CHAPTER V. Breakup of the Nucleus

Breakup of the Nucleus

The positive electric charges within an atomic nucleus repel one another. In the most heavily charged nuclei this repulsion becomes so great that the nucleus can break into two parts, simultaneously releasing a considerable amount of energy. In the case of spontaneous nuclear fission the two parts are more or less equal in size. In the process of alpha decay one of the parts (the alpha particle) is much smaller than the other.

An alpha particle consists of two neutrons and two protons and is identical with the nucleus of the helium atom. (The symbol for this nucleus is He⁴.) Since two neutrons and two protons can simultaneously occupy the lowest energy state, the alpha particle is an especially stable nuclear unit. As a result, from time to time in heavy nuclei, two neutrons and two protons will coalesce into an alpha particle, which may then attempt to escape.

In attempting to escape from the nucleus, however, an alpha particle encounters considerable resistance because of the short-range nuclear attraction of the other neutrons and protons. This resistance which an alpha particle experiences in trying to leave the nucleus is usually referred to as an “energy barrier.” If the alpha particle could acquire a little additional energy, it would be able to overcome the barrier and get away from the nuclear attraction. Once outside the nucleus, just beyond the reach of the nuclear attraction, the alpha particle would be accelerated violently outward by the large electrical repulsion between its two protons and the other protons in the residual nucleus.

The alpha particle needs some extra energy to escape. According to the laws of older physics there is no possibility for it to obtain this extra energy and therefore escape is impossible. But the more newly discovered laws governing the motion of neutrons and protons (the laws of quantum mechanics) are not so stringent; they permit the alpha particle to use “borrowed” energy to overcome the energy barrier. Of course the alpha particle must always repay the loan—which it can easily do out of the large fund of electric energy that is released when it gets out of the repulsive range of the residual nucleus. There is no interest on the loan.

Such energy loans are not automatically granted in nature. There are two factors which make the loan improbable: if the amount is big or if the term is long. These restrictions effectively limit the particles which may apply for an energy loan. Objects of great size and weight are unable to qualify, but the small particles of the atomic world often do.

The more energy carried off by the alpha particle after the alpha decay, the less energy must be borrowed in order to overcome the barrier, and the more rapidly the decay may be expected to occur. So sensitive is the decay to the energy of the alpha particle, that an alpha particle carrying twice the energy is emitted a hundred trillion times fester.

Half-lives for alpha decay vary from a fraction of a second to billions of years. But even the shortest half-life for alpha decay is remarkably long compared to the time required for the alpha particle to cross the nucleus. This means that the alpha particle makes a tremendous number of attempts to escape from the nucleus before it actually succeeds. According to the older classical theory the alpha process should never occur, and in fact it occurs with a very small probability.

A single alpha decay is not usually a sufficient process to bring about stability of the daughter nucleus. A whole chain of radioactive decays is usually required before stability is achieved. Most nuclei which emit alpha particles belong to one of these radioactive decay chains.

The heavy nuclei for which alpha decay occurs all contain a large excess of neutrons. Since the alpha particle carries off exactly two neutrons and two protons, the ratio of the number of neutrons to the number of protons is increased in the daughter nucleus. This has an unstabilizing influence. (Actually, in lighter nuclei stability requires that the ratio of neutrons to protons be closer to unity.) The daughter nucleus is thus apt to be beta-active, converting a neutron into a proton (plus an electron and a neutrino) in order to decrease its ratio of neutrons to protons. In this way a chain of radioactive decays may occur, more or less alternating between alpha and beta emissions, with gamma rays being occasionally emitted also.

There are four radioactive chains. One of them starts with the abundant isotope of uranium, U²³⁸. This isotope undergoes a few alpha decays and a couple of beta decays to become radium, which has a charge of 88 and a weight of 226. All the radium in the world is produced in this manner as a daughter product in the fifth decay of the chain. After a number of further decays, stable lead (weight 206) is produced and the chain terminates.

The other chains are similar to the U²³⁸ chain, though not quite as long. One chain starts with the rare isotope of uranium, U²³⁵; another starts with the isotope of thorium that weighs 232. Both of these terminate in stable isotopes of lead. In all cases the first decay of the chain has a very long half-life. The half-life of U²³⁸ is 4.5 billion years; of U²³⁵, 710 million years; and of thorium, 14 billion years.

The fourth radioactive chain has been made in the laboratory but is not found in nature because its first isotope, neptunium with weight 237, has too short a half-life. It decays in two million years and all the other members of the chain live for even shorter periods. Thus the neptunium chain decayed long ago, whereas the three other chains have survived from the time when the elements were made.

It is interesting to notice that the lesser abundance of U²³⁵, as compared with U²³⁸, is connected with its shorter half-life. Assuming that comparable amounts of both isotopes were present at the beginning of the universe (and there is good reason to believe that this was the case), one would expect to find significantly less U²³⁵ than U²³⁸ after a period of a few hundred million years. After 710 million years (the half-life for U²³⁵) only one half of the original number of U²³⁵ nuclei would still exist. But 90 per cent of the original U²³⁸ nuclei (half-life 4.5 billion years) would remain. From the presently observed ratio of U²³⁵ to U²³⁸ nuclei (1 to 139), it may be calculated, using the law of radioactive decay, that 6 billion years ago natural uranium consisted of equal parts of U²³⁵ and U²³⁸. The age of the universe is hotly debated. With each passing year the universe seems to be a billion years older. Right now six billion years does not seem widely off the mark.

Natural radioactivity occurs mainly among the heavy elements, but there are a few light elements that are naturally radioactive. Of these, potassium⁴⁰ is an especially interesting one because it can decay either by electron emission or by electron capture. The processes are:

potassium⁴⁰ → calcium⁴⁰ + electron + neutrino, (1.1 billion years)

and

potassium⁴⁰ + electron → argon⁴⁰ + neutrino. (11 billion years)

Calcium⁴⁰ and argon⁴⁰ are both stable nuclei. The second reaction is followed immediately by a gamma ray emission from the argon⁴⁰. The one per cent of argon found in the earth’s atmosphere comes almost entirely from the second reaction. These radioactivities are also interesting because appreciable amounts of potassium⁴⁰ are always present in human tissue.

All nuclei at the heavy end of the periodic system are radioactive alpha emitters. Uranium, for example, has no stable isotopes; they all undergo alpha decay. But there is another mode of spontaneous decay of uranium, which is much less frequent than alpha decay but is of much greater practical importance. This is the fission process.

The fission process is just like alpha decay in that the nucleus breaks up into two fragments. The main difference between these processes is in the relative weights of the fragments. In the alpha decay of U²³⁸, for instance, one fragment has a weight of four and the other 234. In the fission process the fragments tend to be more nearly equal in weight. For example, one may weigh 90 and the other 148. Other weight combinations are also possible.

The explanation of spontaneous fission is in essence the same as that of alpha decay. Spontaneous fission, however, is a less probable process because the two fragments are more strongly bound to each other by the nuclear forces than they are in alpha decay. More energy must be borrowed, and it must be borrowed for a longer term in order to penetrate the energy barrier.

The relative likelihoods of spontaneous fission and alpha decay can be appreciated from the following fact. In one hour in a gram of U²³⁸ there occur about 45 million alpha decays but only about 25 spontaneous fissions.

Once the energy barrier has been overcome, the energy released in alpha decay or spontaneous fission is proportional to the charges on the two fragments. For alpha decay, the product of the charges is 2 × 90 = 180; for spontaneous fission, this product will typically be about 40 × 52 = 2,080. Hence one might expect the fission energy release to be 10 to 15 times greater than the alpha energy release. As a matter of fact the fission energy release is even greater than this estimate indicates, being about 30 to 50 times greater than the alpha energy release. That so large an amount of energy is released, is a very important feature of the fission process from the point of view of practical utilization of atomic energy.

Being at the end of the periodic system, uranium requires a large ratio of neutrons to protons for its greatest stability. The fission fragments, however, lie in the middle of the system of elements, requiring a much smaller ratio of neutrons to protons for stability. This has two consequences.

One is that the fragments themselves may be expected to be unstable. They will undergo beta decay (electron emission) several times consecutively before a stable combination of neutrons and protons is reached. This radioactivity of the fission products constitutes a potential hazard in any practical application of fission atomic energy. In later chapters of this book we shall consider particularly the possible hazard from the fallout of radioactive fission products created in atomic explosions, and also the hazard associated with the operation and maintenance of atomic reactors.

The second consequence of the neutron excess is that neutrons may boil off from the fragments immediately after the fission process has occurred. This can happen because a lot of disorderly internal motion is generated by the fission process within the fragments, and these fragments do not have a particularly strong hold on their neutrons. The practical value of the released neutrons is something we shall discuss at length in a later chapter. For the present we mention only that these neutrons provide the mechanism whereby a chain reaction is made possible.

Spontaneous fission and alpha decay are responsible for the fact that elements with charge greater than 92 are not found in nature. There is little doubt that these elements were made in the beginning. But they have long since decayed.

An interesting case of spontaneous nuclear fission is californium²⁵⁴ (charge 98), with a half-life of 55 days. This isotope is formed in large quantities in certain stellar explosions called super-novae. Once in a millennium one of a collection of a billion stars flares into incredible brilliance. For a few weeks this single star shines with the combined energy and luster of a billion ordinary stars—then it fades away gradually. Such a “new” star (nova), with the greatest power of radiation, is called a “super-nova.”

We believe that many nuclear reactions take place in a super-nova. It has been observed that a few weeks after the initial outburst of light, the intensity of light is reduced almost exactly by a factor of two every 55 days for a year or so. This is precisely what would be expected if the energy generated in the star during this time were due to the spontaneous fission of californium²⁵⁴. Here we see a model of what happens to naturally radioactive elements. Of these we have retained on earth only the ones with the longest half-lives, like uranium, thorium, and potassium.