Consider the hypothetical situation where the azimuthal quantum number, $l$, takes values 0 , $1,2, \ldots \ldots \mathrm{n}+1$, where $\mathrm{n}$ is the principal quantum number. Then, the element with atomic number :
Correct Option: 1
$l=0$ to $(\mathrm{n}+1)$
$\mathrm{n}=1$ $\mathrm{n}=2$
$l=0,1,2$ $l=0,1,2,3$
$(\mathrm{n}+l) \Rightarrow \frac{1 \mathrm{~s}}{1} \frac{1 \mathrm{p}}{2} \frac{1 \mathrm{~d}}{3}$
$\frac{2 \mathrm{~s}}{2} \frac{2 \mathrm{p}}{3} \frac{2 \mathrm{~d}}{4} \frac{2 \mathrm{f}}{5}$
$\mathrm{n}=3$
$l=0,1,2,3,4$
$\frac{3 \mathrm{~s}}{3} \frac{3 \mathrm{p}}{4} \frac{3 \mathrm{~d}}{5} \frac{3 \mathrm{f}}{6} \frac{3 \mathrm{~g}}{7}$
Now, in order to write electronic configuration, we need to apply $(\mathrm{n}+l)$ rule
Energy order : $1 \mathrm{~s}<1 \mathrm{p}<2 \mathrm{~s}<1 \mathrm{~d}<2 \mathrm{p}<3 \mathrm{~s}<2 \mathrm{~d} \ldots$
Option 1) $13: 1 \mathrm{~s}^{2} 1 \mathrm{p}^{6} 2 \mathrm{~s}^{2} 1 \mathrm{~d}^{3}$ is not half filled
Option 2) 9: $1 \mathrm{~s}^{2} 1 \mathrm{p}^{6} 2 \mathrm{~s}^{1}$ is the first alkali
metal because after losing one electron, it will achieve first noble gas configuration
Option 3) $8: \quad 1 \mathrm{~s}^{2} 1 \mathrm{p}^{6}$ is the first noble gas
because after $1 \mathrm{p}^{6} \mathrm{e}^{-}$will
enter $2 \mathrm{~s}$ hence new period
Option 4) $6: \quad 1 \mathrm{~s}^{2} 1 \mathrm{p}^{4}$ has $1 \mathrm{p}$ valence subshell.
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