Chapter 30, Problem 43PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# What angles can the spin S of an electron make with the Z-axis?

To determine

The angles which can the spin S of the electron make with the zaxis.

Explanation

Given Data:

Given that spin S of the electron make with the z-axis

Formula Used:

The spin projection referring to spin up is given as

â€ƒâ€ƒms=+12

The spin projection referring to spin down is given as

â€ƒâ€ƒms=âˆ’12

Hence, spin projection is given as

â€ƒâ€ƒms=Â±12

The angle spin S of the electron make with the zâˆ’axis is given as

â€ƒâ€ƒcosÎ¸=SZS

Where SZ= z component of spin angular momentum =ms(h2Ï€)

And

â€ƒâ€ƒS= Intrinsic spin angular momentum

â€ƒâ€ƒS=s(s+1)(h2Ï€)

Calculation:

Given spin S of the electron make with the zâˆ’axis.

We know that The angle spin S of the electron make with the zâˆ’axis is given as

â€ƒâ€ƒcosÎ¸=SZS

Now SZ=ms(h2Ï€)

Substituting ms=Â±12

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