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.