Do Quantum Orbitals in the Atom Overlap at Different Energy Levels?

[Quantom]

My question concerns the orbitals in the atom (s,p,d, and f.) I know that each orbital shell is a probability density that has a quantized energy. My question is, do the orbitals touch, or rather do higher orbitals like say a d have a probability density that overlaps a p or s orbital in a lower shell. Considering that the orbitals are quantized I am assuming that they do not overlap because any overlap would mean that the electrons have the same energy and because they are quantized this can't happen...but I am not sure...thanks in advance for your responses.

 

[malawi_glenn]

I think you are mixing different concepts here.

All these orbital functions extend from 0 to infinite radius, compare with sin(x) and cos(x), you can see that they "overlap".

But the probability for a genera state $\psi$ to be in the energy-eigenstate $\phi _E$ is:

$$\int d\vec{x}\, \phi _E^*(\vec{x}\, ) \psi (\vec{x}\,) = P$$

And different energy-eigenstates are orthogonal:

$$\int d\vec{x} \, \phi _E^*(\vec{x}\, ) \phi _{\epsilon} (\vec{x}\,) = \delta _{E,\epsilon}$$

So you have to think for yourself what you mean by "overlap", the function cos(x) and sin(x) does are overlapping each other as graphs, but their integral:

$$\int _0^{2\pi} dx \, \cos (x) \sin (x) = 0$$

 

[Quantom]

I appreciate the reply, but I am afraid that i have very little clue what that meant considering i am a high school student who is not well versed in the mathematics for quantum mechanics. When i say overlap i mean can an electron in a higher orbital have a probability of existing in a lower orbital like the s, but does not jump to that orbital. My understanding is that electrons can jump to different orbitals i just want to know if electrons that exist in a higher orbital can be found in lower orbitals even though their energy exceeds that of the lower orbital. Hopefully that clears my definition of overlap up, but perhaps not.

 

[malawi_glenn]

You are then talking about the "integral overlap"´and then the answer is "yes" and "no".

No is that the Energy eigenfunctions are orthogonal, if your electron is state 2p, then it has no probability to be in the state 1s, 2s etc.

But that is for unperturbed systems, in reality, we can perturb the system (atom) to make transitions of between these states.

Considering the electron in its ground state, 1s, if it is not perturbed it will stay there for ever. But if we perturb it, with an external source (a photon as an example) its probability density function will become a mixture of 1s, 2s, 2p etc, and you will have a probability to find it in an excited state. And the opposite situation when the electron is in an excited state. This is called perturbation theory.

So let me summarize:
i) In the unperturbed system, atom, you will not have any overlap between different orbital functions.
ii) In perturbed systems, you can have it, and this can induce transitions in energy (jumps)

You will understand more when you learn more about the mathematical formalism of QM, I promise, since QM is basically a mathematical way to describe nature.

 

[Quantom]

thanks that was much more understandable

 

[malawi_glenn]

thanks that was much more understandable

It is hard to know at what level one should answer when the person who asked does not give any clue at what level of understand he is at. Remember that next time to tell that you are a high school student :-)

 

[Quantom]

so what occurs with electrons in the orbitals of an atom when a gas is heated and a photon is emitted? My understanding is that an electron from a lower orbital rises and then falls back down. How does the electron get energy to jump up if it is a higher orbital electron that is being effected? Does the overlap increase thereby giving the lower orbital electron enough energy to jump up?

 

[malawi_glenn]

There you have collision excitation, atoms will 'collide' more often (since you will increase the average kinetic energy of the atoms in the gas. thus resulting in a higher probability per unit time to excite an atom).

You can only excite electron in an atom to a non occupied state. e.g if the all the states up to 3d are occupied, you can't excite a 1s electron to a 2p state, etc.

 

[Quantom]

thank you very much for your help.