The number of subshells associated with n = 4 and m = –2 quantum numbers is

Solution

Chemistry ma’am · 3 steps

Fix n = 4, list its l values, and keep only the subshells big enough to have m = −2.

1. List the subshells. For n = 4, l can be 0, 1, 2, 3. That gives the 4s, 4p, 4d and 4f subshells.
2. Check each for m. For a given l, m runs from -l to +l. So m = -2 is possible only when l ≥ 2.

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

3. So. Only 4d and 4f qualify, so 2 subshells have n = 4 and m = -2.

The idea to keep. A value of m shows up only in subshells with l ≥ |m|. List the allowed l for the given n and count the ones that pass.

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