The maximum number of orbitals which can be identified with n=4 and mₗ=0 is _________.

Solution

Chemistry ma’am · 3 steps

List the subshells for n = 4. Each one has exactly one orbital with mₗ = 0.

1. Allowed l values. For n = 4, l runs from 0 to n - 1. So l = 0, 1, 2, 3, which are the 4s, 4p, 4d and 4f subshells.
2. Allowed ml values. For a given l, mₗ takes every integer from -l to +l. That range always contains mₗ = 0 exactly once.

   Subshell	l	mₗ values	Orbitals with mₗ = 0
   4s	0	0	1
   4p	1	-1, 0, +1	1
   4d	2	-2 to +2	1
   4f	3	-3 to +3	1

3. So. One orbital from each of the four subshells gives 1 + 1 + 1 + 1 = 4 orbitals.

The common slip: 8. Counting electrons instead of orbitals gives 8, because each orbital holds two electrons. The question asks for orbitals, so spin does not enter.

The idea to keep. Every subshell has exactly one orbital with mₗ = 0. So for a given n, the count of mₗ = 0 orbitals equals the number of subshells, which is n.

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