Why is spin quantum number denoted by +/- 1/2?
This is actually pretty arbitrary and driven by the mathematics. Quantum Mechanics is highly mathematical (in fact it is entirely differential operators) as opposed to a real tangible kind of understanding. The quantity of “1/2” is really very arbitrary and arises purely because -1/2 and +1/2 are negatives of each other and are exactly “1” apart. Quantum mathematics, as you may know, involves a lot of “+1” mathematics (because quanta are individual units), so having two opposite number which are exactly 1 apart is very useful.
In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. The spin quantum number is the fourth of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter s.
In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. The spin quantum number is the fourth of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter An electron spin s = 1/2 is an intrinsic property of electrons. Electrons have intrinsic angular momentum characterized by quantum number 1/2. The energy of any wave is the frequency multiplied by Planck’s constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck’s reduced constant which only allows particular or discrete or quantized energy levels. The reduced Planck’s constant is used because in a wave, a
