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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

$l = m \cos θ$

c

$m = \sqrt{l (l + 1)} \cos θ$

d

$m = l \cos θ$

answer is D.

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Detailed Solution

$L = \sqrt{l (l + 1)} (h / 2 π), L_{z} = m (h / 2 π)$ and $L_{z} = L \cos θ$ Hence, $m = \sqrt{l (l + 1)} \cos θ$

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