The conflict this week was over Iran's nuclear program. Also, there is always news reports about progress in making fusion into a practical energy source. So why don't we review what nuclear energy and weapons are all about? More has been added to this.
An atom consists of a nucleus surrounded by electrons in their orbital shells. The nucleus consists of protons, with a positive electric charge, and neutrons with a neutral electric charge. Electrons have a negative charge. A proton is 1,836 times the mass of an electron. A neutron is slightly more massive than a proton, with the mass of a proton and neutron combined. So almost all of the mass comes from the nucleus. An element is defined by the number of protons in it's nucleus. The charge on a proton and an electron is equal but opposite. Atoms ordinarily have equal numbers of protons and electrons, and thus a net charge of zero. Atoms that have an unequal number of protons and neutrons, and thus a net charge, are known as ions. Atoms with the same number of protons, meaning the same element, but different numbers of neutrons are known as isotopes.
The first step in understanding nuclear science is to separate what is nuclear from what is chemical. Nuclear has to do with the nucleus, while chemical has to do with the electrons. The relationship between the two is that ordinary atoms must have equal numbers of protons and electrons, those that don't are known as ions. The outermost shell of electrons defines the atom's chemical properties. Other than the mass, almost all that we have to do with atoms is with the electrons, which is chemical. The forming and breaking apart of molecules, which are grouping of atoms, including combustion involve only the electrons and do not affect the nucleus. Whether an element is a metal depends on whether a large group of atoms share their outermost electrons, and does not involve the nucleus. Most electrons orbit the nucleus in pairs, the aligning of unpaired electrons creates magnetism but this does not involve the nucleus.
There are two basic nuclear processes, fission and fusion. Fission is the splitting of a large atom, by striking it's nucleus with a high speed neutron. Fusion is the opposite process, crunching together small atoms into one large atom. What may be confusing is that both processes release energy. If one nuclear process releases energy then it might seem logical that the opposite process didn't release energy.
Fusion is the process that seems most logical to release energy. Surface area equals energy. A sphere is the three dimensional form with the least surface area per volume, and thus the lowest energy state. We know that the universe always seeks the lowest energy state and this is why stars and planets are in the form of spheres. Fusion releases energy because of the nature of spheres. When two spheres are merged into one larger sphere the new sphere has less overall surface area than the ones that were merged to form it and the lost surface area is released as energy. This is why stars shine. The sun is currently at the stage of crunching four hydrogen atoms into one helium atom.
Another way of looking at why fusion releases energy is that heavier elements tend to have more neutrons, relative to protons, in the nucleus. Neutrons are secondary particles, formed by crunching an electron into a proton. The electron has orbital energy and, when it is joined to the proton in the process known as K-capture, this orbital energy is then released as radiation.
Neutrons are important to both the fission and the fusion process. The inside of the atom consists of charged particles, positive protons and negative electrons. The neutron has a neutral electric charge so that it can pass right through the atom, which is mostly empty space, and maybe strike the nucleus to start the fission process. In the fusion process, where atoms are fused together, an electron is crunched into a proton to form a neutron. This is known as K-capture and is why a neutron has the mass of a proton and an electron combined. This makes heavy elements possible because they must have a higher neutron-to-proton ratio. The orbital energy of the electron is then released as energy. If the new element is unstable, the neutron may possibly break back down into a proton and an electron. Neutrons do not last long on their own, outside of the atom. It will break back down into a proton and an electron in an average of about 15 minutes.
The reason that fission, splitting a large atom by a high speed neutron, releases energy requires some special explanation. Only two elements can undergo fission, plutonium and the 235 isotope of uranium although another fissionable isotope of uranium can be created by bombarding thorium with neutrons. Only about one of every 140 atoms of uranium are the suitable 235 isotope and plutonium is a man-made element. The ordinary fusion process in stars only goes as far as iron. Elements heavier than iron require an input of energy to form and thus form only during the brief time that a large star is actually exploding as a supernova. It is some of this energy that is released during fusion. In the heaviest elements the heavier it is generally the more neutrons per proton. When one of these fissionable atoms are split the excess neutrons are released at high speed. Their speed is how excess energy is released. If these neutrons split other nuclei the chain reaction will continue. Uranium-235 is believed to release an average of about 2.5 neutrons per fission and plutonium an average of about 3.0.
Fusion releases so much more energy per mass than fission because of simple efficiency. The fission in a critical mass chain reaction is actually very inefficient. The mass blasts itself apart well before all of the fissionable atoms have been split, and this halts the reaction. Only about a fifth of the atoms get split before the mass blasts itself apart. So the release of energy by fission works against the reaction. But in fusion, the released energy fuses more atoms together so that it supports the reaction.
Atoms are fused together by the tremendous heat and gravity in the centers of stars. It originally started with hydrogen and the heat from the Big Bang fused some of it into helium and traces of the next heavier elements. We might expect that lighter elements will be more common than heavier elements, and that is generally the way it is. But it is not a strict rule. There is also a "factor tree" effect that sometimes makes elements more common than those that are lighter than them. It is also true that elements with even numbers of protons and neutrons are more stable, and thus more common, than those with odd numbers. There are also the "Magic Numbers" that bring stability and apply to both protons and neutrons. These are 2, 8, 20, 28, 50, 82 and, 126.
Both fission and fusion occur naturally. Fusion takes place in stars. The release of the remaining energy is why stars shine. Cosmic rays are actually high-velocity particles and can split certain atoms. This is called "cosmic ray spallation" and form light elements, such as lithium, beryllium and, boron.
Elements are defined by the number of protons in the nucleus, although the number of neutrons may vary. But that is just one way of looking at it. Nuclides are defined as a certain combination of protons and neutrons. The difference between an element and a nuclide is that an element can have different isotopes, meaning numbers of neutrons, but each different isotope would be a different nuclide. A nuclear isobar is just defined as a number of nucleons in a nucleus, regardless of whether they are protons or neutrons.
Fission has been providing energy for nearly eighty years. Although what it ultimately comes down to is just another way to boil water. The 235 isotope of Uranium is fissionable, but not the much more common 238 isotope. Plutonium, a synthetic element, can also be used. It is not necessary for the fissile material to be 100% pure. In a bomb it must be around 90% pure.
Fusion has long been a sought after source of energy. Unlike fission, fusion would produce no dangerous byproducts or radiation. Only two rare and very expensive atoms can be used in fission but any matter can be used for fusion. We can accomplish fusion, atoms can be fused together using lasers. But, at the time of this writing, no one has yet made fusion into a practical source of energy. Large scale fusion would require extremely high temperatures, that no matter could withstand, so the fusion process has to be contained by a magnetic field.
Of all uranium atoms only about one in 140 is the fissionable 235 isotope. The rest is the 238 isotope, with 3 more neutrons. These extra neutrons hold the nucleus together tighter so that it cannot be split by one of the high speed neutrons. What that means is that the rare 235 atoms have to be very painstakingly separated out from the rest. One way to accomplish this is by centrifuges. The spinning of the centrifuge causes the many heavier atoms to be pulled to the outside, like a washing machine, and the lighter 235 atoms can be separated out. The "enrichment" of uranium means separating out the 235 atoms so that the sample has an increased proportion of them, relative to 238 atoms.
Plutonium is a man-made element that is also fissionable. It is made by bombarding atoms of the 238 isotope of uranium with neutrons. The neutrons can become part of the uranium nucleus, but that makes it unstable. What happens is that first one neutron breaks down into a proton and electron. This creates a new element, neptunium, with 93 protons. But neptunium is also not stable if bombarded with neutrons. Another neutron breaks down into a proton and electron. This creates plutonium, with 94 protons, that is stable and also fissionable. Despite this laborious process, plutonium is generally easier to obtain than uranium-235.
A fission bomb can be made with either plutonium or uranium-235. There is a tradeoff in that plutonium is easier to obtain than uranium-235 but is more difficult to build a bomb with. A uranium bomb is a simple mechanism with an explosive charge thrusting one sub-critical mass into another to form a super-critical mass. A plutonium bomb is more complex in that it is necessary to compress a sub-critical mass using conventional explosives. The first bomb tested, in New Mexico, was a plutonium bomb. The uranium bomb was considered as so simple that it didn't need to be tested. The bomb dropped on Hiroshima was a uranium bomb, the one on Nagasaki was a plutonium bomb. Most bombs today use plutonium because of it's higher yield.
The so-called "critical mass" is so important to the nuclear chain reaction due to simple geometry. As a nucleus is split by a high speed neutron it releases more neutrons that move at high speed and split other nuclei, and thus the chain reaction continues. But the nucleus is at the center of the atom and surrounded by a vast empty space, with the electrons in orbitals high above. The odds, for each atom that the neutron passes through, are overwhelming that it will miss the nucleus. But if it passes through enough atoms the odds are that it will eventually hit a nucleus, and thus continue the chain reaction. If enough neutrons escape the fissionable mass without splitting a nucleus the reaction will cease. The logical form of the critical mass is a sphere, because it has the least surface area per volume so that the least number of neutrons escape. The volume of a sphere increases faster than it's surface area, meaning that a larger sphere has less surface area per volume. So there is a cutoff in the volume of the sphere that determines whether or not a chain reaction can be sustained. This is known as the critical mass.
Some facts that would be useful in calculating the critical mass are as follows. Avogadro's Number, 6.02 ^23, tells how many atoms are in a mass of a given element weighing it's total number of nucleons in the atom in grams. The average atom in a spherical mass is .707 of the distance from the center of the mass to the edge. .707 is the square root of one-half. The fission of a uranium-235 atom releases an average of about 2.5 neutrons and the fission of a plutonium atom releases an average of about 3 neutrons. Given that the vast majority of an atom is empty space my estimate is that when a nucleus passes through a fissionable atom the odds of it striking the nucleus so that it will fission are about one in 100,000. The critical mass is the minimum mass of a sphere in that enough moving neutrons will split a nucleus, before they escape from the mass altogether, to sustain the chain reaction.
As far as the mathematics of calculating the critical mass, if we play a game of pure chance with the odds of winning being 1 / X and we play it X number of times, the odds of winning decrease as the number increases but never drops below 1 / 2. If the odds of winning were infinitesimal but we played it an infinite number of times the odds of winning would be exactly 1 / 2. So if the odds of a neutron hitting the nucleus so that it would split as it passed through an atom were 1 / 100,000, and it passed through 100,000 atoms, the odds of splitting one would be a shade over 1 / 2. So if it passed through 200,000 atoms the odds would be a shade over 3 / 4. If it passed through 300,000 atoms the odds would be a shade over 7 / 8. But the limiting factor in building a nuclear bomb is obtaining the fissionable U-235 or plutonium, rather than knowing the critical mass.
Testing nuclear weapons is not done to make sure that they work but to make them more efficient, so that they can be miniaturized and thus made easier to deliver. Testing used to be done in the Nevada desert and watching it from Las Vegas was a tourist attraction. The U.S. Government once planned to detonate a nuclear device on the moon. The "mushroom cloud" is caused by earth's atmosphere and there wouldn't be one if a bomb was detonated on the moon or in outer space. There was a space test in 1962, codenamed "Starfish Prime". It was done above the Pacific, within view of Hawaii. The electromagnetic pulse (EMP) generated shut down much of the electricity and communications in Honolulu. Aurora were generated along the earth's magnetic lines of force as atoms were broken apart, protons went in one direction in the magnetic field and electrons in the other, and energy was released when they united into hydrogen atoms when they met.
Heavy water is simply water in which both of the hydrogen atoms in the H2O molecule are deuterium. This means that the two hydrogen atoms in the molecule both have a neutron, along with the one proton. As the name implies this makes heavy water about 10% heavier than ordinary water. This makes heavy water useful as a moderator in a nuclear reactor, slowing down neutrons without absorbing them. Heavy water doesn't absorb neutrons because it's hydrogen atoms already have a neutron. Heavy water is also useful in thermonuclear, or hydrogen, bombs. A hydrogen bomb, which is based on fusion rather than fission, is basically an ordinary fission bomb surrounded by a layer of heavy water. The tremendous heat and pressure generated by the detonation of the fission bomb fuses the molecules of heavy water and this releases much more energy than the fission bomb. Deuterium, hydrogen with one neutron, is the easiest material to fuse because it already has the two extra neutrons so that it is not necessary to crunch electrons into protons to form these two neutrons. The same principle applies to brown dwarfs, a type of sub-star with only enough mass to fuse deuterium.
The splitting of nuclei in a nuclear mass cannot just be shut off. Control rods are made of metals, often cadmium, that absorb fast-moving neutrons. If enough of these neutrons are absorbed then the chain reaction will cease. This is unlike a moderator, such as heavy water, that only slows down the neutrons to the optimum speed to attain fission, rather than being absorbed by the heavier isotope nuclei. To start up the reactor, and begin the chain reaction, the control rods are pulled out.
Nuclear reactors, in which the chain reaction is controlled, use a moderator to slow down neutrons that are moving too fast. The original nuclear reactors used bricks of graphite. Modern reactors might use heavy water. The reason for slowing fast neutrons down, aside from the fact that it converts their kinetic energy into heat is that either the absorption of, or fission by, moving neutrons works best when the neutron is moving at a certain speed. Depending on what the reactor is being used for, the process is less efficient if the neutron is moving too fast.
Elements heavier than iron are formed only when a large star explodes in a supernova. The formation of these heavy elements requires a net input of energy, which the supernova explosion provides. This is why elements up to iron are exponentially more common than elements heavier than iron. We can see how the ordinary fusion process only goes as far as iron by how common it is in the inner Solar System. Iron is the most common element on earth by mass. We know that our sun and Solar System were formed by the explosion of a previous large star, only the largest stars will explode in a supernova, because the sun contains heavier elements that are beyond it's current stage in the fusion process. Some of these new heavy elements are less-than-stable and the atoms gradually release particles or radiation to seek a more stable state. These emissions are known as radioactivity and release energy gradually. Radioactive material can thus be used to make an atomic battery.
Nuclear power is sometimes considered as a disappointment. But it really isn't. Part of the problem is that it's early proponents made too many promises.
