On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.

Explanation

In the long form of the periodic table, each period starts with the filling of a new shell. The sixth period begins with the filling of n = 6 (principal quantum number = 6) shell. For this shell, since n = 6, I = 0, 1, 2 and 3 (higher values are not permissible). Thus, the subshells required to be filled are 6s, 6p, 6d and 6f. But, according to Aufbau principle, the energies of 6d- and 6f-subshells are higher than that of 7s-subshell. Therefore, these subshells can not be filled till 7s subshell is filled. Moreover, the energies of 5d- and 4f-subshells are lower than that of 6p-subshells. Therefore, in `6^(th)` period, electrons can be filled only in 6s, 4f, 5d and 6p-subshells. The number of electrons that can be accommodated in these subshells are 2, 14, 10 and 6 respectively, i.e. , a total of 32 electrons. This is why sixth period has 32 elements only.