Which of the following is not permissible arrangement of electrons in an atom ?

Which of the following is not permissible arrangement of electrons in an atom ?
  1. $\mathrm{n}=4, \mathrm{l}=0, \mathrm{~m}=0, \mathrm{~s}=-1 / 2$
  2. $\mathrm{n}=5, \mathrm{l}=3, \mathrm{~m}=0, \mathrm{~s}=+1 / 2$
  3. $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}=-3, \mathrm{~s}=-1 / 2$
  4. $\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}=-2, \mathrm{~s}=-1 / 2$

Solution

Key Idea For an electron, $n$ may be $0,1,2 \ldots$ and $\mathrm{l}=0$ to $\mathrm{n}-1$ and $\mathrm{m}=-\mathrm{l}$ to $+\mathrm{l}$ (including 0) and $\mathrm{s}= \pm \frac{1}{2}$ Hence, if $\begin{aligned} \mathrm{n} & =3 \\ \mathrm{l} & =0 \text { to }(3-1) \\ & =0,1,2 \\ \mathrm{~m} & =-\mathrm{l} \text { to }+1 \\ & =-2-1,0,+1,+2 \\ \mathrm{~s} & = \pm \frac{1}{2} \end{aligned}$ Therefore, option (c) is not a permissible set of quantum numbers.

Asked in: NEET 2009 (Screening)

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