But there is electrical repulsion between protons. What is its effect? For the lightest nuclei, not much. We have deuterium (one proton and one neutron), carbon-12 (six protons and six neutrons), oxygen-16 (eight of each), and neon-20 (ten of each). But as the number of protons grows, the repulsive forces between them begin to work their will. Heavier nuclei are more stable if they have more neutrons than protons. The stable isotope of aluminum, for example, has 13 protons and 14 neutrons. The most common isotope of barium has 56 protons and 82 neutrons, and of uranium 92 protons and 146 neutrons. Beyond a certain point, the electrical repulsion among the protons is more than the strong force can cope with. Element number 83, bismuth, is the heaviest element with any stable isotope at all. Beyond that, there are only unstable nuclei, extending currently up to element number 118 (that is, the element whose nucleus contains 118 protons).
What is the effect of this on our graphical line of stability? The electrical repulsion between protons causes the line of stability to bend and to end. As shown in Figure 2, as neutrons gain on protons the line of stability becomes a curve, bending toward greater neutron number. And because there are no stable nuclei beyond a certain point, the curve ends.
At this point the reader may reasonably ask: What has all of this to do with fission and fusion? The linkage occurs because as one marches through the elements (or, more exactly, their nuclei) from hydrogen to uranium and beyond, what is called the nuclear binding energy changes in a regular way, driven by the competing effects of the nuclear and electrical forces. The nuclear force wants to pull nucleons together. The electrical force wants to push some of those nucleons—the protons—apart. For the least massive nuclei, containing few protons, the strong force is the clear winner. In the range of intermediate masses, the two forces coexist in uneasy harmony. For the heaviest nuclei, the strong force surrenders to the electrical forces. These nuclei, when they exist at all, live only briefly. Beyond bismuth, all elements are radioactive.
The “binding energy” of a nucleus is the energy needed to pull it apart, to completely disassemble it. Consider the lightest nucleus other than a single proton: the deuteron. It is the nucleus of “heavy hydrogen” and consists of one proton and one neutron. Its binding energy is 2 million electron volts (2 MeV).[35] The mass of each of its constituent particles is, in energy units, approximately 1,000 MeV, so the binding energy of 2 MeV is about one one-thousandth of the mass of the nucleus. To phrase it differently, the mass of the nucleus is less than the combined mass of a proton and a neutron by about one part in a thousand. Not much, but easily measured.
Let’s look next at the nucleus of helium-4, which contains two protons and two neutrons. For this nucleus (which is the same as an alpha particle), the nuclear force easily outcompetes the electrical force, and its binding energy is much greater than that of the deuteron—28 MeV instead of 2. This means that 28 MeV of energy would have to be poured into this nucleus to pull it apart into two protons and two neutrons, or 24 MeV to separate it into two deuterons. It also means—here comes fusion—that if two deuterons coalesce to form an alpha particle, 24 MeV of energy will be released. That is exactly what happened in the first thermonuclear explosion, the “Mike” shot in late 1952. (I discuss below why this doesn’t happen spontaneously and why it was such a chore to make it happen.)
In considering nuclear energy, it is useful to use as a unit the binding energy per nucleon. This is 1 MeV/nucleon for the deuteron, 7 MeV/nucleon for the alpha particle. Moving toward heavier nuclei, this number grows, but only slowly. It reaches a maximum of about 9 MeV/nucleon for the nucleus of iron, which contains 26 protons (and whose most abundant isotope contains 30 neutrons). By this point, the repulsive electrical force is beginning to overcome the hegemony of the strong interaction. As the line of stability bends with the addition of more nucleons, the binding energy per nucleon declines, sliding back to around 7 MeV/nucleon at uranium.
We call iron the element with the “most stable” nucleus. This means that combining less-massive nuclei to form a nucleus closer in mass to that of iron releases energy. For light elements, fusion releases energy. It means, too, that splitting apart a heavy nucleus to create two nuclei closer in mass to that of iron releases energy. For heavy elements, fission releases energy.
If fission and fusion release energy when they occur, why don’t they occur spontaneously? Why does it take so much scientific and engineering effort to induce these processes to take place?[36] (Radioactivity, by contrast, does occur spontaneously. In fact, nothing can be done to start it or stop it. When concentrated, it can be a health hazard, but is otherwise largely harmless.)[37]
Fusion is inhibited by the electrical repulsion between nuclei (recall that all nuclei are positively charged). One might at first think that when two deuterons find themselves close together, they would fall into each other’s arms, combine to form an alpha particle, and release energy. Under normal conditions they can’t get close enough for that to happen. “Close enough” really means touching, and that requires that their centers be not much more than 10–15 meter apart, a distance that is nearly 100,000 times smaller than the size of an atom. In normal jostling at ordinary temperatures, the mutual electrical push they exert on each other keeps them much farther apart than that. One way to push them close enough to fuse is by using an accelerator to send a beam of high-energy deuterons toward a deuterium target, which is in fact commonplace in the laboratory but releases very little energy by normal standards since the number of particles involved is less than in a minuscule speck of matter. The other way to cause fusion is to heat the material to enormous temperature—tens of millions of degrees. Then thermal energy is large enough to propel some deuterons (or other light nuclei) within reaction range of each other. That is what happens in the center of the Sun and in an H bomb, and what someday may happen in a controlled fusion reactor.
Fission is inhibited in a different way. A fissionable nucleus—that of uranium-235, for instance—is like a boulder in the cone of an extinct volcano. If the boulder can get up and over the lip of the cone, it will tumble down into the valley, releasing energy. If the nucleus can surmount the energy barrier that holds it together, it will fall apart into two pieces, also releasing energy. The bit of added energy to get the process started, it turns out, can be supplied by a neutron, which can sneak up on a nucleus (since no electric force holds it back), be absorbed by the nucleus, and add some 7 MeV of energy to the nucleus as it (the neutron) is pulled in and joins its fellow nucleons. That 7 MeV of extra energy is enough to allow the nucleus to surmount its energy barrier and come apart. If, in addition to undergoing fission, the nucleus releases more neutrons, these added neutrons can, in turn, stimulate more fission events, and a chain reaction is the result.
35
The electron volt (eV), the standard unit for measuring both mass and energy in the atomic and nuclear world, is the energy acquired by an electron or proton when it moves through a potential difference of one volt.
36
Actually, there is
37
What we might call an agreeable consequence of radioactivity is that over Earth’s history it has created the vast underground reservoirs of helium that we find so useful in technical applications such as cooling superconducting magnets. (An alpha particle brought nearly to rest after being emitted in a radioactive-decay event latches onto a couple of electrons to balance its charge, and, presto, a helium atom is born.)