Preference for lower energy states?

[pivoxa15]

"The electron tends to be in its lowest energy state."

"When an electron reaches an excited state, it does not stay there but quickly de-excites by decreasing its energy (emitting a photon)."


These statements are made considering an electron trapped in an infinite 1-D potential well. But these general principles should also apply to more realistic cases of a trapped electron. My question is why does the electron prefer lower energy states? This seems to be a recurring theme in all of physics and chemistry. But is it a scientific law?

 

[vanesch]

"The electron tends to be in its lowest energy state."

"When an electron reaches an excited state, it does not stay there but quickly de-excites by decreasing its energy (emitting a photon)."


These statements are made considering an electron trapped in an infinite 1-D potential well. But these general principles should also apply to more realistic cases of a trapped electron. My question is why does the electron prefer lower energy states? This seems to be a recurring theme in all of physics and chemistry. But is it a scientific law?

Entropy !

In fact, a system doesn't want to be in a lower energy state for its own sake, it just wants to be there because it is more probable. There are more available states of low energy than of high energy in most system+environment ensembles, which, when looking at one single individual system, usually tends to have it with high probability be in a low energy state (not necessarily the lowest).
But of course, the more energy is available, the more there's a finite probability NOT to be in the lowest state. However for that to be the case, the temperature of the environment must be so that the higher energy states are not far from k-boltzmann x T above the lowest state.

 

[pseudovector]

Potential energy emenates from force, so where there is an energy difference, there will be a force that drives the system towards the lower energy state.

 

[pivoxa15]

Potential energy emenates from force, so where there is an energy difference, there will be a force that drives the system towards the lower energy state.

There could also be an opposing force opposite this force arisen from potential energy (i.e. after the absorption of a photon). But why does the electron emit it away so quickly instead of staying at the excited level a bit longer?

 

[pivoxa15]

Entropy !

In fact, a system doesn't want to be in a lower energy state for its own sake, it just wants to be there because it is more probable. There are more available states of low energy than of high energy in most system+environment ensembles, which, when looking at one single individual system, usually tends to have it with high probability be in a low energy state (not necessarily the lowest).
But of course, the more energy is available, the more there's a finite probability NOT to be in the lowest state. However for that to be the case, the temperature of the environment must be so that the higher energy states are not far from k-boltzmann x T above the lowest state.

So each level is equally as likely to be in but there is most combinations of going to the ground level than other levels. So over larger systems, there is most probability of finding the electron in the lowest state.

So what I stated which was 'preference for lower energy states' isn't correct, its more a particle in a low energy environemnt experiences higher multiplicitiy in the lowest energy state and that is why it tends to be there most often which is a consequence of the second law of thermodynamics. So it is a scientific law.

But I have read that the second law isn't a fundalmental in physics because it can't be derived from energy conservation laws whereas all others can.

 

[lalbatros]

pivoxa15,

"The electron tends to be in its lowest energy state."

This is simply because a "moving" electron is radiating electromagnetic energy.

Fortunately, in the ground state it cannot radiate anymore.
This explains the stability of our universe, and it is maybe the most striking consequence of quantum mechanics as compared to classical mechanics.
This is understood as a result of the wave-like nature of the electron.
In the ground state, an electron cannot drop further on the nucleus because -for a ewave- this would mean an increase in momentum and energy. The ground state looks like an equilibrium state.

But as you know, ... quantum mechanics cannot really be understood.

Of course, the electron can jump to a higher energy if energy is available.
This has more chances to happen in a high temperature environment.
The rate of such low-to-high transition increases with temperature but also with density.
When a thermodynamic equilibrium is reached, the fraction of electrons in excited states is given by the Gibbs distribution. It is a function only of temperature (ideal gases), increasing with temperature.

Michel

 

[Careful]

Of course, the electron can jump to a higher energy if energy is available.
This has more chances to happen in a high temperature environment.
The rate of such low-to-high transition increases with temperature but also with density.
When a thermodynamic equilibrium is reached, the fraction of electrons in excited states is given by the Gibbs distribution. It is a function only of temperature (ideal gases), increasing with temperature.

Michel

I agree with Vanesch here: strictly speaking if you include *all* interactions, the total energy of the universe is conserved. So the reason why an excited electron would drop to a lower (non occupied) orbit is because it is simply more likely that the other degrees of freedom (in the universe) get excited too. Considering that the ``photon'' can fly in all directions, this provides an aleph_1 number of more states. Now pivoxa15 is correct that this is not a deterministic law which can be derived (except for black holes in gravity), but any dynamics would be incredibly conspirational if it would imply the total configuration to stay in this zero measure box of phase space.

Careful

 

[vanesch]

But I have read that the second law isn't a fundalmental in physics because it can't be derived from energy conservation laws whereas all others can.

Tongue in cheek, I'd say that the second law of thermodynamics is the most probable of all physical laws

Honestly, I find that a rather arbitrary definition of what is "fundamental physics": it should be derivable from energy conservation.

The second law of thermodynamics, in its microscopic interpretation, simply says that it's more probable to find systems in a macrostate which is "more probable" in the sense of: there are more ways to realize it.
In other words, if you have a class of macrostates which can be realized by 10^(254532) possible configurations, and you have a class of macrostates which can be realized by 12 possible configurations, and there's a dynamical law which makes one configuration evolve (rather "randomly", that is, unrelated to this division) into another, then chances are higher that you are in the first, than in the second macrostate, and moreover, even if you would be in one of those 12 states, after a second, it would be highly surprising if you'd have evolved in one of these other 12 states, and have avoided the big lot of others.
The crux here is that there is an apparent "independence" between the way we classify macrostates, and the way the microdynamics evolves, so that, from the PoV of the macrostates, the dynamical evolution seems rather "random" (even though it might be determined by deterministic microlaws).

For instance, you've decided to classify the macrostates in "excited atom" and "desexited atom + radiation". But that split is "independent" from the actual dynamical law which will couple both. So if you now classify possible states as a box with "desexited atom" and another box with "exited atom", you'll see that many much more configurations exist for the former than for the latter. The dynamical law not caring about YOUR splitting up of the configuration space that way, it can be seen as jumping back and fro "randomly" between configurations, and so most of the time you'll be in the big box.

 

[lalbatros]

Hi all,

I agree with everything that was said.
However, the most direct way to explain the tendency to the fundamental state is sponteneous emission (radiation), I think.

Why this irreversible tendency can then be related to the interaction between -say- a smal system (atom) and an infinite system (empty space accepting radiation).

If the experience happens in a closed space, then thermodynamic equilibrium might come into play for the state occupation statistics. However, the (spontaneous) emission rate does not depend on the thermodynamic state of the system. It is a property of the atom, not more.

"The tendency to the fundamental state" is a property of the atom. This tendency, measured by its rate, spontaneous emission rate, does not depend on anything else than the atom and its coupling to radiation.

See the http://qwiki.caltech.edu/wiki/Einstein_A_coefficient"

Michel

 

[pivoxa15]

Hi all,

I agree with everything that was said.
However, the most direct way to explain the tendency to the fundamental state is sponteneous emission (radiation), I think.

Why this irreversible tendency can then be related to the interaction between -say- a smal system (atom) and an infinite system (empty space accepting radiation).

If the experience happens in a closed space, then thermodynamic equilibrium might come into play for the state occupation statistics. However, the (spontaneous) emission rate does not depend on the thermodynamic state of the system. It is a property of the atom, not more.

"The tendency to the fundamental state" is a property of the atom. This tendency, measured by its rate, spontaneous emission rate, does not depend on anything else than the atom and its coupling to radiation.

See the http://qwiki.caltech.edu/wiki/Einstein_A_coefficient"

Michel

I assume the spontaneous emission rate is fast. Hence the word spontaneous in there. Is there a general or brief explanation for this fast emission rate as I have only known second year QM.

 

[lalbatros]

pivoxa15,

I assume the spontaneous emission rate is fast.

No, it is called spontaneous because it occurs without external influence.
"No need to push the electron to the lower level".
What means 'fast' anyway. Is 1 nanosecond fast? For a human maybe yes, for an atom I don't know.
However, in a sense, there is an external influence. It is the vacuum fluctuations of the electromagnetic field. As you know, the EM field also has a fundamental level. The EM fundamental level corresponds to the smallest level of EM field possible in QM, and it is not zero. There is always some small electromagnetic radiation, even when no sources are present. These "vacuum radiation" is no source of energy. Yet, it can induce "spontaneous emission".

Here are some lifetime for hydrogen levels (neglegting fine structure):

2s:0.14 ns
2p:1.6 ns
3s:158 ns
3p:5.3 ns
3d:15.5 ns
4s:227 ns
4p:12.3 ns
4d:36.2 ns
4f:72.5 ns
​

You can find transition probabilities (rate per second) on http://physics.nist.gov/Pubs/AtSpec/node18.html" as well as further explanation.

You should also know that the transition probabilitiies (level n to level m) are determined, in first approximation, by the dipolar interaction of the atom with the EM field. In this first approximation, some transition maybe forbiden. However, the forbidden transitions may become possible in second approximation. Then, the decay rate should be much lower.

Note that the basic concept is the decay rate (units: s-1) from a level to another, rather than the lifetime of a level which results usually from several possible transitions.

If you web find a site that gives clear data and explanations, let me know, I was not very successful.

Michel

 

[pivoxa15]

So it seems that it is not preference to lower energy states but there are random causes (i.e. nonzero energy fluctuations) that drive systems to their equilibrium point and so when talking about systems in general it is best to describe them as being more on the average in the ground level. In the end it is a cause and effect phenomena (on the microscopic level) which is linked to the conservation of energy. But on the macroscopic scale it is connected to the 2nd law of thermodynamics. Is this correct?

 

[lalbatros]

pivoxa15,

Here is how I picture it for myself:

electrons in an atom should radiate and lose energy according to classical physics,
in quantum mechanics they also radiate and lose energy, but there are big differences that are the fingermarks of quantum mechanics:

1) there are discrete energy levels (but also Rydberg states or free electrons)
2) each level can be stable some time, but with a certain transition probability
3) there is a fundamental level from which an electron never radiates energy
... this is because of the wave aspect of the electron:
... a lower level of energy would mean more precise localisation
... and therefore more momentum, and therefore more energy
4) there are two mechanisms for emision
5) spontaneous emission is driven by "quantum fluctuations"
6) stimulated emission is driven by excitation by other photons
​

in a open and cold universe, all atoms would reach their fundamental level,
in thermal equilibrium with background radiation (black body oven e.g.) the atoms can be excited with probabilties given by the Gibbs distribution
​

Michel