Electric Potential and Electron Energy Levels

[sv3]

Hi,

I was reading over electric potential in physics and am wondering why it is in chemistry that the quantum energy level N=1 has electrons with the lowest energy? It seems that electrons closest to the nucleus have the most electric potential (Ep = KQ/r). Are these two concepts not related at all and perhaps I would be better served not thinking of them along the same lines?

I understand that electrons closest to the nucleus are closest to where they would like to be but also that the electric field is strongest here. I'm just having a tough time figuring out why the electron energy levels are lowest here.

thanks in advance
steve

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[Fort]

Not sure if this was covered in any of your physics classes but the equation relating electron potential energy in the hydrogen atom is

U(r) = -ke^2/r

Notice the negative sign in the equation. As the electron moves further out from the nucleus, the potential energy becomes less negative and approaches zero as r increases to infinity.

Now ask yourself, is it easier to put an electron at a distance r from the nucleus, or at 3r?

It's easier to put an electron at a distance r than 3r because the electron and the nucleus attract each other. Hence, they want to be near one another, not further away. In general, the more negative the potential energy, the better.

Electrons in, say, and N = 4 state are much further away from the nucleus than the N = 1 state. The energy states for the electron are quantized and are directly related to the potential energy equation I stated above.

Hope this helps.

 

[sv3]

Not sure if this was covered in any of your physics classes but the equation relating electron potential energy in the hydrogen atom is

U(r) = -ke^2/r

Notice the negative sign in the equation. As the electron moves further out from the nucleus, the potential energy becomes less negative and approaches zero as r increases to infinity.

Now ask yourself, is it easier to put an electron at a distance r from the nucleus, or at 3r?

It's easier to put an electron at a distance r than 3r because the electron and the nucleus attract each other. Hence, they want to be near one another, not further away. In general, the more negative the potential energy, the better.

Electrons in, say, and N = 4 state are much further away from the nucleus than the N = 1 state. The energy states for the electron are quantized and are directly related to the potential energy equation I stated above.

Hope this helps.

Hey, thanks very much, it helps quite a bit as I never seen that equation before (interesting that e is squared since there is only one electron in an H atom.....not sure why though). So electrons have the most negative energy closest to the nucleus, and the further away electrons are, the less negative (or more positive in relative terms) their energy levels are and thats why N=4 is greater than N=1 as far as energy levels go?

One last thing......what did you mean by: "In general, the more negative the potential energy, the better". Are you just saying the more negative the closer they are to the nucleus? Not sure what "better" meant....that's all. thanks again.

steve

 

[Fort]

Basically the more negative the potential energy, the easier it was to get that electron there in the first place. It's harder for the electron to move further away from the proton because it takes work and electrons want to be near protons.

The e^2 is there because for a hydrogen atom with a single electron, your charge q is simply e, which is the fundamental charge constant 1.6*10^-19 C. Since the charge on the proton and electron are both e or (or q, whichever you prefer), you essentially have e*e, which is e^2. Remember Coulomb's Law?

F = kq1q2/r^2

Well Coulomb's Law is related to electric potential energy, that's where the e^2 originates.

 

[sv3]

right. Thanks. Is this the Bohr atom? TPR didn't cover it.....this sounds like it.

Also, your original formula had "r" in the denominator - so this difference to coloumbs law is because your talking about energy, and not force or electric fields right?

thanks very much, finally got this through my thick head now!

cheers
sv3