# Discrete energy levels

1. Apr 9, 2014

### BOAS

Hello,

I have a question regarding discrete energy levels of atoms.

If electrons must inhabit certain energy levels, when they are excited up to a higher energy level, do they instantaneously jump to that level, or do they exist for some short time 'in between'?

Furthermore, if the wavefunction of an electron extends over space (infinitely far?), does it really mean that there is the highest probability that the electron inhabits the energy level, or does an energy level correspond to a large 'space'?

We've been looking at the bohr model which would suggest that these energy levels must exist on equipotential lines, but I remember from A-level chemistry the shape of different orbitals and clearly something else is going on here...

I know that's a bit of a loose question, but i'd enjoy a wide ranging answer :)

Thanks!

2. Apr 9, 2014

### ZapperZ

Staff Emeritus
There is no "in between". Our current understanding is that this transition is instantaneous.

Note that these electrons are no longer classical particles, and these are energy states.

Zz.

3. Apr 9, 2014

### BOAS

The way you wrote that made me realise something, I think.

The picture I had in my head was the electron having to go from a to b, i.e travel some distance to correspond to it's new energy level. But if it's gain in energy is dictated by the energy of a photon, which is itself a discrete packet of energy, the moment that absorption takes place, the electrons energy has jumped to the new level.

4. Apr 9, 2014

### ZapperZ

Staff Emeritus
Just so you know, the transition to higher energy states can due NOT to just photon absorption. In a fluorescent light, the gasses are bombarded by electrons that have been accelerated in the gas tube. Atoms can be excited via many mechanism, not just photon absorption. Collisions with other particles are quite common!

Zz.

5. Apr 11, 2014

### Jano L.

If you allow only a discrete set of states, the transition has to be instantaneous, because there is no state in between that could be occupied in the mean time. If by state you mean one of discretely indexed states of definite energy, you are making a preference for states associated with definite energy and not other physical quantities, say position or momentum.

If you allow continuous set of states, the transition may take some time. If by state you mean $\psi$ function figuring in the Schroedinger equations, there is a continuous set of states and no physical quantity is preferred. If you assume $\psi$ changes according to the time-dependent Schroedinger equation, it changes continuously and transition from one Hamiltonian eigenfunction to another, if it happens at all, takes some time.