CHAPTER VII. Fission and the Chain Reaction

Fission and the Chain Reaction

Neutrons are ideal projectiles for nuclear bombardment because they carry no charge, can approach nuclei easily, and interact with them strongly. These neutral particles, discovered by James Chadwick in 1932, were used soon afterward by Enrico Fermi and his collaborators to bombard most of the elements of the periodic table. Very often in these experiments a nucleus would capture a neutron and become unstable with too much weight for its charge. Stability would then be restored by a beta decay, leaving the nucleus with one more unit of charge than it had to begin with. In 1934 Fermi tried this experiment with uranium, charge 92, the most highly charged element known at that time. He hoped to make a transuranic element with charge 93.

Throughout the experiments the uranium was observed with radioactive counters and found to become far more radioactive than uranium ordinarily is in its natural state. There was no way to account for all this radioactivity except to assume that new elements had been formed in the process of neutron bombardment. A chemical analysis revealed no elements with charges between 86 and 91. From this evidence Fermi concluded that no elements of charge less than 92 had been made and therefore the radioactivity must be due to charges greater than 92. He concluded that transuranic elements had been made in the laboratory.

Neither Fermi nor anyone else, however, was happy with this conclusion. There was far too great a variety of radioactivity for comfort. It had to be assumed that not only was the element with charge 93 being made, but also elements with charges 94, 95, and many more. This was very hard to understand. Ida Noddack, a chemist, published a paper proposing an alternative explanation of the experiment: that a nucleus of uranium, when it captures a neutron, might break up into two fragments that could have any of various weights and charges. In other words, she suggested that Fermi had produced nuclear fission.

Fermi, however, believed that the fission process was an impossibility. He had a convincing proof, based on the measured values of the weights of nuclei and the formula of Einstein, E = mc². From this formula Fermi calculated the energy liberated when uranium breaks into two pieces; then he took into account the energy of electric repulsion between the pieces and found that the energy barrier was so large that the fission process could not take place. This proof was absolutely correct. The only trouble was that the measured values of the weights of nuclei happened to be inaccurate at that time!

But for this accident, fission would have been discovered in 1934 instead of 1938. If it had been, Nazi Germany might easily have been the first country to make the atomic bomb. At that time some German scientists were active in the field of military applications. The American physicists had not yet turned much attention to the subject.

An important feature of Fermi’s experiment is the large amount and variety of radioactivity that he found. The reason for this variety, as we now know, is that the fission process does not take place in a unique manner. The two primary fission fragments are very rarely of equal weight and charge. On the average the lighter fragment weighs about 90, and the heavier one about 140. Sometimes the lighter fragment will weigh as little as 75, and the heavier one as much as 160. As the weight varies, of course, so also does the charge. The charge of the lighter fragment averages 38, which is strontium, and the heavier one 54, which is xenon. All in all there are more than a hundred different species of nuclei represented among the primary fission fragments.

Practically all of these nuclei are radioactive and undergo three or four disintegrations before reaching stability. Overall therefore, several hundred distinct radioactive species are created by the fission process in uranium. Elements with charges 43 and 61 (which are not found in nature) have been identified as fission products in fairly appreciable quantities. Most of the fission products are short-lived electron and gamma emitters that can contribute only to the local and immediate radioactive hazard. Two of the long-lived products are abundant and important. These are cesium¹³⁷ and strontium⁹⁰.

Cesium¹³⁷ has a half-life of 30 years and emits a gamma ray with an energy of 0.6 million electron-volts. Strontium⁹⁰ has a half-life of 28 years and emits an electron with an average energy of 0.22 million electron-volts. The daughter nucleus in this process is yttrium⁹⁰, which emits another electron with an average energy of one million electron-volts. The half-life of yttrium⁹⁰ is 64 hours. In effect, therefore, strontium⁹⁰ emits two electrons, each with an average energy of 0.6 million electron-volts. For the long-term radioactive hazard, particularly the world-wide fallout associated with atomic explosions, the two isotopes cesium¹³⁷ and strontium⁹⁰ are the most significant. Strontium⁹⁰ is the more dangerous to living organisms because it is deposited in the bones and retained in the body for long periods.

Besides radioactivity there is another feature of the fission process which is so conspicuous that it may seem hard to understand how Fermi failed to notice it—namely the large amount of energy released. The fission of a single nucleus of uranium releases an energy of 200 million electron-volts as contrasted with ordinary radioactive decay energies of 5 to 10 million electron-volts. (The energy released from the burning of one atom of coal is only 4 electron-volts.)

Of the 200 million electron-volts released in fission, about 10 million go into gamma rays and neutrons created in the fission process itself. This energy contributes to the immediate and local radiation danger. Another 24 million electron-volts go into radioactivity of the fission products, and of this, about half go into neutrinos, which are neither dangerous nor useful; the other half is carried by electrons and gives rise to the delayed radioactive hazard. But the bulk of the energy, over 160 million electron-volts, goes into kinetic energy of the two primary fission fragments. Of this amount, 100 million, on the average, go to the lighter fragment.

One hundred million electron-volt fission fragments should certainly have been noticed by Fermi’s radioactive counters—if they had been able to reach the counters. The fragments were not able to reach the counters, however. The reason is that Fermi was a careful worker. He knew that his sample of uranium would emit some radioactive particles even before neutron bombardment. This natural radioactivity he did not want to get mixed up with the radioactivity that would be produced in the experiment. So he put an absorbing foil between the uranium sample and the radioactive counters. The fission fragments could not get through the foil.

It is amusing that shortly afterward another noted physicist repeated Fermi’s experiment, but this time without the foil. He reported that he was unable to get any significant results because his counter, for reasons unknown, started to spark.

Thus fission remained a secret. But in England Leo Szilard obtained patent papers on the nuclear chain reaction. He pointed out that in some nuclear reactions free neutrons might be released. These neutrons might then succeed in producing further reactions which would produce more neutrons. Provided that at least one neutron made in each reaction were able to induce a reaction in another nucleus, a chain reaction would take place.

The main problem, of course, was to avoid excessive neutron losses. There are two ways in which the losses mainly occur. One is by wasteful, nonreproductive capture in the nuclei; the other, by neutron leakage from the material surface. This second loss, Szilard showed, could be minimized by using a sufficiently large amount of chain-reacting material.

The point is that a neutron born in a nuclear reaction must travel on the average a certain distance before it can produce another reaction. If the size of the chain-reacting material is much less than this distance, practically all of the neutrons produced will be able to escape through the material surface, and no chain reaction will be possible. If the size of the material is large compared to this distance, the leakage loss becomes negligible, and the possibility of a chain reaction depends entirely on the magnitude of the first kind of loss, the wasteful captures in nuclei. If this loss is not too great, and a chain reaction is possible, there will be a critical size of the material at which on the average exactly one neutron per reaction will be able to induce another reaction. A just critical chain reaction of this kind is what is needed for an atomic reactor.

If the size of the material is greater than the critical size, on the average more than one neutron per reaction will cause another reaction and the chain reaction will run away. If, for example, two neutrons can cause another reaction, there will be two neutrons after the first generation, four after the second, eight after the third, and so forth. This is the principle of the atomic bomb.

After about 80 generations, an appreciable fraction of all the nuclei in the material will have undergone a nuclear transformation and so much energy will have been released that the material will not stay together even for the short time needed to produce the next generation. The whole material begins to fly apart, the system becomes sub-critical, and the chain reaction stops. The entire process lasts only a fraction of a microsecond.

Thus even before fission was discovered, Szilard laid the basis for constructing the atomic bomb and the nuclear chain reactor. As materials in which a chain reaction might conceivably be made to occur he named thorium, uranium and beryllium. On beryllium he was wrong because the mass of this atom was incorrectly known. On thorium, his guess was good. On uranium, he hit the bull’s eye.

Finally in December 1938 the secret broke. Hahn and Strassmann in Germany made a chemical analysis of a uranium target that had been exposed to neutrons. They were far more thorough than previous investigators had been, and they found barium, charge 56, which had not been present in the target material before the experiment. The only possible explanation was the fission process. Within a few weeks the violent kicks caused by the fission products in counters were found, and in the following days this experiment was repeated around the world.

There was no doubt that neutrons could induce fission in uranium nuclei. A few more weeks, and it was ascertained that the fission process released neutrons which might lead to more fissions.

The chain reaction, however, was still far from a reality. Niels Bohr and John Wheeler proved that a neutron could not cause fission in U²³⁸ unless its energy were greater than about one million electron-volts. When the neutrons are first made in the fission process, many of them do have energies greater than one million electron-volts. But before they can cause a fission, they usually make a few nonfission collisions with uranium nuclei, giving part of their energy to the nuclei and escaping with the remainder. The nuclei are then left with too little energy to undergo fission and the neutrons with too little energy to cause fissions in their next encounters. Thus too few neutrons reproduce themselves and no chain is possible.

Bohr and Wheeler suggested, however, that the rare isotope of uranium, U²³⁵, can undergo fission when any neutron, even a slow neutron, hits it. Thus a chain reaction is possible in U²³⁵. This was confirmed experimentally shortly afterwards by John Dunning and Alfred Drier and their co-workers at Columbia University.

Why the isotopes 235 and 238 behave so differently, is not difficult to understand. The 235 is more explosive and more prone to undergo fission than 238 because it is smaller and therefore its protons repel each other more strongly. More important still, when a neutron is captured by 235, it acquires a greater kinetic energy by virtue of the short-range nuclear attraction than a neutron acquires when it is captured by 238. This happens for the simple reason that nuclei tend to be more stable when they have an even number of neutrons (or protons) than when they have an odd number. U²³⁵, having an odd number of neutrons, is more eager to receive an additional neutron than 238, which already has an even number of neutrons. Consequently, the capture of a slow neutron by 235 almost always eventuates in the fission process; while in 238, the excess energy, introduced by the neutron, is merely ejected from the nucleus in the form of a gamma ray, and U²³⁸ becomes U²³⁹.

A chain reaction is possible in U²³⁵ , but it is necessary to separate this rare isotope from the abundant U²³⁸. The separation process is anything but simple since isotopes of the same element are chemically indistinguishable. Even the weight difference in this case, is little more than one per cent. Bohr rejected the idea of a large-scale separation with the remark: “You would have to turn the whole country into a factory.” Of course it is now a matter of history that the job was actually done under the Manhattan project during World War II. During the war Bohr (alias Nicholas Baker) again visited the United States and was shown the separation plants. He said: “You see I was right. You did turn the country into a factory.”

Natural uranium contains U²³⁵ in the ratio of 1 part to 139 of U²³⁸. It was hoped at first that this concentration would be sufficient to make a chain reaction, and that the expensive enrichment processes could be avoided. This seemed possible because at energies of a fraction of an electron-volt the neutrons are much more easily caught by U²³⁵ than by U²³⁸, which compensates for the low concentration. Actually neutrons are slowed down until their energy is as low as the energy of all other particles participating in the general agitation caused by the temperature. This energy is low enough for the purpose.

However, the neutrons are made in the fission process with an energy of about a million electron-volts. Before they slow down sufficiently, they must pass through a stage in which their energy is about 7 electron-volts. In the neighborhood of this energy, it happens that the U²³⁸ has an extremely high probability for capturing a neutron and changing into U²³⁹. Near some other energies, similar though smaller absorption hurdles must be passed. Therefore natural uranium by itself cannot be used to make a chain reaction. In 1940, Fermi and Szilard, working now in the United States, found a way around this difficulty.

Their trick was to mix the natural uranium with a material whose nuclei are so lightweight that they suffer a big recoil when struck by a neutron and thus absorb a large fraction of the neutron energy. The neutron is thus moderated down to a low energy, rapidly and in big energy jumps, so that either it does not spend much time at the unfavorable energies where it can be caught by U²³⁸ or else it misses these energies altogether. By imbedding the uranium in lumps in the moderating material instead of making a homogeneous mixture of the two, the absorption can be circumvented even better.

For the purpose of making a controlled chain reaction, one may use the method of enrichment, or the method of moderation, or both. But to produce a violent chain reaction, an atomic bomb, only the enrichment method will work. The reason is that all the energy of the bomb must be generated in a time that is as short as the time it takes the bomb to fly apart, which is a fraction of a microsecond. If natural uranium were used, the reaction would be slow and sluggish and would be extinguished before a substantial fraction of the nuclei could have reacted.

It is interesting to consider that chain-reacting substances could have been obtained easily six billion years ago, before the U²³⁸ had time to decay and become a rare isotope. (The U²³⁵ was then about as abundant as U²³⁸.) A chemical separation would still have been necessary and so we do not need to imagine that chain-reacting mixtures accumulated spontaneously on the young earth.

On the other hand, six billion years from now U²³⁵ will have become so rare that it will be impossible to get a reactor going by moderation. At the same time the isotope separation will have become most expensive since the isotope to be separated will be present in an abundance of less than 100 parts in a million. For those who like to worry about the distant future we should hasten to add that other methods of obtaining atomic energy will remain possible. And in any case there is good reason to believe that some stellar explosions produce fresh supplies of U²³⁵ which space merchants could undoubtedly make available.

As to our present terrestrial supplies: uranium, like other heavy elements, is quite rare. But the earth is divided into layers of which the topmost 10 miles, forming something of a slag or scum, contain quite a few rare compounds. In particular almost all of the uranium in our planet is conveniently collected right under our feet, for us to use as we see fit.