neatly for many of the facts of radioactivity.

Why radioactivity at all, for instance? The more complex a nucleus is, the more protons must be squeezed together and the harder, it would seem, it must be to keep them together. More and more electrons seemed to be required. Finally, when the total number of protons was 84 or more, no amount of electrons seemed sufficient to stabilize the nucleus.

The manner of breakup fits the theory, too. Suppose a nucleus gives off an alpha particle. The alpha particle is a helium nucleus made up, by this theory, of 4 protons and 2 electrons. If a nucleus loses an alpha particle, its mass number should decline by 4 and its atomic number by 4 - 2, or 2. And, indeed, when uranium-238 (atomic number 92) gives off an alpha particle, it becomes thorium-234 (atomic number 90).

Suppose a beta particle is emitted. A beta particle is an electron and if a nucleus loses an electron, its mass number is almost unchanged. (An electron is so light that in comparison with the nucleus, we can ignore its mass.) On the other hand, a unit negative charge is gone. One of the protons in the nucleus, which had previously been masked by an electron, is now unmasked. Its positive charge is added to the rest and the atomic number goes up by one. Thus, thorium-234 (atomic number 90) gives up a beta particle and becomes protactinium-234 (atomic number 91).

If a gamma ray is given off, that gamma ray has no charge and the equivalent of very little mass. That means that neither the mass number nor the atomic number of the nucleus is changed, although its energy content is altered.

Even more elaborate changes can be taken into account. In the long run, uranium-238, having gone through many changes, becomes lead-206. Those changes include the emission of 8 alpha particles and 6 beta particles. The 8 alpha particles involve a loss of 8 × 4, or 32 in mass number, while the 6 beta particles contribute nothing in this respect. And, indeed, the mass number of uranium-238 declines by 32 in reaching lead-206. On the other hand the 8 alpha particles involve a decrease in atomic number of 8 × 2, or 16, while the 6 beta particles involve an increase in atomic number of 6 × 1, or 6. The total change is a decrease of 16 - 6, or 10. And indeed, uranium (atomic number 92) changes to lead (atomic number 82).

It is useful to go into such detail concerning the proton-electron theory of nuclear structure and to describe how attractive it seemed. The theory appeared solid and unshakable and, indeed, physicists used it with considerable satisfaction for 15 years.

—And yet, as we shall see, it was wrong; and that should point a moral. Even the best seeming of theories may be wrong in some details and require an overhaul.

Protons in Nuclei

Let us, nevertheless, go on to describe some of the progress made in the 1920s in terms of the proton-electron theory that was then accepted.

Since a nucleus is made up of a whole number of protons, its mass ought to be a whole number if the mass of a single proton is considered 1. (The presence of electrons would add some mass but in order to simplify matters, let us ignore that.)

When isotopes were first discovered this indeed seemed to be so. However, Aston and his mass spectrometer kept measuring the mass of different nuclei more and more closely during the 1920s and found that they differed very slightly from whole numbers. Yet a fixed number of protons turned out to have different masses if they were first considered separately and then as part of a nucleus.

Using modern standards, the mass of a proton is 1.007825. Twelve separate protons would have a total mass of twelve times that, or 12.0939. On the other hand, if the 12 protons are packed together into a carbon-12 nucleus, the mass is 12 so that the mass of the individual protons is 1.000000 apiece. What happens to this difference of 0.007825 between the proton in isolation and the proton as part of a carbon-12 nucleus?

According to Einstein’s special theory of relativity, the missing mass would have to appear in the form of energy. If 12 hydrogen nuclei (protons) plus 6 electrons are packed together to form a carbon nucleus, a considerable quantity of energy would have to be given off.

In general, Aston found that as one went on to more and more complicated nuclei, a larger fraction of the mass would have to appear as energy (though not in a perfectly regular way) until it reached a maximum in the neighborhood of iron.

Iron-56, the most common of the iron isotopes, has a mass number of 55.9349. Each of its 56 protons, therefore, has a mass of 0.9988.

For nuclei more complicated than those of iron, the protons in the nucleus begin to grow more massive again. Uranium-238 nuclei, for instance, have a mass of 238.0506, so that each of the 238 protons they contain has a mass of 1.0002.

By 1927 Aston had made it clear that it is the middle elements in the neighborhood of iron that are most closely and economically packed. If a very massive nucleus is broken up into somewhat lighter nuclei, the proton packing would be tighter and some mass would be converted into energy. Similarly, if very light nuclei were joined together into somewhat more massive nuclei, some mass would be converted into energy.

This demonstration that energy was released in any shift away from either extreme of the list of atoms according to atomic number fits the case of radioactivity, where very massive nuclei break down to somewhat less massive ones.

Consider that uranium-238 gives up 8 alpha particles and 6 beta particles to become lead-206. The uranium-238 nucleus has a mass of 238.0506; each alpha particle has one of 4.0026 for a total of 32.0208; each beta particle has a mass of 0.00154 for a total of 0.00924; and the lead-206 nucleus has one of 205.9745.

This means that the uranium-238 nucleus (mass: 238.0506) changes into 8 alpha particles, 6 beta particles, and a lead-206 nucleus (total mass: 238.0045). The starting mass is 0.0461 greater than the final mass and it is this missing mass that has been converted into energy and is responsible for the gamma rays and for the velocity with which alpha particles and beta particles are discharged.

Nuclear Bombardment

Once scientists realized that there was energy which became available when one kind of nucleus was changed into another, an important question arose as to whether such a change could be brought about and regulated by man and whether this might not be made the source of useful power of a kind and amount undreamed of earlier.

Chemical energy was easy to initiate and control, since that involved the shifts of electrons on the outskirts of the atoms. Raising the temperature of a system, for instance, caused atoms to move more quickly and smash against each other harder, and that in itself was sufficient to force electrons to shift and to initiate a chemical reaction that would not take place at lower temperatures.

To shift the protons within the nucleus (“nuclear reactions”) and make nuclear energy available was a harder problem by far. The particles involved were much more massive than electrons and correspondingly harder to move. What’s more, they were buried deep within the atom. No temperatures available to the physicists of the 1920s could force atoms to smash together hard enough to reach and shake the nucleus.

In fact, the only objects that were known to reach the nucleus were speeding subatomic particles. As early as 1906, for instance, Rutherford had used the speeding alpha particles given off by a radioactive substance to bombard matter and to show that sometimes these alpha particles were deflected by atomic nuclei. It was, in fact, by such an experiment that he first demonstrated the