On the other hand, suppose you have lithium-7, which was thought to be made up of 7 protons and 4 electrons. If the 7 protons were all +½ and the 4 electrons were all -½ in their spins, the nuclear spin would be ⁷/₂ - ⁴/₂ = ³/₂.
If you have an odd number of particles in the nucleus, you will find that any combination of positive and negative spins will never give you either zero or a whole number as a sum. The sum will always include a fraction.
Consequently, if one measures the spin of a particular atomic nucleus one can tell at once whether that nucleus contains an even number of particles or an odd number.
This quickly raised a problem. The nuclear spin of the common isotope, nitrogen-14, was measured accurately over and over again and turned out to be 1. There seemed no doubt about that and it could therefore be concluded that there were an even number of particles in the nitrogen-14 nucleus.
And yet, by the proton-electron theory of nuclear structure, the nitrogen-14 nucleus, with a mass number of 14 and an atomic number of 7, had to be made up of 14 protons and 7 electrons for a total of 21 particles altogether—an odd number.
The nuclear spin of nitrogen-14 indicated “even number” and the proton-electron theory indicated “odd number”. One or the other had to be wrong, but which? The nuclear spin was a matter of actual measurement, which could be repeated over and over and on which all agreed. The proton-electron theory was only a theory. It was therefore the latter that was questioned.
What was to be done?
Suppose it is wrong to count protons and electrons inside the nucleus as separate particles. Was it possible that an electron and a proton, forced into the close confinement of the atomic nucleus might, by the force of mutual attraction, become so intimately connected as to count as a single particle. One of the first to suggest this, as far back as 1920, was Rutherford.
Such a proton-electron combination would be electrically neutral and in 1921 the American chemist William Draper Harkins (1873-1951) used the term “neutron” as a name for it.
If we look at the nitrogen-14 nucleus in this way then it is made up, not of 14 protons and 7 electrons, but of 7 protons and 7 proton-electron combinations. Instead of a total of 21 particles, there would be a total of 14; instead of an odd number, there would be an even number. The structure would now account for the nuclear spin.