Lowest Energy State Preference
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.
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
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
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
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."
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.
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
There are many other such interactions among particles. All we see is the
average effect of these interactions.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012