Question

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

Answer 1

In the periodic table of the elements, a period indicates the value of the principal quantum number $(n)$ for the outermost shells. Each period begins with the filling of principal quantum number $(n)$. The value of n for the sixth period is $6$. For $n$ = $6$, azimuthal quantum number $(l)$ can have values of $0, 1, 2, 3, 4$.

According to Aufbau's principle, electrons are added to different orbitals in order of their increasing energies. The energy of the $6d$ subshell is even higher than that of the $7s$ subshell.

In the $6 ^{th}$ period, electrons can be filled in only $6s, 4f, 5d,$ and $6 p$ subshells. Now, $6s$ has one orbital, $4f$ has seven orbitals, $5d$ has five orbitals, and $6p$ has three orbitals. Therefore, there are a total of sixteen $(1 + 7 + 5 + 3 = 16)$ orbitals available. According to Pauli's exclusion principle, each orbital can accommodate a maximum of $2$ electrons.
Thus, $16$ orbitals can accommodate a maximum of $32$ electrons.

Hence, the sixth period of the periodic table should have $32$ elements.