In the sixth period, the orbitals that are filled are :

Solution

Chemistry ma’am · 4 steps

A period opens with its ns orbital and closes with its np. Fill everything between in Aufbau order.

1. Start and end. Period 6 begins when 6s starts filling (Cs, Ba) and ends when 6p is full (Rn). Every orbital that fills between these two belongs to period 6.
2. Aufbau order. Orbitals fill in increasing n + l. When two orbitals have the same n + l, the one with the lower n fills first.

   Orbital	n + l	Fills in period
   6s	6 + 0 = 6	6
   4f	4 + 3 = 7	6 (lanthanides)
   5d	5 + 2 = 7	6 (La, Hf to Hg)
   6p	6 + 1 = 7	6
   5f	5 + 3 = 8	7 (actinides)
   6d	6 + 2 = 8	7

3. Check the count. 4f, 5d and 6p all have n + l = 7, so they fill in order of increasing n. Their capacities with 6s give 2 + 14 + 10 + 6 = 32, which matches the 32 elements of period 6.
4. So. The sixth period fills 6s, 4f, 5d and 6p, which is option (b).

The idea to keep. For period n, the orbitals that fill are ns, (n-2)f, (n-1)d and np, in that order. Add 2 + 14 + 10 + 6 = 32 to check you have the right set.

Answer from the NTA final answer key. Solution by PrepWiser.