# Multiple values for the magnetic quantum number and the spin projection quantum number?

The valence electron configuration of boron is $2\mathrm{p}^1$.

So, $n=2$, and $l=1$. $m_l$ ranges from $-l$ to $l$. Can I say $m_l$ (for the specified electron) may be (-1 or 0 or +1) or should I just say (-1)?

As you know the $\mathrm{p}$ subshell has three orbitals ($\mathrm{p}_x, \mathrm{p}_y, \mathrm{p}_z$).

Can I associate $\mathrm{p}_x$ with $m_l = -1$, $\mathrm{p}_y$ with $m_l = 0$ and $\mathrm{p}_z$ with $m_l = +1$? (associate each magnetic quantum number with a particular orbital)

I tried to explain what I meant in the following illustration :

$m_s$ is either $+\frac{1}{2}$ or $-\frac{1}{2}$. Can I say $m_s$ (for the specified electron) equals ($+\frac{1}{2}$ or $-\frac{1}{2}$)? (both values) or $+\frac{1}{2}$ because it's alone in the orbital (not paired)

• Part of your question (regarding the assignment of $m_l$ to p orbitals) is answered here: chemistry.stackexchange.com/questions/33645 Oct 27 '15 at 18:59
• For the other part, at this level, I believe all you need to know is that the three p orbitals are degenerate, as well as the two spin states of the electrons. Therefore, regardless of which p orbital the electron is in, and regardless of whether the spin is +1/2 or -1/2, the energy is the same. As such, you would save yourself lots of time if you just wrote one quantum number instead of all the possible quantum numbers, since they all have the same energy. Of course, it's not that simple. There is something called spin-orbit coupling, which changes the energy levels slightly. Oct 27 '15 at 19:02