# How does Nitrogen transition between a quarter and a doublet state?

My degree was in Electrical Engineering, and as a result I don't fully understand the formatting of the ${}^4S_{3/2}$ ${}^2D_{3/2}$ and ${}^2P_{1/2}$ of the different 2p orbitals, and I don't believe this is the proper forum for learning something undoubtedly more complex than my basic knowledge. I do however know some basics, such as the selection rule that says you cannot transition between orbitals that have the same quantum l number. So my question is the following:

How does Nitrogen transition between these three 2p orbitals? Or are the higher energy states naturally occurring? If so how, don't atoms strive to be in the ground state? Can the transition be forced somehow, such as photon absorption or electron collision to move to the left, or a photon emission to move to the right; perhaps using stimulated emission?

I feel like there are so many more questions worth asking and perhaps these cannot be answered without asking them, but this is my starting point.

• You need to specify the filling: $(2p)^n$, for what n? For Nitrogen, I guess you are interested in $(2p)^3$? – hft May 2 '15 at 1:45
• ...Yeah, that's consistent with the given terms. I will answer. – hft May 2 '15 at 1:55

## 1 Answer

I'm going to assume you are interested in regular old Nitrogen with configuration $(2p)^3$.

In this case there are "6 choose 3" (i.e., twenty) different configurations consistent with the exclusion principle (you should be able to pretty easily write them all down pictorally). It's pretty easy to see that one of the configurations has $M_L=2$ and $M_S=1/2$, which is the highest possible $M_L$ and which implies the existence of the state ${}^2 D$ (which accounts for ten of the twenty states). It's also easy to see that the highest possible $M_S=3/2$ and for that state $M_S$ must be zero, which implies the existence of the ${}^4S$ state (which accounts for another four states). The remaining 6 states have $M_L$ and $M_S$ values consistent with the ${}^2P$ state.

A great reference for this sort of work is "The Theory of Transition-Metal Ions" by Griffith. Especially section 4.2 "Electron configurations".

These states are characterized by total angular momentum $L$ and total spin $S$ rather than the single-particle angular momentum and spin, because it is only the total angular momentum and spin that is conserved for the interacting system. The lowest energy state will be the one that is populated at zero temperature, but transitions between the states can be induced by hitting the atom with electromagnetic radiation, or thermal effects (if the temperature is comparable to the level spacing) and so on.

Transitions between these states can occur because they don't have the same quantum numbers. For example ${}^2D$ has $L=2$ and ${}^2 P$ has $L=1$. A good candidate for an electromagnetic-induced transition (with $\Delta L=1$ and $\Delta S=0$).