Which quantum number describes electron spin values?

The spin quantum number, which takes only two values for an electron, conventionally written as plus and minus one half - up and down. It is the fourth of the four numbers that specify an electron's state, and it was added because the first three could not explain the spectra.

Nothing is spinning. The name comes from an early picture of the electron as a rotating ball, which fails immediately: to produce the observed magnetic moment, a sphere the size of an electron would have to turn faster than light, and the electron has no measurable size anyway. Spin is an intrinsic property with no classical equivalent, like charge - the particle simply has it.

It is also the reason matter takes up space. Because electrons have half-integer spin they obey the exclusion principle, so no two in an atom can share all four quantum numbers; that forces them into successive shells, which produces the periodic table, chemical bonding and every property of every material. Two graduate students proposed spin in 1925 and tried to withdraw the paper as obviously wrong; their supervisor told them it had already been sent, and that they were young enough to afford a stupidity.