Question

What is the smallest angle in degrees that L makes with the z -axis for an...

What is the smallest angle in degrees that L makes with the z -axis for an l = 2 electron?

Here is what I did:
L = ?(2(2+1)h) L = ?6
A: m = –2: ? = cos–1 (–2/?6) = 144.7356103
B: m = –1: ? = cos–1 (12/?6) = 114.0948426
C: m = 0: ? = cos–1 (0/?6) = 90
D: m = 1: ? = cos–1 (1/?6) = 65.90515745
E: m = 2: ? = cos–1 (2/?6) = 35.26438968

WRONG...the answer is 26.565 but I don't know how it is!!!

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Answer #1

The answer you obtained is correct for state

The smallest angle in degrees that L makes with the z-axis for an l = 2 electron is

However, for state, the z component is and total angular momentum is

Therefore the smallest angle in degrees that L makes with the z-axis for an electron is

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