# Subtle implications of quantum numbers

Question:

Given the subshells $\ce{1s, 2s, 2p, 3s, 3p}$ and $\ce{3d}$, identify those that meet the following descriptions:
a) has $l=2$ b) Can contain two electrons with spin $m_{s}=\pm\frac{1}{2}$.

For a): from my understanding $l=n-1$. Therefore $\ce{3s, 3p}$ and $\ce{3d}$ should be correct but according to my solutions manual, the answer is only $\ce{3d}$. Why is this so?

For b) The answer is $\ce{2p, 3p}$ and $\ce{3d}$. Why are these the answers?

a) You are wrong. $l=2$ simply means $\ce{d}$-orbitals, thus, only $\ce{3d}$ is the right answer.
b) Assuming that the meaning of the question is to specify subshells that can contain two electrons in the same spin state, i.e. both with $m_s = +1/2$ or both with $m_s = -1/2$, $\ce{s}$-orbitals should indeed be excluded.
• @user3814584 each $s$-subshell consists of just one orbital, an orbital holds at most 2 electrons, but they should have the opposite spin if placed on the same orbital. Thus, $s$-subshell could contain 2 electrons, but not with the same spin. Starting from $p$-subshell, you have more then one orbital in a subshell, and thus, the subshell could contain 2 electrons even with the same spin. – Wildcat Aug 7 '14 at 15:42