Question

what is magnitude of total orbital, total spin and total angular momenta for the ground state 4f of vanadium.

Answer 1

Answer on Question #43892, Physics, Atomic Physics

Task: what is magnitude of total orbital, total spin and total angular momenta for the ground state 4f of vanadium.

Solution:

ground state 4f $\Rightarrow n = 4, l = 3, s = \frac{1}{2}, j = l - s = \frac{5}{2}$.

$$P _ {l} = \hbar \sqrt {l (l + 1)} = 2 \hbar \sqrt {3};$$ $$P _ {s} = \hbar \sqrt {s (s + 1)} = \hbar \frac {\sqrt {3}}{2};$$ $$P _ {j} = \hbar \sqrt {j (j + 1)} = \hbar \sqrt {\frac {3 5}{4}} = \frac {\hbar}{2} \sqrt {3 5}.$$

$P_{l} = 2\hbar \sqrt{3}$ - magnitude of total orbital momenta for the ground state 4f;

$P_{s} = \hbar \frac{\sqrt{3}}{2}$ - magnitude of total spin momenta for the ground state 4f;

$P_{j} = \frac{\hbar}{2}\sqrt{35}$ - magnitude of total angular momenta for the ground state 4f.

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