Question

Why spin quantum number is introduced?

Answer 1

Do you remember spectrum of hydrogen atom . When strong magnetic field is applied these lines/ spectrum further splits into fine lines. This behavior and many other behavior of electron (in magnetic field) can be explained by associating a magnetic behavior with spin of electron.

The quantum spin is very different from classical spin and not yet fully understood. Moreover, exact value of spin can not be determined. But it's component can be determined which is written as 1/2. Generally counterclockwise spin is denoted by + 1/2 and clockwise spin as -1/2

Answer 2

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When we observe spectrum of yellow light by using high resolution spectroscope it has very closely spaced doublet. Similar patterns are shown by Alkali and Alkaline earth metals. In order to account this spin quantum number is introduced.