Fissionable uranium (U235) cannot break up into two iron atoms because iron has 56 nucleons, and uranium has 235, which is a lot more than two times 56. To break it up into three or four big pieces would be very unlikely. So uranium fissions into two atoms larger than iron: typically, into krypton (Kr89) and barium (Ba144), whose atomic numbers add up to 233. There are then two neutrons left over, and it is these that carry off the generated energy and keep the chain reaction going. The energy released is not maximal since uranium moves only about halfway down the right-hand slope.

Now look at fusion at the extreme left of Fig. 4.2. When heavy hydrogen in the form of deuterium (H2) and tritium (H3) combine to form helium (He4), with one

Box 4.1 What is Binding Energy?

Suppose we have two pitchers, one 30 cm (1 feet) tall and the other 60 cm (2 feet) tall. We then drop a ripe tomato into the short pitcher. The tomato releases some energy by making a plunk! sound. It is bound to the pitcher because it takes energy to lift it out. Now we drop another ripe tomato into the tall pitcher. It releases more energy by, perhaps, going splat! It is more tightly bound to its pitcher because it takes twice as much energy to lift it out. When each tomato drops down, it loses gravitational potential energy and gains bind­ing energy. Therefore, binding energy is the negative of potential energy. That is why Fig. 4.2 makes more sense than Fig. 4.1. Since the sum of potential energy and kinetic (motion) energy remains the same, kinetic energy is increased when potential energy is decreased; or, equivalently, binding energy is increased. In nuclear reactions, the increase in kinetic energy goes mainly to the lightest resultant particles, usually the neutrons. In both fission and D-T fusion, the neutrons are captured and their kinetic energies turned into heat.

Of course, it is impossible to pick a nucleus apart one nucleon at a time to measure how tightly each is bound. Binding energy is actually inferred from the mass difference. Einstein’s equation E=mc2 predicates that energy and mass can be converted into each other. The mass of a uranium atom can be measured to be larger than the sum of the masses of the fission products. In splitting uranium, therefore, mass has been lost. This mass has been converted into the energy of the products that fly out of the reaction. Since the velocity of light, c, is a very large number, c2 is larger yet, and a small mass defect leads to a large energy output. Similarly, in combining deuterium with tritium, the masses of the helium and neutron that are produced are smaller than those of the fusing hydrogen nuclei, and therefore mass has been lost and energy gained.

Number of nucleons in nucleus

Fig. 4.2 An inverted binding energy diagram showing that going downhill from either side will release energy
neutron left over, there is a very sharp increase in binding energy. The curve is so steep that a lot more energy is released than in fission. However, this is energy per nucleon, and uranium has many more nucleons than hydrogen. After this is accounted for, the total energy gained per reaction is larger in fission than in fusion. This is not important. The end result is that both processes create large amounts of energy by forming elements closer to the middle of the periodic table.

The materials involved are, however, very different. In fission, uranium has to be mined and transported to huge isotope separation plants. Raw uranium is mostly U238. Only 0.7% of it is U235, the part that is fissionable. The separation plants enrich the mix so that there is a higher percentage of the good stuff. The products of fission are highly radioactive, some for thousands or millions of years. This is a well — known problem with fission.

By contrast, fusion uses only hydrogen, which occurs in three forms. Normal hydrogen, labeled as H1 in Fig. 4.1, contains only a single proton. Deuterium (H2) contains one proton and one neutron; it is “heavy hydrogen.” Tritium (H3) is heavier, containing one proton and two neutrons. The sun produces its energy by converting H1 hydrogen into helium through a sequence of reactions which we cannot duplicate on earth. Here, we cannot do as well and must be content with converting heavy hydrogen, H2 or H3, into helium, but the energy gain is still very large. The reaction product is helium, whose nucleus, also called an alpha particle, consists of two protons and two neutrons. It is very tightly bound, so helium is very stable. This stability causes it to be the harmless gas used to fill birthday balloons. Deuterium, which we will call D, occurs naturally in water. In heavy water, D replaces the H in H2O. There is one part of D2O for every 6,400 parts of H2O, and it is easy to separate it out. No mining or large separation plants. However, the other fuel, tritium (H3 or T for short), does not occur naturally. It is also radioactive and decays in 12.3 years. It has to be bred from lithium in a fusion reactor. You may have noticed that deuterium contains one proton and one neutron, while helium contains two protons and two neutrons. Why not fuse two D’s together to get helium? Well, this is hard and will come only in the second generation of fusion reactors. Right now, we are trying to fuse D with T to get helium plus an extra neutron. That neutron carries away most of the energy generated, but it also causes some radioactivity, but much less than in fission. For the future (Chap. 10), there are other advanced reactions involving helium-3 (He3), lithium, or boron which are completely free of radioactivity. Note that lithium and boron are abundant and safe elements on earth.