# Does energy of an electron tells anything about its orbital it's in?

1. Oct 31, 2008

### Chaste

Does the energy of an electron happen to be related by any chance to En= -13.6/n2?

2. Oct 31, 2008

### ZapperZ

Staff Emeritus
You need to look at the Rydberg formula and figure out under what restricted condition is that energy formula was derived.

Zz.

3. Oct 31, 2008

### Staff: Mentor

Yes, assuming you mean an electron in a hydrogen atom.

(If you want a more specific answer, you need to ask a more specific question. )

4. Oct 31, 2008

### Chaste

so does En necessary equates to the energy of an electron in an hydrogenic atom?

or does it tell just the energy of that atomic orbital?

I wanna clarify my doubts if it's possible for an electron to have high energy in a lower n quantum number atomic orbital.

5. Oct 31, 2008

### Staff: Mentor

No. An electron in a hydrogen atom, in (for example) an n = 2 orbital must have an energy of -3.4 eV, or nearly so. There is a very small variation in energy between some orbitals with the same n because of fine-structure effects. Also, you can make the energies of the orbitals slightly different by applying an external magnetic field (the Zeeman effect). However, both of these effects are very small.

6. Oct 31, 2008

### Chaste

So the energy of the electron in an hydrogenic atom only can have that energy given by the formula ?
En= -13.6/n2?

so what does this formula really says? The energy of the entire atom or the energy of the electron?

7. Nov 1, 2008

### Staff: Mentor

Yes.

Actually, the energy of the atom, but people often use sloppy language and say the energy of the electron.

8. Nov 1, 2008

### Chaste

so that doesn't apply for non-hydrogenic atoms right?
anyway, it's not possible for electron to have high energy at low n quantum numbers?
Then what about relativistic effects of Gold? its electron in higher n quantum number S orbitals have electrons that are a significant factor of the speed of light.

9. Nov 1, 2008

### ZapperZ

Staff Emeritus
Why not? When you write down the Hamiltonian for ANY atom, where do you think the central potential come from? This is not just due to the electron, but also due to the WHOLE atom (i.e. both the nucleus, and the interactions of other electrons in the atoms).

http://theochem.chem.rug.nl/~broer/RelQuant/Relativ.html

In particular, pay attention to the last line that reads:

"There is no real contraction because there is no "non-relativistic" atom and there is no "relativistic" atom either. The contraction is the result of the two different models, the Schrödinger and the Dirac model, that are used and it has nothing to to with a real physical process."

Zz.

10. Nov 1, 2008

### Chaste

what about particle in a box? the smaller the box, the higher the energy of the particle(electron)? can we relate the box to an orbital? which means at smaller n quantum number, the electron will have higher energy?

11. Nov 2, 2008

### ZapperZ

Staff Emeritus
Have you ever solved the Schrodinger Equation for a particle in a box? Did you ever get the $Y_{lm}$ spherical harmonics the way you get for the hydrogenic atom?

Zz.

12. Nov 3, 2008

### Chaste

I have no idea what you're saying. Can you please enlighten me?

13. Nov 3, 2008