Why are the sublevels of an energy level called S, P, D, and F?

My chemistry told us S, P, D, and F stood for something, but for some reason did not tell us what.

S is spherical, I think. What are the rest?

Now that’s a damn good question.

After S and P, it goes in alphabetical order, skipping E:

S, P, D, F, G, H, I

So I don’t think the letters stand for anything, but I have no idea why they were chosen.

S = sharp, p = principal, d = diffuse, f = fundamental.


And some poking around on Google indicates these names originally described certain lines in the emission spectra of the alkali metals. The shells above “f” are alphabetical.

Essentially calling shells K, L, M, N, O, P, Q and subshells s, p, d, f, g and so on instead of using number series for both, is just to avoid getting all the different numbers confused. Thus s p d f will do the trick just as well as any other system, although they don’t have much to do with their original meanings anymore.

Really, the letters s, p, d and f don’t stand for anything. They may be thought of as representing sharp, principal, diffuse and fundamental (or faint), but there’s nothing sharp about an s-orbital or diffuse about a d-orbital.

The azimuthal quantum number l (properly a script l) represents the shape of an orbital (an area of electron density probability). The value may range from 0 to (n-1), where n is the principal quantum number or “energy level”. If l = 0, the orbital is called s, traditionally; if l = 1, it is called p, and so on.

The names “sharp”, “principal”, “diffuse” and “fundamental/faint” come from early work on spectral analysis of hydrogen and other elements. Lines in the spectrum were described qualitatively as “sharp”, “diffuse”, and so on.

We now understand that the lines arise from a transition between two orbitals – orbitals with different azimuthal quantum numbers. The ‘sharp’ lines are from p --> s transitions, the ‘principal’ are from s --> p transitions, the ‘diffuse’ are from d --> p transitions and the ‘faint’ are from f --> d. See here.

Since there’s no consistent correlation between the orbitals involved in the transition and the type of line observed, it’s not strictly accurate to name the orbitals s, p, d and f, but the names have stuck.

Eurograff: I don’t like the idea of “shells” and the labels K, L, M, N… It’s a rather Bohr-Rutherfordian concept (though I think it refers to de Broglie’s model, actually); outdated since the early 20’s. Numbered energy levels (the principal quantum number n seem more appropriate for dealing with quantum-mechanical electrons, which are most certainly not confined to anything resembling a shell. =)

Minor correction, although I’m sure Roches already knows this: that l is between 0 and n - 1 is true for Coulombic systems, and is not a general constraint. In the example of a spherical harmonic oscillator, we instead have that l is between 0 and n, with steps of 2 rather than 1.

For what it’s worth… the S orbital shells tend to be spherical in shape. Electrons in the P shell tend to follow an orbit that looks like a three-dimensional peanut. However, I don’t believe this has anything to do with the labels.

Grelby: And the d orbitals look something like a flower – maybe a daisy. =) (well, not d[sub]z²[/sub], but oh well.)