# Relationship between Energy Level and electron position

In Bohr's Model of the atom there are set energy levels that are used to show the energy of the electrons in the atom. In the quantum model there are orbitals that show a probable location of the electrons within the atom.

How does the changing energy level of an electron affect it's position in the atom? For example, Helium has two electrons that both fit in the first "s" orbital. When the Helium electrons absorb the correct quanta of energy they would jump up to the next energy level, but what happens to their position in their orbital? As I understand, they can't move to the second "s" orbital, right, so would their distance from the nucleus just become greater while remaining in the first "s" orbital, or is its change in energy level a difference in the oscillation of the electron within its orbital?

• There are a few problems here. One is that it only works for one-electron systems, so it can't be applied to hydrogen. Another is that the position of electrons isn't exactly known, so we need to work with probabilities instead. If you know that an electron is excited from one orbital to another, you can calculate and compare the probabilities for the two orbitals at a given radius from the nucleus. Sep 15, 2017 at 21:07
• @pentavalentcarbon guess u meant 'Helium' Jun 26, 2021 at 8:10

The term "position in their orbital" is incorrect. The position of the electron is smeared out over the whole orbital.

I guess, you are still thinking about the electron as a particle, which moves around in the space defined by the orbital. That's wrong!

The orbital IS the electron (at least for one-electron systems; for many-electron systems this is just approximately true). The "probability density" is just about the likelihood of a measurement, if you would do one. Then the electron suddenly behaves like a particle, and needs to decide on a certain position.

One might try to make many of such measurements with very small time steps in between them. Any attempt to connect them to some continuous path or trajectory would fail. The electron would just appear to be randomly jumping around, popping up at different locations, no matter how short the time steps between the measurements.

During a transition to a higher state, the electron does not move. It just changes its wavefunction, instantaneously when absorbing the photon. And as the probability density depends on the orbital (aka wavefunction), the probability density changes as well. There is no need to consider the exact position, as in quantum mechanics we cannot grab it. It is smeared out. It is at every position at the same time (just with varying probabilities).

You have a little misunderstanding. An electron bound to an atom can't change position "within an orbital" - in fact it does change position between different orbitals. You are probably confused because people always talk about which orbitals the electrons go into. But these are only where the electrons go at their lowest energy. When electrons get more energy they jump up to higher orbitals. The "position" of an electron and which orbital it is in are the same thing. The only "positions" the electron can have are the orbitals.

You might find it interesting to know that after some time the electrons will jump back down to the "normal" lower energy level (orbital) and release some radiation (light). The gaps in energy levels between the different orbitals correspond to different amounts of released energy and so different wavelengths of light. That's what gives each atom it's characteristic spectral colours.