When electrons absorb energy and get excited then jump to a higher energy level do they do so in steps or do it directly?

Question

So I was reading about Fermi surfaces. One of the first things that is obvious is that energy excitations happen at the boundary of the surface as the electrons deeper inside the surface do not have room to'grow' as higher states are occupied and those will have to emptied first.

Lets say there is a state at a higher energy level than the Fermi energy, if energy input is exactly the difference between that energy level and that of the electron deep inside the surface would that electron make the transition? If the electron progress in energy levels directly then it makes sense to me that it should. But apparently it cannot. Unless I have something confused.

Answer 1

They can actually do both, but the step wise transition is actually two sequential transitions rather than a single transition. Whether a transition occurs depends on more than just the energy difference between states. The quantum numbers of the two states makes some transitions highly probable (allowed) and others improbable (forbidden). When you study the quantum mechanics of angular momentum and spin, you will learn the rules of these transitions.