Which of the following sets of quantum numbers is correct for an electron in $4 \mathrm{f}$ orbital?

Which of the following sets of quantum numbers is correct for an electron in $4 \mathrm{f}$ orbital?
  1. $\mathrm{n}=3, \ell=2, \mathrm{~m}_1=-2, \mathrm{~m}_{\mathrm{s}}=+1 / 2$
  2. $\mathrm{n}=4, \ell=3, \mathrm{~m}_1=+1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$
  3. $\mathrm{n}=4, \ell=3, \mathrm{~m}_{\mathrm{l}}=+4, \mathrm{~m}_{\mathrm{s}}=+1 / 2$
  4. $\mathrm{n}=4, \ell=4, \mathrm{~m}_1=+4, \mathrm{~m}_{\mathrm{s}}=-1 / 2$

Solution

For a 4f- orbital, $n=4$ and $1=3$ For a given value of $l$, there can be $(2 l+1)$ values of $\mathrm{m}_l$ ranging from $-l$ to $+l$. Thus, $\mathrm{m}_l=+1$ is possible. $ \mathrm{m}_{\mathrm{s}} \text { can be }+\frac{1}{2} \text { or }-\frac{1}{2} $

Asked in: AP EAMCET 2023 (19 May Shift 1)

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