So, that's the second quantum number.
I think this is taken about two years after they discovered the fourth quantum number.
It required the introduction of a fourth quantum number, a highly counterintuitive move as the new quantum number represents nothing that can be visualised.
So, we need to actually add on this fourth quantum number, and it's either going to be plus 1/2 or negative 1/2.
So, that's an important distinction to make -- what three quantum numbers tell us, versus what the fourth quantum number can fill in for us in terms of information.
And as the story goes, as Goudsmit was leaving and the door with slamming, Wolfgang Pauli was already writing down this idea into a scientific paper of the idea of a fourth quantum number.
But at the time, they didn't have a well-formed name for it, they were just saying OK, there's this fourth quantum number, there's this intrinsic property in the electron.
So I think we are, in fact, ready to move on to multi-electron atoms, and what happens is when we solved the relativistic version of the Schrodinger equation and we're discussing more than one electron, we actually have a fourth quantum number that falls out and that we need to deal with and this is called the electron spin quantum number.
So we can completely describe an orbital with just using three quantum numbers, but we have this fourth quantum number that describes something about the electron that's required for now a complete description of the electron, and that's the idea of spin.
Although the model was augmented by more elaborate specifications of the orbits (most notably, first, by allowing for elliptical orbits and introducing a second quantum number to specify the elongation of the ellipse and, second, by allowing for the effects of relativity), the failure to generalize to many-electron atoms remained a fatal flaw.
In 1925, however, two Dutch physicists, Samuel Goudsmit and George Uhlenbeck, realized that, in order to explain fully the spectra of light emitted by the atoms of alkali metals, such as sodium, which have one outer valence electron beyond the main core, there must be a fourth quantum number that can take only two values, −1/2 and +1/2.
