy. Thus enormously more energy can be obtained from suitable nuclear reactions than from chemical reactions.

  1. Uranium has 92 protons. Two isotopes are important. U-235 has an atomic mass of 235 and U-238 has an atomic mass of 238. Natural uranium as it comes from mines contains 140 times as much U-238 as U-235. Because the 235 is the total of protons and neutrons U-235 has 235 – 92 = 143 neutrons. Likewise U-238 has 146 neutrons.
  2. Plutonium has 94 protons. Its important isotopes are Pu-239, which is used in power plants and bombs, and Pu-240 which is ok in power plants but which is a nuisance for those making bombs out of plutonium. There is also Pu-238 which is not fissionable but emits alpha particles and thereby generates heat. The amount of heat produced is convenient for powering spacecraft systems. There is very little natural plutonium.
  3. When an atom of U-238 absorbs a neutron in a nuclear reactor, it becomes U-239, which decays in a short time to Pu-239. If a Pu-239 atom stays in the reactor long enough, it absorbs another neutron and becomes an atom of Pu-240 if it doesn’t fission.
  4. When an atom of U-235 or plutonium absorbs a neutron it almost always fissions. Namely, it splits into two atoms of lighter elements and emits neutrons – on the average a bit more than two. The emitted neutrons can cause further fissions in a chain reaction. In a bomb the chain reaction is very fast; in a power reactor it is slow. The two fragments are emitted at high velocity, and when they are absorbed in the fuel rod a lot of heat is produced. This heat is what powers the nuclear power plant.
  5. Separating the isotopes of elements is very expensive. There are big plants for separating U-235 from the U-238 in natural uranium. For nuclear reactors, it is economical to use uranium that has been enriched to contain 4 to 5 percent U-235 instead of the 0.7 percent U-235 of natural uranium. Bombs need over 90 percent U-235.
  6. Separating Pu from U is not very expensive, and bombs are mostly made of Pu made from U in special reactors in which the Pu-239 is promptly removed. In ordinary power reactors, the Pu-239 gets contaminated with Pu-240. Separating Pu-240 from Pu-239 is very expensive. (Production of Pu-239 for bombs is the whole reason for the construction of the Hanford Nuclear Reservation. The reactors built for the Manhattan Project were designed to produce Plutonium. Separating the Pu from the U remaining in the irradiated fuel rods made much of the radioactive chemical mess that we are still dealing with today.)

Here are some facts about nuclear power plants.

  1. Present nuclear power plants consume uranium (specifically U-235) as fuel. When the power plant is loaded with fuel, it can run for 18 months or 2 years before it has to be refueled, a process that takes a month or two. As the power plant operators have become more experienced, they have learned to operate longer between refuelings and take a shorter time to refuel.
  2. When an atom of U-235 absorbs a neutron it fissions, i.e. it breaks up in parts. These parts consist mainly of two atoms of smaller elements and some neutrons.
  3. When a reactor is operating, fission of an atom of U-235 generates on the average a bit more than two neutrons.
  4. If each of two neutrons produced by a fission was absorbed by an atom of U-235 the number of fissions would double in a fraction of second and then double again and again. If this were allowed to continue, in a few seconds the reactor would be generating enough power to melt.
  5. When the reactor is turned on, the multiplication of fissions is allowed to continue until the reactor is generating power at the desired rate. Then control rods that absorb neutrons are inserted until exactly one neutron from each fission causes another fission.
  6. Because some of the neutrons caused by a fission are emitted from the fission products only after a delay of a minute or so, it is not difficult to control the power level of the reactor. Nevertheless, there are safety systems that will shut down the reactor if the power level gets too high or if the cooling water stops flowing.
  7. The power to produce electricity comes from the fact that the two atoms produced by the fission of a U-235 atom fly off at high speed, but they don’t get even an inch before they hit something and are stopped. Stopping converts their energy of motion into heat, and the reactor heats up. If the heat weren’t taken away, the reactor would melt.
  8. The heat from fission is taken up by water or steam pumped through the reactor. The hot steam goes through turbines connected to electric generators.
  9. About 2/3 of the heat energy is lost, and is emitted to the atmosphere or to a body of water, a river or the ocean. This loss is a consequence of the Second Law of Thermodynamics and applies to all power plants, nuclear or coal-burning.
  10. If the highest temperature in the steam plant is T1 and the temperature at which heat is exhausted to the environment is T2, the fraction of the heat generated that can be turned into electricity is (T1 – T2)/T1. The fraction of the heat energy transformed into electric energy is called the efficiency of the power plant. For high efficiency T1 should be as high as possible and T2 as low as possible. How high T1 can be, is determined by how high a temperature the materials of the reactor can be without softening. How low T2 can be is limited by the environment. Cold seawater gives a good T2.
  11. After 18 months or two years, most of the U-235 in the fuel is used up, and the fuel rods consist mainly of the products of fission, which remain radioactive and continue to generate heat. The fuel rods are placed in large pools of water which takes the remaining heat. The fuel rods become less and less radioactive with time.
  12. After the rods have cooled off for a while, they should be chemically reprocessed to extract left over uranium and some plutonium that has been produced. The left-over uranium and the plutonium can then be converted to more reactor fuel. The fission products can then be buried in stable rock formations.
  13. France, Britain, Japan and most other countries have their used fuel rods reprocessed. For bad political reasons, the US stopped reprocessing and hasn’t yet managed to agree on how to store the fission products. There is no actual hurry, because the fuel rods become less and less radioactive as time passes. 2002 Note: Congress has just passed a bill and the President has signed it that provides for storing the waste in tunnels dug into Yucca Mountain in Nevada. Probably this will happen, but first there will be lots of lawsuits from opponents of nuclear power. Most environmental organizations mistakenly oppose nuclear energy. The consequence has been pollution from coal burning plants. (we added the boldface)

OK, the last two points are controversial. (but so true)

 John McCarthy’s home page at Stanford.