Answer to Question #149272 in Quantum Mechanics for Shane

Question

Why is the spin quantum number of an electron either -1/2 or 1/2 and not other values. Please support via the use of mathematics if possible. Infinite thanks.

Answer 1

Answer

This all related to Stern Gerlach experiment. When electrion beam passed through magnetic field then Two lines are found.

Before this experiment we only consider that orbital angular momentum quantum no. $l$ so

$(2l+1)$ now we put l=0,1, 2,3.....

We get lines 1,3,5...according we caould not found two lines.

Finally spin Quantum no. s is considered as

$(2s+1) =2$

By solving this we found s=1/2

And then only two type of value of

s=$\pm$ 1/2

No other value is possible to take which can satisfy the above equation.