"Understanding the Spin Quantum Number -1/2 & +1/2

[i.mehrzad]

Homework Statement

Why is the spin quantum number either +1/2 or -1/2

Homework Equations

N.A.

The Attempt at a Solution

I am not sure but this is the way i thought of it.

Whatevrr quantum numbers i have known of so far: Principal, Azumithal tc. all of them have a diffrence of one between any two consecutive quantum numbers. Therefore the magnitude of the quantum numbers are +/- 1/2.

Same magnitude because the the electrons are the same in all respects.Negative because the elecrons are spinning in opposite direstions.

This explanation has no mathematical backup and is just by observation and just wanted to know wether the observation was good enough.

 

[malawi_glenn]

That is not true.

Spin is an instritinc quantity of a particle, and there are many different particles. Bosons, who has integer spin; 0,1,2,..

Fermions has half-integer spin; 1/2 ; 3/2 ; ...

Now the direction of the spin, the so called "magnetic quantum number" in many atomic physics text; is the $$m_l$$. Which obeys, precisely as the quantum number $$l$$ does; $$m_s = -s, -s +1 , ..., 0, ... , s-1, s$$.

The $$s$$ and $$l$$ is the magnitute of the spin, and the $$m_l$$ and $$m_s$$ is the direction (the magnitude of the spin/angular momentum projected on the z-axis, the z-axis is just a convention)

Now, electrons are fermions with spin 1/2, the possible values of that spin in the z-direction is -1/2 and 1/2