Lowest Energy State

[Pugdaddy]

Can anyone tell me why an electron when excited to a higher energy state will try to get to it's lowest energy state? I assume it has something to do with Coulomb Law. It is just a property of the electromagnetic field or is some deeper spacetime parameter involved?

[swansont]

Can anyone tell me why an electron when excited to a higher energy state will try to get to it's lowest energy state? I assume it has something to do with Coulomb Law. It is just a property of the electromagnetic field or is some deeper spacetime parameter involved?

 

 

The short answer is because it can.

 

In classical physics, the presence of an energy gradient means there is a force — things spontaneously roll downhill to where the potential energy is lowest. I assume you aren't surprised by that phenomenon. An atomic system seeking its lowest energy state is the analogue of that. In this case the electron is subject to the Coulomb force and since the energy states are quantized, it's a little more like bouncing down some steps, but we focus on energy rather than forces, because position isn't a good variable in quantum mechanics.

[Strange]

since the energy states are quantized, it's a little more like bouncing down some steps

 

Nice analogy. And the reason the electron doesn't reach the nucleus is because there are no more steps: the ground floor is at a non-zero energy level.

[Pugdaddy]

Thank you. I am not sure I really get it though. The orbital of the electron has to be an integer multiple of the wavelength of the electron. So is the lowest energy state when the integer is 1?

[studiot]

 

Today, 03:40 PM

Can anyone tell me why an electron when excited to a higher energy state will try to get to it's lowest energy state? I assume it has something to do with Coulomb Law. It is just a property of the electromagnetic field or is some deeper spacetime parameter involved?

 

Several things need amplification here.

 

First and foremost the energy state belongs to the environment of the electron, not to the electron itself.

 

Secondly the above quickly glosses over the means by which the excitation occurs.

 

Thirdly it may not be that specific electron that 'falls back' to the lower state.

 

So please tell us more about the context of the question.

 

Is the electron in an atom, a molecule, a metal, free space or what before excitation?

 

Secondly what method of promotion are we discussing, light, heat, electric field or what?

[swansont]

Thank you. I am not sure I really get it though. The orbital of the electron has to be an integer multiple of the wavelength of the electron. So is the lowest energy state when the integer is 1?

 

 

That's the Bohr model view, but in that model, yes. In truth the lowest energy state has no momentum (linear or angular) which is one reason we know the Bohr model to be incorrect.

 

Secondly the above quickly glosses over the means by which the excitation occurs.

 

...

 

Secondly what method of promotion are we discussing, light, heat, electric field or what?

 

Not sure why this matters. Are you suggesting that there is a method of excitation where the atom won't ever undergo relaxation, while an identical atom with a different method of excitation will?

[Pugdaddy]

Lets use the hydrogen atom. A photon with energy to excite to the second energy level. The electron emits a photon and returns to the more stable lower state.

[swansont]

Lets use the hydrogen atom. A photon with energy to excite to the second energy level. The electron emits a photon and returns to the more stable lower state.

 

 

In that case, if it's in the 2P state, it can emit a 10.2 eV photon, which carries away 1 unit (h-bar, i.e. the reduced Planck's constant) of angular momentum.

 

If it's in the 2S state it will stay there a while, because there's no direct way to get to the ground state — the angular momentum is the same, and a photon always carries away one unit of angular momentum. It either has to emit two photons (much less likely than the 2p-1S transition, so it takes longer) or first decay to the 2P state, which also takes a long time because they are vey close in energy.

[Pugdaddy]

 

Thirdly it may not be that specific electron that 'falls back' to the lower state.

 

 

 

I thought electrons were indistinguishable from each other and would therefore lack specificity.

[swansont]

 

 

I thought electrons were indistinguishable from each other and would therefore lack specificity.

 

They are, which is why atoms have the structure that they do. But of you have a multi-electron atom and you excite a tightly-bound electron, you can get a cascade of electrons filling in lower levels. The originally excited electron may not end up in the state it was originally in.

 

But the concept here is the same — the system is reverting to its lowest energy state.

[studiot]

 

Lets use the hydrogen atom. A photon with energy to excite to the second energy level. The electron emits a photon and returns to the more stable lower state

 

Thank you.

 

A single hydrogen atom has one electron.

So this is the only case in which the issue of which electron does not arise.

swansont's replies show that even here the possibilities are beginning to get complicated, and I am struggling a little bit to find a level to answer.

 

So here goes, here is the simplest answer I can think of.

 

Moving the electron to a higher energy level moves it further out from the attracting positive nucleus.

So electrostatic attraction will pull it back in, if at all possible.

 

This is similar to saying that if you throw a stone up, gravity will pull it back down to Earth.

 

Also similar to gravity, where if you (or the HULK) throws it up hard enough the stone can leave the Earth entirely,

it is possible to remove that electron and take it away somewhere so that it will never fall back o its original state.

 

That is what I meant by the environment and the process of excitation.

Not important in single hydrogen atoms, but very important in thermionic emission or conduction bands in semiconductors or conductors.

[Carrock]

In truth the lowest energy state has no momentum (linear or angular) which is one reason we know the Bohr model to be incorrect.

Surely it has at least zero point momentum.

[swansont]

Surely it has at least zero point momentum.

 

 

Time-averaged linear momentum is zero. At any instant it will have some linear momentum.

[Enthalpy]

 

 

Time-averaged linear momentum is zero. At any instant it will have some linear momentum.

Ouch!

An orbital is a stationary wavefunction, that is, it does not depends on time except for the phase rotation.

All the information of a particle resides in its wavefunction.

And a measure "at an instant" is impossible to make, so it's of no interest to QM, which does not answer it.

 

The nearest possible experiment is to measure the momentum of an electron over a short time, and then the interaction with the measuring particle is inevitably at high energy and momentum if the interaction happens. This does not require the electron to have this momentum prior to the interaction.

[swansont]

Ouch!

An orbital is a stationary wavefunction, that is, it does not depends on time except for the phase rotation.

All the information of a particle resides in its wavefunction.

And a measure "at an instant" is impossible to make, so it's of no interest to QM, which does not answer it.

 

The nearest possible experiment is to measure the momentum of an electron over a short time, and then the interaction with the measuring particle is inevitably at high energy and momentum if the interaction happens. This does not require the electron to have this momentum prior to the interaction.

 

 

Momentum is not a good quantum number, so it's not going to be part of the wave function.

 

You're reading too much into "instant". Also losing the context of the question that was asked.

 

If you object to the idea that it has some linear momentum, you must also know that you can't say it has no momentum, and that's a much stronger objection. It's localized, and the Heisenberg Uncertainty Principle precludes knowing the momentum is zero. But not being able to know what the momentum is is not the same as knowing it has zero at any point in time.