what is the meaning of "1/2 spin" of a particle?

Answer 1

When you get down to atomic sizes, a lot of things can only exist in multiples of a certain fundamental constant (Planck's Constant, to be specific). When looking at the angular momentum of electrons, scientists found they tended to be integer multiples of Planck's Constant. But then they found another property that acts kinda like angular momentum, but comes in multiples of half Planck's Constant. This is "spin", which really isn't exactly like anything we can think of at our scale, but it behaves more like spinning than anything else, so the name stuck.

This has been a vast oversimplification, of course.

Answer 2

Spin is a name for the intrinsic angular momentum property of a particle. The math could be rewritten according to an integral convention for spin numbers. Perhaps it would make the equations more clear, perhaps less clear. But it's too deeply ingrained to changed now. You might as well decide that the electron charge should be called positive and the proton negative.

Answer 3

1/2 spin refers to the direction in which the particle is moving about its axis, sort of like the earth rotating around its axis to bring us day and night. 1/2 spin means one direction, and -1/2 spin means the other direction.

Also, no two electrons with the same spin can occupy the same electron shell