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.