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An orbital is a mathematical function describing an exact or approximated one-electron wavefunction in either an atom ( for atomic orbitals) or in a molecule (molecular orbitals).

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If atomic electron is in $f$-state, what values of the total angular momentum are allowed?

If $l=3$ and $s=1/2$ then the values of total angular momentum can take lie within the following range: $$|l-s|\leq J\leq l+s$$ With $J$ incrementing by 1 between these two bounds. $$\therefore 5/2\le …
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