what's the difference between energy levels of electrons in physics and electron shells/orbitals in chemistry

Question

I've just had a lesson on energy levels and the different wavelengths of photons emitted from exited electrons when they drop down energy levels and I was just wondering what the difference is between the electron levels and the electron orbitals/shells that I study in chemistry. Thanks :)

Answer 1

Probably you learned that the energy levels can be labeled with an integer number $n = 1, 2, \cdots$ and that photons emitted from excited levels have frequency that depend on the the difference $1/n_{\rm final}^2 - 1/n_{\rm initial}^2$. That is actually not the whole story, if you want to describe the state of an electron you actually need three different numbers (four including the spin), Physicists often call them $n$, $l$ and $m$, but in Chemistry you may have heard of them as

• Principal quantum number: $K$, $L$, $M$, $\cdots$ that mean $n = 1$, $n=2$, $n=3$, $\cdots$ respectively.

• Azimuthal quantum number: $s$, $p$, $d$, $\cdots$ that mean $l = 0$, $l=1$, $\cdots$ respectively

• Magentic quantum number: Used to label $m$

There is a whole bunch of allowed transitions between these states (not only between states with diffferent $n$'s). For instance keeping all these quantum numbers the same, an electron still can flip its spin, emitting a photon with a wavelength of $\sim 21$ cm, which is one of the most useful tools to study the interstellar medium