The number of orbitals associated with quantum number n = 5, mₛ = +1/2 is :

Solution

Chemistry ma’am · 3 steps

Spin adds no orbitals: count the orbitals in shell 5, and each holds one +1/2 electron.

1. Count the subshells. For n = 5, l runs from 0 to n - 1 = 4. That gives the 5s, 5p, 5d, 5f and 5g subshells, and each holds 2l + 1 orbitals.

   1 + 3 + 5 + 7 + 9 = 25 = n²

2. Role of spin. Spin mₛ describes an electron inside an orbital. It does not add orbitals. Every one of the 25 orbitals can hold exactly one electron with mₛ = +1/2.
3. So. All n² = 25 orbitals qualify. That is also the number of electrons with mₛ = +1/2, so the answer is (b).

The idea to keep. A shell has n² orbitals and 2n² electrons. Fixing mₛ halves the electron count, but the number of orbitals stays n².

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