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

[Chaste]

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

 

[ZapperZ]

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

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

Zz.

 

[jtbell]

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

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. )

 

[Chaste]

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. )

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

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

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

 

[jtbell]

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

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.

 

[Chaste]

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.

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

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

 

[jtbell]

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

Yes.

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

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

 

[Chaste]

Yes.



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

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.

 

[ZapperZ]

so that doesn't apply for non-hydrogenic atoms right?

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).

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.

Read this:

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.

 

[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?

 

[ZapperZ]

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?

Have you ever solved the Schrödinger 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.

 

[Chaste]

Have you ever solved the Schrödinger 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.

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

 

[Lasand]

Hello Chaste;

This wiki article on ionization potential may be helpful on the energy of an electron.

http://en.wikipedia.org/wiki/Ionization_potential