Hi Aspirant!

Electrons exist in orbits and these orbits are known as levels. We number them as 1, 2, 3, and so on. In which the first level is closest to the nucleus and remaining levels become more and more distant with the increasing levels.

The levels can be broken down into sub-levels and we have s, p, d and f sub levels.

>> Level one has on sub level - 's'.

>> Level 2 has 2 sublevels - s and p.

>> Level 3 has 3 sublevels - s, p, and d.

>>Level 4 has 4 sublevels - s, p, d, and f.

=> Now, these sublevels contain orbitals and orbitals are the area in which electrons exist. The maximum electrons which an orbital can aquire is 2.

The  1 level has only s orbital, so it has only 2 electrons. The p sublevel has 3 orbitals, so can contain 6 electrons max. The d sublevel has 5 orbitals, so can contain 10 electrons max. And the 4 sublevel has 7 orbitals, so can contain 14 electrons max.

*** Now, coming to the 2n2 formula, according to which an atom's electron shell can accommodate 2n ² electrons (where n is the shell level). For example, the first shell can accommodate 2 x (1) X (1) or 2 electrons. The second shell can accommodate 2 x (2) X (2), or 8, electrons and third shell can have 2 X (3) X (3) , or 18 electrons.

So, basically both the systems : 2n2 formula and s,p, d, f are right. The 2n2 formula is not for sub-levels (s, p, d, f) , instead it is for a complete level (orbit).

You are mixing orbits (levels) with the sub- levels (s, p, d, f).

Hope you get it, thankyou!