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Q.

If θ is the angle made by orbital angular momentum with the z-axis, then the quantum number l and m of an atom are related to each other through the expression

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a

m={l(l+1)}cos⁡θ

b

l=mcos⁡θ

c

m=l(l+1)cos⁡θ

d

m=lcos⁡θ

answer is D.

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Detailed Solution

L=l(l+1)(h/2π),  Lz=m(h/2π) and  Lz=Lcos⁡θ  Hence, m=l(l+1)cos⁡θ

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If θ is the angle made by orbital angular momentum with the z-axis, then the quantum number l and m of an atom are related to each other through the expression