On the basis of quantum numbers, justify that the fourth period of the Modern periodic table should have `18` elements.

Answer

In the modern periodic table, each period starts with the filling of a new principal energy level. Thus, the fourth period begins with the filling of principal quantum number, `n = 4`. When `n = 4, l = 0, 1,2,3`. But accoring to Aufbau principle the electrons are added to different orbitals in order of their increasing energies. Now, the energy of `4d`-subshell is higher than that of `5s`-subshel but energies of `3d`-subshell is lower than that of `4p`-subshell. Therefore, in `4th` period, electrons can be filled in only `4s, 3d` and `4p`-subshells, whose energies increases in the order: `4s lt 3d lt 4p`. Now, `s-`subshell has one, p-subshell has three and d-subshell has five orbitals. Hence, in all there are `9 (1 +3 +5)` orbitals that can be filled in this period. Since according to Pauli's exclusion principle, each orbital, at the maximum, can accommodate two electrons. Therefore, `9` orbitals, at the maximum, can have `18` electrons and hence, fourth period has `18` elements.