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.