Questions: Sgt. Snorkel returns to ground state

Posted on August 3, 2011


One of Beetle Bailey‘s well-loved tropes (or at least, oft-used tropes) is that of Sarge hanging from a small tree growing from the side of a cliff. In the above strip, he’s fallen over because he was reaching for a doughnut (say what?), and while he’s hanging there — and you’re really going to like this because it’s waaay funny — he gains weight from thinking about food and the branch breaks.

I know, right? Comedy gold.

The question here isn’t really why does Sarge fall; the question is, since Sarge is hanging from and tree, and therefore not falling, what changes to make him fall (aside from, in this instance, gaining weight from thinking about food)? In other words, since he obviously is managing to resist the pull of gravity for the moment, what changes to make him stop resisting?

The answer, of course, is that Sarge is temporarily able to resist the pull of gravity because he has enough energy to keep hanging on. Unfortunately, as he’s hanging a number of changes are occurring that decrease his energy. The fuel needed for his muscles is slowly being depleted and he may even be experiencing tiny rips in his muscle tissue.

Eventually, the balance tips the other way and Sarge is no longer able to hold on.

Even if he had superhuman strength, however, Sarge’s fall is inexorable. He may be able to hang on for a thousand years, but in that time the tree itself is undergoing small changes and will eventually die, or the roots will eventually come loose. If nothing else, erosion will wear away the cliff face, plunging Sarge and the tree both into the canyon below.

So there’s no problem understanding why Sarge will eventually fall — but everything changes when we bring this to an atomic level.

For purposes of visualisation, I’m going to use a picture of the classic Rutherford model. Obsolete almost before it was first released, it nevertheless is good enough for this discussion, unless someone says otherwise and can explain why.

In place of gravity, we have a magnetic pull. The nucleus is positive, the electrons are negative, and just as the north end of one magnet is drawn toward the south pull of another magnet, the electrons are pulled towards the nucleus.

So why don’t they fall in? In our analogy with Sarge and the tree, this would be like Sarge hanging from nothing.

In the case of the atoms, the “tree branch” would be the electron’s orbital energy. Just as the Earth is drawn toward the Sun by gravity, yet never actually falls into it because of its orbital velocity,  the electrons are drawn toward the nucleus, but are spinning too fast around it to fall in. (In reality, we no longer think of the atom in these terms, but I think the similarities between this, and the modern concept of probability shells, is close enough for my purpose.)

Now, electrons have a “ground state,” which is the lowest energy orbit allowable by the constraints of whatever particular element they’re part of. If we think of it like a little solar system, then Mercury stays in its orbit, Venus in its orbit, and so on. Think of this as Sarge standing on the ground. When energy is imparted to an electron, however, it jumps to a higher orbit, called an “excited state.” This is the point at which the electron is equivalent to Sarge hanging from the tree.

What’s important here, however, is that as long as the electron has enough energy to resist the inward pull, it will continue to remain in its excited state. Like Sarge, the electron’s state will be stable only for so long as it doesn’t weaken in its resistance.

The difference, however is significant.

Sarge, the tree, the cliff face, and everything else in the physical world, weaken incrementally. Energy is lost in small quantities. The requirements of the body to simply stay alive will deplete Sarge’s energy resources.

But — how does the electron “weaken”?

In some instances, it weakens because it’s interfered with — by a stray photon or other outside force. But what I’m interested in are the “spontaneous emissions” in which the electron fires off a photon and returns to the ground state because — well, because it’s time.

In its excited state, it is in equilibrium. It obviously has enough energy to resist the pull of the proton, because it’s still in orbit. Unlike the Enterprise, its orbit cannot “decay” because it can only be in one orbit or the other — there is no “in between” for an electron.

Now we could imagine that the electron is losing little tiny bits of energy until it loses enough that it falls back to its natural orbit. The only problem with this is that it’s not possible. That’s because the electron can only lose energy in certain amounts, and the base amount is a photon. This, in fact, is exactly what happens when the electron does finally return to its ground state — it releases a photon. It can’t release half a photon. It can’t release a quarter of a photon.

It has to release a photon’s worth of energy, then down it goes.

But how? For a certain length of time the electron remains in its new orbit, and then it undergoes what is called a “spontaneous” release of a photon, thereby going back home.

So if it has enough energy to stay in this new orbit for any length of time, what causes it to “spontaneously” lose energy? It’s not “weakening,” because that means that it’s losing smaller bits of energy, but it can’t do that.

So what happens?

If you have a clue about this, or know someone who may have a clue about this, please let me know.