Consider the hypothetical situation where the azimuthal quantum...

For $n = 1$ value of $l = 0, 1, 2$

For $n = 2$ value of $l = 0, 1, 2, 3$

So, according to $n + l$ rule the filling order of subshells will be :

$1s1p2s1d2p3s2d3p4s . . . . .$

(1) ${1}^{st}$ alkali metal will have configuration $1{s}^{2}1{p}^{6}$ so atomic number will be $8$.

(2) ${1}^{st}$ alkali metal will have electronic configuration $⇒ 1{s}^{1} ⇒ \left(Z = 1\right)$

(3) Electronic configuration of $C\left(Z = 6\right) ⇒ 1{s}^{2}1{p}^{4}$

(4) $Z = 13$, Electronic configuration $= 1{s}^{2}1{p}^{6}2{s}^{2}1{d}^{3}$

So it will not have half-filled electronic configuration.