Question 3.4 On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.
Class XI Classification of Elements and Periodicity in Properties Page 92
Answers
and principal quantum number of element = period of that element.
hence, sixth period of the periodic table means principal quantum number = 6 e.g., n = 6
we know, A/C to Aufbau principle ,
in the ground state of any atoms , the orbitals are filled in order of their increasing energies .
so, for 6th period , electrons enter in 6s , 4f, 5d and 6p subshells.
hence, total number of orbitals = 1 { for 6s } + 7 { for 4f } + 5 { for 5d } + 3 { for 6p } = 16
now, According to Paul's exclusion principle ,
each orbital can accommodate maximum two electrons.
hence, in 16 orbitals number of electrons = 2 × 16 = 32 .
hence, in sixth period , there are 32 elements .
Answer: 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 6th period electrons can be filled in only 6s, 4f, 5d and 6p 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.