Why is spin quantum number assigned + or - 1/2 & not + or -1 ?

Question

IT IS BASED ON THE QUANTUM MECHANICAL MODEL OF AN ATOM.

Answer 1

Spin is an example of quantized angular momentum. The general theory of this is purely mathematics, and deals with "unitary representations of the rotation group O(3)".

Now that is not very relevant here, but what is relevant is the following conclusion: the eigenstates (defined states) for an angular momentum operator (such as spin) can be characterized by two numbers ("quantum numbers"):

- the number J, which can take integral and half-integral values: 0, 1/2, 1, 3/2, 2, 5/2, etc.
- the number m, which can take on the values -J, -J+1, ... , J-1, J.

For instance, if J = 2, the possible values for m are -2, -1, 0, +1 and +2. If J = 3/2, the possible values for m are -3/2, -1/2, +1/2, +3/2.

Given the value for J, the number of possible m-values is equal to 2J+1. Electrons have a definite J-value, but can have two possible m-values. It follows immediately that J = 1/2, so that m is either -1/2 or +1/2.

If a angular momentum can be assigned quantum numbers m = +1 and m = -1, the value m = 0 would also be possible, giving three possible states. This is the case, for instance, with the orbital angular momentum of p-orbits, or the total angular momentum of triplet states.

Answer 2

The main reason is that the amount of angular momentum associated with spin is half the smallest amount associated with orbital motion. Since the smallest orbital angular momentum had already been given the designation of 1, that meant that spin had to be assigned the value 1/2. Also, in terms of Planck's constant, the spin angular momentum is (1/2)hbar, while that for orbitals is hbar.

There *are* particles with spin 1: photons. Some mesons also have spin 1.

Answer 3

Unlike the other quantum numbers, the electron spin can not be associated with a physical effect but result from the barely mathematical requirements of tensor calculation.

I fondly remember my physical chemistry professor telling a gaping audience "Now things become a bit abstract" after a couple of weeks doing quantum mechanics... ;)

Answer 4

Chem guy is sweet with regard to the fact the s is the quantum extensive form that determines spin, yet he's incorrect whilst he says the electrons themselves are spinning, they do no longer seem to be spinning. It only has a magnetic field as though its spinning. Electron spin is in basic terms a attractiveness for the intrinsic angular momentum of the electron. Electrons like many subatomic debris have spin, its in basic terms a thank you to describe the magnetic field that the particle reflects. s=+a million/2 l s= -a million/2

Answer 5

They are still expanding and testing and developing the theory, but some string theorists hypothesize that there are particles that DO have spin 1 and spin -1. Maybe we just haven't found them yet.

Answer 6

I think it is purely instrumental, these values since they do not represent any 'real' property are just the values that make the math work