The number of orbitals with n = 5, m₁ = +2 is ___________. (Round off to the Nearest Integer).

Solution

Chemistry ma’am · 3 steps

Each l allows mₗ only from -l to +l, so ask which subshells of n = 5 can reach +2.

1. Allowed l values. For n = 5, l runs from 0 to n - 1, so l = 0, 1, 2, 3, 4. These are the 5s, 5p, 5d, 5f and 5g subshells.
2. Where +2 fits. For a given l, mₗ takes the values -l, …, 0, …, +l. So mₗ = +2 is possible only when l ≥ 2.

   l	Subshell	Allowed mₗ	Has mₗ = +2?
   0	5s	0	no
   1	5p	-1, 0, +1	no
   2	5d	-2 to +2	yes
   3	5f	-3 to +3	yes
   4	5g	-4 to +4	yes

3. So. Each allowed mₗ value in a subshell is exactly one orbital. The 5d, 5f and 5g subshells each have one orbital with mₗ = +2, which gives 3 orbitals.

The common slip: 6. Counting electrons instead of orbitals gives 6, because each orbital holds two electrons. The question asks for orbitals.

The idea to keep. To count orbitals with a fixed mₗ, list every allowed l for the shell and keep only those with l ≥ |mₗ|. Each such subshell gives exactly one orbital.

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