Spin Quantum Number: Why is it Always + or - 1/2?

[dhruvarora22]

My chemistry teacher gave us a question just to make us search that why is the Spin Quantum Number always + or - 1/2. I tried searching on the net, but i got different answers on different websites. Why exactly is it, why can't it be 1,2,3 or some other number.

 

[Fenn]

Electrons are fermions, which are particles that have a an intrinsic spin of 1/2. Maybe a good resource for you to start with is http://hyperphysics.phy-astr.gsu.edu/HBASE/spin.html#c1

 

[Borek]

I am afraid as of now the only answer to the question "why" is "because that's the way it is". This is intrinsic characteristic of electron - period.

Hyperphysics site discusses different aspects of the electron behavior - but these are effects of the electron having a spin of ±1/2, not the reason for the spin to be ±1/2.


--

 

[Fenn]

A great quote I once heard went something like, "It is easy to describe what light does, but it is hard to describe what light is." I suppose that can be applied to various fundamental concepts.

When I think back to my undergraduate quantum mechanics course, my professor introduced orbital angular momentum, and described a lot of implications and observations based on its nature. Spin angular momentum was introduced since it behaved analogous to orbital angular momentum. The initial picture of an electron was a spherical object, spinning on its own axis like a top. As another picture, imagine the Earth rotating around the sun as depicting orbital angular momentum, and the Earth rotating about its own axis (night/day) as depicting spin angular momentum. Very crude, but it kinda illustrates the initial picture.

This intrinsic angular momentum associated with its spin about its own axis helped explain a lot of observations (like why electrons would deflect into two beams in a http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment" ). The value of 1/2 came out from the fact that only two possible outcomes were possible.

 

[Sunny09]

There is a long derivation to prove this requiring a theorem which i think is not even included in M.Sc. So don't stress urself out too much.
Btw, I haven't studied much about spin q. no. till now(just one class!) but my teacher said that there is a single orbital and according and the electrons rotate opposite to each other.
So, the value is +1/2 and -1/2.
I'm not so sure abt this anyways