Consider the hypothetical situation where the azimuthal quantum number, l, takes values 0, 1, 2, ……..n + 1, where n is the principal quantum number. Then, the element with atomic number:
(1) 6 has a 2p-valence subshell
(2) 9 is the first alkali metal
(3) 8 is the first noble gas
(4) 13 has a half-filled valence subshell
(3) 8 is the first noble gas
Explanation:
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: 1s 1p 2s 1d 2p 3s 2d 3p 4s ……..
(1) 1st noble gas will have configuration 1s2 1p6 so atomic number will be 8.
(2) 1st alkali metal will have electronic configuration => 1s1 => (Z = 1)
(3) Electronic configuration of C (Z = 6) => 1s2 1p4
(4) Z = 13, Electronic configuration = 1s2 1p6 2s2 1d3 So it will not have half-filled electronic configuration.