In an atom, total number of electrons having quantum numbers n=4,| mₗ|=1 and mₛ=-1/2 is _________.

Solution

Chemistry ma’am · 3 steps

The modulus sign means mₗ can be +1 or -1, so count two orbitals in every subshell that has them.

1. List the subshells. For n = 4, l can be 0, 1, 2 or 3. That gives the 4s, 4p, 4d and 4f subshells, and each one has mₗ values from -l to +l.

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

2. Add the spin. That makes 2 + 2 + 2 = 6 orbitals. Each orbital holds two electrons with opposite spins, so exactly one electron in each has mₛ = -1/2.
3. So. The number of electrons with n = 4, |mₗ| = 1 and mₛ = -1/2 is 6 × 1 = 6.

The common slip: 3. Counting only mₗ = +1 and missing mₗ = -1 gives 3 orbitals and 3 electrons, not 6.

The idea to keep. Count the orbitals that satisfy n, l and mₗ first. Then multiply by 2 for both spins, or by 1 if mₛ is fixed. A modulus on mₗ always means two values.

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