Question

second and third periods can accommodate 8 and 18 electrons respectively. Since their outermost shells can contain only 8 electrons, there are only 8 elements in boththe periods.

so what is the sense of 2n square then?

and why there are 18 in the next group then?

Answer 1

The system of 18 electrons have been described to explain the electronic configuration and it is only possible if the next shell is also filled with the eectrons .
For ex: in Copper with atomic no. = 29 , the configuration is , 2,8,18,1 (1s²2s²2p⁶3s²3p⁶3d¹⁰4s¹) here see that third shell 3s,3p and 3d combine to give 18 electrons.