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

To justify why the 6th period of the periodic table has 32 elements, we can use the concept of quantum numbers, especially the principal quantum number (n) and the azimuthal quantum number (l).

🔷 Quantum Numbers Recap:

1. Principal Quantum Number (n):

   • Determines the energy level (shell).

   • For the 6th period, n = 6.

2. Azimuthal Quantum Number (l):

   • Determines the subshell type (s, p, d, f):

     • s → l = 0 (2 electrons)

     • p → l = 1 (6 electrons)

     • d → l = 2 (10 electrons)

     • f → l = 3 (14 electrons)

🔍 For n = 6 (6th period):

We consider orbitals filled according to increasing energy using the Aufbau principle.

Electrons fill the following subshells:

1. 6s → 2 electrons

2. 4f → 14 electrons (even though n = 4, it is filled after 6s)

3. 5d → 10 electrons

4. 6p → 6 electrons

🔢 Total Elements in 6th Period:

✅ Conclusion:

The 6th period contains 32 elements because all the orbitals that are filled during this period — 6s, 4f, 5d, and 6p — together accommodate 32 electrons.
This distribution is justified using quantum numbers and the Aufbau principle.