# Velocity of electrons during transition to different energy

I was watching a documentary of quantum mechanics (this video). They said something about quantum leap, jumping of electrons from one energy state to other.

I want to ask how electrons travel though the different orbitals? They can only have discrete amount of energies (energy levels). If it doesn't have enough energy to go to higher energy level, it will come back to the lower one. This happens instantaneously.

So does it move with infinite velocity within two energy levels during transition?

I want to ask how electrons travel though the different orbitals?

Electrons are quantum mechanical entities,they cannot be described by the motions of classical billiard balls. That is why the terminology "orbital" was invented. We only know about the electron around the proton in the hydrogen atom that when probed, it has a probability of being within the orbital solution.

As far as the mathematics goes there is only the probability and no continuity between two space points so that a classical velocity could be defined.

They can only have discrete amount of energies (energy levels). If it doesn't have enough energy to go to higher energy level,

The electron remains at its energy level, unless a photon with the appropriate energy hits the atom. Orbitals might mathematically overlap in space, particularly if there are many electrons, this does not mean there is an energy exchange, it just means that the probabilities of two energy orbital can overlap in space. Only if there is a probability for an energy transfer to a lower state then the space overlap has a meaning. This is how electron capture happens with nuclei , the S level overlaps with the nucleus and there exists a probability for the electron to be captured by a proton given the energy balances of the system.

it will come back to the lower one. This happens instantaneously.

See above. The electron is not moving like a billiard ball. Its path is not consecutive. There are only probabilities.

There is nothing instantaneous in quantum mechanics . If one wants to go to the details of "electron interacting with a photon" one has to go to quantum field theory, where the interactions are described with Feynman diagrams and there are constants characterizing them which define the order of magnitude of the time transition.

So does it move with infinite velocity within two energy levels during transition?

No , there are no infinities . If the electron is in an energy level that can release a photon and relax to the lower level, there exist time constants coming from the probability distributions which give a lifetime for the decay and a width to the energy line.

If it is at the ground state it will stay in the ground state forever, unless an appropriate energy photon hits the atom, either to kick it up an energy level or free it from the material completely, as in the photoelectric effect.

Electron orbitals are more than just orbitals... it's really best to think of it as a shell, rather than an orbit.

The Heisenberg uncertainty principle comes to play, stating the the electron doesn't orbit, but rather it is positioned at the nucleus with an uncertainty amounting to the size of the shell. The size of that shell can change if the electron has more or less energy.

To answer your question about the transition time between the orbital-shells. As best as we know a photon of the right energy immediately energizes the electron and increases the shell, and equally immediate when the shell drops back down.

The subatomic nature of these particles does not indicate any sort of elastic interaction period, where a photon-electron interaction takes a certain amount of time.

The answer is correct by Michael. Though, I think it would be useful for you to think about the average lifetime of the excited state of an Atom. The reason for that is, that the average lifetime of the excited state should include in this case

1. a photon absorption (transition to the excited state)
2. and an emission (transition back to ground/lower state).

Now not every transition will have a photon absorbed/emitted but that is (emission) what we can test/measure. So then if you can measure the average time gap between two consecutive photon emissions (on a test surface around the light source), you get the answer to your question where you say "This happens instantaneously. So does it move with infinite velocity within two energy levels during transition?". So the average time needed for the whole process of transition to excited state, then back to lower state is the answer. Here is a link to a similar (that is not asking of the speed, but the time needed) question: H atom's excited state lasts on average $10^{-8}$ secs, is there a time gap (of max 2*$10^{-8}$ secs) betwn. two consec. photon absorpt.-emiss. pairs?