Nuclear Spin
What Rutherford did not (and could not) take into account were the consequences of a completely new type of nuclear bombardment involving a type of particle unknown in the 1920s (though Rutherford speculated about the possibility of its existence).
The beginnings of the new path came about through the reluctant realization that there was a flaw in the apparently firmly grounded proton-electron picture of nuclear structure.
The flaw involved the “nuclear spin”. In 1924 the Austrian physicist Wolfgang Pauli (1900-1958) worked out a theory that treated protons and electrons as though they were spinning on their axes. This spin could be in either direction (or, as we would say in earthly terms, from west-to-east, or from east-to-west). Quantum theory has shown that a natural unit exists for what is called the angular momentum of this spin. Measured in terms of this natural unit of spin, the proton and the electron have spin ½. If the particle spun in one direction it was +½, if in the other it was -½.
When subatomic particles came together to form an atomic nucleus, each kept its original spin, and the nuclear spin was then equal to the total angular momentum of the individual particles that made it up.
For instance, suppose the helium nucleus is made up of 4 protons and 2 electrons, as was thought in the 1920s. Of the 4 protons, suppose that two had a spin of +½ and two of -½. Suppose also that of the 2 electrons, one had a spin of +½ and one of -½. All the spins would cancel each other. The total angular momentum would be zero.
Of course, it is also possible that all 6 particles were spinning in the same direction; all +½ or all -½. In that case the nuclear spin would be 3, either in one direction or the other. If 5 particles were spinning in one direction and 1 in the other, then the total spin would be 2, in one direction or the other.
Wolfgang Pauli lecturing in Copenhagen in April 1929.
In short if you have an even number of particles in a nucleus, each with a spin of +½ or -½, then the total spin is either zero or a whole number, no matter what combination of positive and negative spins you choose. (The total spin is always written as a positive number.)