# What energy do electrons actually take in an orbital?

1. Dec 21, 2008

### feynmann

If electrons are found somewhere within an orbital, what kind of energy they have?
In other word, if kinetic and potential energy of electrons change with time in the ground state of atoms?

2. Dec 21, 2008

### Staff: Mentor

The total energy is fixed and definite, because an orbital is an energy eigenstate. The potential and kinetic energies are both indefinite until they are measured, so in the meantime we can speak only of probability distributions and expectation values, and the constraint that the two (kinetic and potential) must add up to the fixed total energy.

3. Dec 21, 2008

<cough> .. And ,.. that the "fixed" total-energy for all known electrons is "variable" over time

4. Dec 22, 2008

### Staff: Mentor

I assume that by "orbital", feynmann was referring to bound states of atomic electrons that have specific values for the quantum numbers n, l, and $m_l$. The energies of these states do not vary with time unless there is an externally-applied magnetic or electric field that varies with time. Maybe you're thinking of something different?

5. Dec 22, 2008

yes that is the line of reasoning .. just that at every duration of time that we are able to measure they are subject to environmental EMF flux to some degree or other - at least as far a we are aware that is the case . thus always in a state of Delta .

Only under certain circumstances of energy/geometry etc .. does the transfer of energy mean a shift in orbital level .. most of the time it must be just flux - more like resonating vibrations

Last edited: Dec 22, 2008
6. Dec 22, 2008

### ZapperZ

Staff Emeritus
Where is this "environmental EMF flux" in the Hamiltonian that one sets up for, say, the typical hydrogenic atom?

So the $\Psi_{nlm}$ that one gets when solving such a system doesn't tell you the energy state of that orbital?

Zz.

7. Jan 4, 2009

### feynmann

Suppose the electron of hydrogen atom is in the ground state, so the total energy is -13.6 eV,
It's possible to find the electron very far away from the proton, the potential energy is zero at infinity, since the total energy is fixed, this left the kinetic energy of electron to -13.6 eV. Can kinetic energy of electron be negative in quantum mechanics?

Last edited: Jan 4, 2009
8. Jan 5, 2009

No kinetic energy cannot be negative.
You are cheating. Once you argue with quantum mechanics, you need to check what the classical proposal that you are making means.

You still seem to assume that there are small electrons flying around in their orbitals, but they don't. The whole orbital is the electron. When you check, "where the electron is", you will get a result, which is governed by the wavefunction, it doesn't mean that the electron was there at the time of measurement, it only means, that's where it turned up. At least in the Copenhagen interpretation.
Classically there doesn't seem to be a difference between the two statements, but for a clean Copenhagen interpretation, the electron must not be assumed to exist in another form than the wavefunction, it is especially not "flying around imitating an orbital".
- put electron in ground state
- measure position and find it far away from the atom
- measure kinetic energy

When the Electron is in the ground state it is in an Eigenstate of the Energy, so pretty much all hat we know about it, is its Energy*
We don't know its position. When me measure it's position sufficiently accurately we force it into a new eigenstate of the position operator, now its Energy is not known anymore, and it has a new probability distribution. Actually if you measure with very high accuracy the probable outcome for the kinetic energy skyrockets, because of the increasing with of the momentum.

There are a few more ways to look at the problem, some deal with the kinetic energy you induce with the measuring apparatus, but that would strengthen your ideas about a classical explanation that you need to get away from imho.

*yeah yeah and whatever is commutating with it...

9. Jan 5, 2009

### edguy99

-13.6 is a relative level. To me it means that the electron needs at least 13.6 evolts of energy to completely break from the proton. The electron itself would never have a negative kinetic energy. A bounded electron far from the atom has 13.6 potential energy and very low kinetic energy. An electron close to a proton can have kinetic energy from 0 to 13.6 evolts but not more and still be "bound".