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

(N/A) In the periodic table,a period corresponds to the principal quantum number $(n)$ of the outermost shell.
For the $6^{th}$ period,$n = 6$.
The orbitals available for filling in the $6^{th}$ period are determined by the Aufbau principle,which dictates the order of increasing energy: $6s < 4f < 5d < 6p$.
- $6s$ subshell: $1$ orbital
- $4f$ subshell: $7$ orbitals
- $5d$ subshell: $5$ orbitals
- $6p$ subshell: $3$ orbitals
Total number of orbitals = $1 + 7 + 5 + 3 = 16$.
According to the Pauli exclusion principle,each orbital can hold a maximum of $2$ electrons.
Therefore,the total number of electrons that can be accommodated is $16 \times 2 = 32$.
Since each element corresponds to the addition of one electron,the $6^{th}$ period contains $32$ elements.