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Name: Kathy
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Question:
Why does the atom, or nucleus, prefer to be in the lowest energy state? I understand that no two identical particles can occupy the same energy state with the same quantum numbers. Otherwise, all atoms would collapse to the lowest state.

However, it just seems to me that it would be the other way around. Newton's Law (which I realize is classical and atoms are not) basically says that if an objet is lifted to a higher potential energy and dropped, it will fall to the lower potential energy, not because it prefers to (it would prefer to remain at rest right where it is), but because there is a force acting on it (gravity).

However, unlike the classical dropped object I just described, the atom "falls" to a lowest energy level because it prefers to. Maybe I'm just making a really bad analogy, but it seems to me that it would be more obvious if the atom preferred to either remain in its condition (possibly a higher state) and only move to the lowest energy state if some force made it do so.



Replies:
I think it's as good an analogy as you can get in classical physics.

The reason the lowest energy level is the lowest is because there *is* a force acting on the electrons. The electrostatic force between the protons in the nucleus and the electrons draws them together, and the lowest energy state is the one in which the electron is as close to the nucleus as it can get.

People, and textbooks, talk about electrons "preferring" to do this or that partly because the relationship between the electrostatic force and the potential energy of an electron is not as easy to write down as it is for a mass in a laboratory near the surface of the Earth. Recall that gravitational potential energy is usually written as "mgh", where "m" is the mass, "g" is the acceleration due to gravity (at the surface of the Earth), and "h" is the height from the surface of the Earth. This is simple only because we are regarding "g" as a constant -- which it nearly is, if you stay near the surface of the Earth. If "g" were not approximated as a constant, we would have to write an integral, which is more difficult to grasp than a multiplication. The math would obscure the simple and valuable notion that potential energy is just a force ("mg") multiplied by a distance.

We can get away with approximating "g" as a constant only because our laboratory is small compared to its distance from the center of the Earth. But in the case of electrons in an atom, the interesting stuff happens over a range of distances between the electron and nucleus, and in this range the electrostatic force is not approximately constant. So we are never going to see a simple expression like "mgh" for the potential energy. Instead we are either going to get a integral, or something vague like "the electron prefers to be near the nucleus."

Tim Mooney


You have raised two issues here. Let us address them one at a time.

1. "Energy" is a relative term (except in the sense of E = m c^2), so it does not make any difference for the most part where we decide where energy = 0 occurs. It is strictly a convention that smaller numbers, including negative numbers are assigned to "lower" energy. Nothing "bad" happens if the whole energy "scale" is reversed. A related issue is assigning larger numbers to hotter temperatures. It is only history that keeps us from doing the opposite. That is, instead of: T (kelvins), we define T' (inverse kelvins) = 1/ T (kelvins). There are in fact some advantages. For example, the inability to obtain "absolute" zero is no longer mysterious because on the T'(inverse kelvins) scale this is equivalent to saying that "absolute" zero is trying to reach infinite temperature, and that does not seem so mysterious.

2. Your statement (and you are excused for not knowing this, since it is not a topic usually introduced in high school) "I understand that no two identical particles can occupy the same energy state with the same quantum numbers." If you "truly" can explain that, publish immediately, because that is a statement of "fact" about one category of particles, called "Fermions", which are particles with 1/2 integer spins. Electrons and some atomic nuclei fall into this category, as well as some sub-atomic particles. Your statement "Otherwise, all atoms would collapse to the lowest state." is on the verge of a discovery. There are a whole other category of particles, called "Bosons" that behave exactly as you suggest. They do all fall into the lowest energy state. Particles with whole number spins behave in just this way. Such particles are the subject of a lot of research, both theoretical and experimental. If you look up (or search the topic "Bose Einstein condensates") the links will lead you to as simple, or as complex, explanations that you wish.

3. The forces that prevent two "Fermions" from occupying the same space (more precisely from having the same set of quantum numbers) is not infinite. And there is some research on the behavior of such Fermions at extremely high pressure in which you "crowd" the atoms into the same place, but only recently has it been possible to achieve such high pressures in the lab.

Vince Calder


Kathy,

Perhaps one of the most important things to realize with particle physics is that what we see on our scale is just an average effect.

At the particle level, the nucleus of one atom seldom even interacts with the nucleus of its neighboring atom. Most of this interaction is a function of the outer electrons. Even this is not the pushing or pulling as we know it. Particles called fermions (protons, neutrons, electrons, and such) send out particles bosons (photons, W particles, gluons, and such). Bosons are received by other fermions. This sea of exchanged particles transfers energy and momentum across the void between the fermions. Sometimes it even changes the identity of the fermions.

One of the simplest of these effects is electrons releasing photons. There is always a certain probability of an electron releasing a photon. To do this, it must release one of the proper energy. The electron releases a photon when it drops to a lower energy level. This photon flies off. It might or might not find an electron in an atom. If it has the correct energy to boost the electron to a higher energy level, the electron can hold the energy for a while. The photon has been absorbed. If the electron does not end up in an allowed energy level, the photon is immediately shot back out. There is such a wide open space between the atoms that many of these photons end up leaving the material.

Electrons are bouncing up and down in energy all the time. This is part of the interaction that holds a material together. When a large group of electrons absorb more than they emit, the AVERAGE effect is that the temperature rises. Not all of the electrons rise in energy. None of the electrons even stay at a higher energy. It is just that there are enough photons flying, of the correct energy, to keep pushing many of the lower energy electrons back up. When an object cools, many of the released photons leave the material, but fewer come back in.

When atoms join, electrons obtain a new energy level that is lower than its current level. This electron sometimes releases a photon that drops it into this new level. Now, the atoms are stuck together until an incoming photon can push the electron out of this new level. When only a few pairs of atoms are bonded, this correct energy photon is rare. Nothing is emitting it. The atoms remain bonded. Many other such pairs will bond. Now more of these photons have been released. Occasionally they will hit a pair, thus splitting them apart. This creates a balance that affects how quickly two different elements can join, as well as how much energy is needed to split them apart.

There are many other such interactions among particles. All we see is the average effect of these interactions.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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