CHAPTER III. Nuclei

Nuclei

Up to now we have regarded atoms as being divisible into electrons and nuclei. Electrons and nuclei, however, we have regarded as indivisible entities. This point of view is perfectly adequate to account for all the facts of chemistry and most of the facts of physics. Even in physics, it has not been necessary to ascribe an internal structure to the electron. The electron is a truly elementary particle in this sense. However, to understand some physical phenomena, and radioactivity is one of these, it is necessary to recognize that the nucleus is not indivisible but consists of parts. The parts of the nucleus are called protons and neutrons.

The simple statements of the previous chapter apply to these smaller particles also. All electrons are equal—precisely equal. All protons are equal and all neutrons are equal. There are methods which would have shown up exceedingly small differences between these particles. No such differences have been discovered. As far as we know these particles are always the same. We cannot pour energy into them and excite them as was the case with the atoms. When we come to consider these small particles, the complex structure of the world has an end. Instead what we find is simple.

A proton and a neutron have almost exactly the same weight. The proton has one unit of positive charge, which means that its charge is the same as that of the electron except that it is opposite in sign. The neutron, as its name implies, is an electrically neutral particle. Hence the charge of the nucleus is equal to the number of protons it contains, and is independent of the number of neutrons. The weight of the nucleus, however, taking the proton (or the neutron) as a unit of weight, is equal to the number of protons plus the number of neutrons.

Imagine that we have two atoms whose nuclei have the same number of protons but a different number of neutrons. Such atoms exist in nature and are called isotopes. The point about these isotopes is that since they have the same number of protons, they have the same nuclear charge, the same electron structures, and hence they have almost the same chemical properties. Their nuclei have somewhat different volumes. But the nucleus is small in any case. It is almost as though we tried to look for the difference between nothing and twice-nothing. The difference in the weights of isotopes due to the difference in their numbers of neutrons, has only a negligible influence on their chemical behavior. An important consequence of this fact is that molecules which differ only in that one isotope has been substituted for another are biologically indistinguishable. They taste the same and smell the same. They are ingested in our bodies in the same way, and they are deposited or excreted in the same way.

The simplest isotopes are the isotopes of hydrogen. Most of the hydrogen atoms we find in nature have a nucleus which is a single proton. This is the common hydrogen or light hydrogen. A few hydrogen atoms, however, have nuclei which consist of a proton and a neutron. This is the heavy hydrogen, found in heavy water. In all natural sources of water these two kinds of hydrogen are mixed in a ratio which is practically the same for every sample. The electron circulating around the nucleus behaves almost exactly the same way whether the extra neutron is present or not. On the state of that electron depend most properties of the atom and the molecules which contain it. Of course, heavy hydrogen has twice the weight of common hydrogen, and heavy water is somewhat more dense than light water. But otherwise there is little difference.

The story of the discovery of the hydrogen isotopes is amusing. About half a century ago—before the discovery of any isotope—two scientists tried to measure the density of water. They purified the water by boiling it and condensing the vapor. But the more they purified, the lighter it became—slightly but perceptibly. Finally they gave up: water seemed to have no density!

What really happened was this: Light water boils a little bit more easily than heavy water. Without realizing it, these scientists had started to separate isotopes.

Many years later Harold Urey—on the basis of some mistaken experiments of other people—concluded that heavy hydrogen must exist. He looked for it and found it, but found much less than he had expected. There was so little heavy hydrogen that on the basis of correct experiments Urey never would have guessed its presence. It seems that an unfounded idea is much more fruitful than the absence of an idea.

Almost all naturally occurring elements are found to consist of more than one isotope. Uranium, for example, is composed mainly of two, one having 143 neutrons and the other having 146. Since both of these isotopes have 92 protons, their weights are 92 + 143 = 235 and 92 + 146 = 238 respectively. It is customary to refer to these isotopes as U²³⁵ and U²³⁸. The U²³⁵, which is valuable in atomic reactors and in the manufacture of atomic bombs, is comparatively rare, occurring as only one part in 140 of natural uranium. The separation of this rare isotope from the common 238 was one of the major undertakings of the two billion dollar Manhattan Project during World War II.

We come now to a most important question, one that will lead us to the idea of radioactivity: What is it that determines which isotopes a given element will have? For example, uranium has isotopes weighing 235 and 238. Small amounts of U²³⁴ and U²³⁶ are also found in nature. Why do we not find U²³², U²³³, U²³⁷ or U²³⁹? Evidently only certain numbers of neutrons will hang together with 92 protons.

Consider another example, this time of the lightest known element, hydrogen. We have already mentioned two isotopes of hydrogen: light hydrogen with weight 1 (symbolized H¹), having a nucleus consisting of a single proton and no neutrons, and heavy hydrogen (also called deuterium) of weight 2 (H²), having one proton and one neutron. The latter isotope occurs as only about one part in 5,000 of natural hydrogen. There is also a slight trace of tritium (H³), having one proton and two neutrons. But here the sequence stops. What has happened to H⁴, H⁵, H⁶, etc?

This question is related to the earlier one: why there are no atoms in nature of charge 43, 61, 85, and 87, and why there are none with charges greater than 92. To answer these questions requires a little knowledge about the laws which govern the motion of neutrons and protons within the nucleus, and the nature of the forces which are exerted by a neutron on a neutron, a neutron on a proton, and a proton on a proton.

The motion of neutrons and protons within the nucleus is governed by the same laws which govern the motion of electrons within the atom. For both the nucleus and the atom there is a ground state of motion which has more stability (less energy) than any other state. Of course the arrangement and motion of electrons in the atom depend not only on this general rule but also on the specifically electrical nature of the forces which act between the electrons and the nucleus. In the same way the arrangement and motion of the neutrons and protons within the nucleus depend upon the nature of the forces which act between neutrons and protons.

These forces are definitely not of gravitational origin. Gravitational attraction is extremely weak compared to the attraction between neutrons and protons, and is utterly negligible in the realm of nuclear phenomena. Neither can the nuclear forces be electrical in origin. The neutrons are electrically neutral; and the protons actually repel each other by virtue of their electrical charge. The nuclear forces are something entirely new. They are the strongest forces yet encountered, and they are without a counterpart in the macroscopic world.

Nuclear forces are not yet completely understood. But to understand nuclear stability we need to know only one peculiar fact governing the behavior of neutrons and protons (and incidentally also electrons): They want to be different. To each particle a state or pattern of motion can be assigned. When any two neutrons are compared, their pattern of motion must be essentially different. The same holds for any two protons. A neutron and a proton, however, may be found in similar patterns since they differ anyway in their charge.

Now among the possible patterns of motion some have lower and some have higher energies. Individual neutrons and protons will first occupy the lowest energy states, in accordance with the rule of least energy for maximum stability. Then the demand for a difference will force subsequent particles into patterns of higher and higher energies.

Since a neutron does not exclude a proton from being in the same pattern, the lowest energy state may be occupied simultaneously by one neutron and one proton. If another neutron or proton is added, it must be put into the next state of higher energy. For this reason we would expect that nuclei are most stable when they contain an equal or nearly equal number of neutrons and protons. For nuclei which are not too heavy, this is indeed the case. For example, nitrogen, which has seven protons, has two stable isotopes, N¹⁴ and N¹⁵, with seven and eight neutrons respectively. For heavy nuclei, however, the situation is a little different.

The nuclear force between neutrons and protons acts only over a very short range—the particles must almost be in contact with each other in order to experience a sizeable attraction. Consequently a neutron or a proton interacts only with its immediate neighbors in the nucleus. The electrical repulsion between the protons, however, acts over a much longer range. A proton is repelled by all the other protons in the nucleus. For heavy nuclei this repulsion is sufficient to reduce the number of protons relative to the number of neutrons. Lead, for example, with 82 protons, has four stable isotopes, with 122, 124, 125, and 126 neutrons.

We have said that seven protons will combine stably with seven or eight neutrons. What happens if seven protons are combined with six or nine neutrons (to make N¹³ or N¹⁶)? Our rule does not prevent them from sticking together; it says only that these combinations would be more stable if a proton could be converted into a neutron (in the case of six) or a neutron into a proton (in the case of nine).

Actually seven protons and nine neutrons do stick together, but such a nucleus is not stable and does not continue to exist indefinitely. The reason is quite simple and a little surprising: The conversion of a neutron into a proton is actually a physically realizable process, and furthermore it releases some energy. Similarly a nucleus containing seven protons and six neutrons will have an existence of only finite duration because the conversion of a proton into a neutron can also occur. Of course the proton is charged and the neutron is not. What happens to the charge during these transformations? Actually the neutron is transformed, not into a proton, but into a proton plus an electron. The proton is transformed likewise into a neutron plus something else. This something else is called a positron and is identical with the electron in every respect except in having a positive instead of a negative charge.

The changes just described occur spontaneously. They are examples of radioactivity. More specifically they are called “beta decay” processes because an electron (or a positron) when emitted by a nucleus is called a beta ray. Such beta-radioactive substances are produced whenever nuclear energy is used in an explosion or in a power plant. Many of the difficulties and worries concerning nuclear energy are connected with these beta activities. We shall be concerned with them often as harmful, sometimes as helpful agents.

When a neutron is converted into a proton and an electron inside a nucleus, the electron escapes immediately, but the proton remains in the nucleus. Similarly, when a proton is converted into a neutron and a positron, the positron escapes and the neutron remains in the nucleus. Since the electron and the positron have a negligible weight compared to a proton or a neutron, the process of beta decay leaves the weight of the nucleus nearly unchanged. Since the electron and the positron are charged, the process of beta decay increases or decreases the charge of the nucleus by one unit.

After beta decay a nitrogen nucleus with seven protons and six neutrons (N¹³) becomes a nucleus with six protons and seven neutrons—carbon with weight 13 (C¹³), which is a stable combination. Similarly a nitrogen nucleus with seven protons and nine neutrons (N¹⁶) becomes a nucleus with eight protons and eight neutrons, oxygen with weight 16 (O¹⁶), which is ordinary stable oxygen.

Sometimes after a beta decay the residual nucleus finds itself with a “correct” number of neutrons and protons but with an excess of energy. That is, the residual nucleus is not in its ground state but is excited. This happens in about two thirds of the known cases of beta decay. It happens, for instance, when N¹⁶ decays to O¹⁶.

In this situation the excited nucleus will behave like an excited atom. An excited atom, the reader will recall, gets rid of its excess energy by emitting electromagnetic radiation, usually visible or near-visible light. The excited nucleus will get rid of its excess energy in exactly the same way. The only difference is that the amount of energy carried by the electromagnetic radiation from the nucleus is approximately a million times greater than that carried by the electromagnetic radiation from the atom—an indication of the large quantity of energy stored up inside the nucleus. Such energetic electromagnetic radiation emanating from a nucleus is usually called a gamma ray. Gamma-ray emission, or gamma decay, like beta decay, is an energy-releasing process which changes an unstable nucleus into a stable one, or at least into a more stable one. More generally, any spontaneous energy-releasing process (which tends to stabilize the nucleus) is called radioactivity. Beta and gamma decay are two examples. Later on we shall consider a third example called alpha decay. An alpha particle is the nucleus of the helium atom and consists of two neutrons and two protons.

The decay of a neutron and the decay of a proton appear to be quite analogous processes. Actually there is an important difference between the two. A free neutron—one not confined inside a nucleus—will decay into a proton and an electron; but a free proton will not decay into a neutron and a positron. This difference is due to the fact that the proton has a slightly lower weight than the neutron and therefore has less energy. For the proton to decay, it must be inside a nucleus where it can absorb some energy from the other protons and neutrons.

One sometimes finds pairs of nuclei which could transform into each other by a proton-neutron (or neutron-proton) conversion; nevertheless neither of these conversions can occur in the way we have just described. The reason is that in a proton-neutron or neutron-proton conversion an additional electron or positron has to be emitted. Now according to Einstein the mass of the electron or positron corresponds to some energy (E = mc²), and it may happen that neither the neutron-proton transformation or the proton-neutron transformation releases enough energy to make an electron or a positron.

In such cases one of the innermost electrons of the atom may combine with a proton to make a neutron. Such an electron-capture process will always release energy provided that the reverse process—the transformation of a neutron into a proton and an electron—is connected with an energy deficit. Thus, excluding the possibility of a really exact coincidence of two energies, one of the two transformations from neutron to proton or proton to neutron will always be possible.

It is one of the most firmly established laws of nature that energy is always conserved. One would therefore expect that the energy of a beta ray would be exactly equal to the difference between the energy of the nucleus before the beta decay and the energy of the nucleus after the beta decay. As a matter of fact the energy of a beta ray is found never to be as great as this amount. Frequently it is much less. Some of the energy has apparently disappeared and the suspicion has been voiced that energy may not be conserved after all. It has turned out, however, that the missing energy is smuggled out of the nucleus, and the smuggler (who has only recently been caught) is called the neutrino.

The neutrino is an electrically neutral particle, like the neutron, but its weight, like the weight of a ray of light, is equal to zero. Like such a ray, it moves with the velocity of light.

The energy released by the nucleus in the beta-decay process is shared more or less equally between the neutrino and the beta ray. We shall see later that the electron gives rise to a number of effects. Some of these are harmful. The neutrino, however, is not in the least dangerous. Like an ideal smuggler it passes unnoticed and practically without a trace. It interacts so slightly with matter that several billion of them may go right through the whole sphere of our earth before a single collision occurs.

Very recently this strange little particle has upset one of our most unquestioned concepts about symmetry. We have always believed that nature made no distinction between her right hand and her left hand; that for every natural process that exists, there exists also the mirror image of this process. The neutrino, however, is an exception. It has a definite symmetry, like a screw. This fact may turn out to be most important in the development of science. It has no bearing, however, on the questions to be discussed in this book.

Neutrinos reach us from some distant and hidden places like the interior of our sun and of exploding stars. It may become possible to use neutrinos as messengers to reveal the kind of nuclear reactions from which the energy of the stars is derived.

Neutrinos are also emitted every time we release some nuclear energy. Among all the remarkable practical consequences of nuclear energy, the neutrinos have a unique distinction: they are never useful, and they are never harmful. They have not even been suspected of any mischief.