# How does an electron go between two points, without crossing the space inbetween?

So, today I got out of my Introduction to Chemestry class, and the professor had explained the modern theory of the atom. While explaining the various shells of electrons, he pointed out that in some shells, there are areas where there is a high probability of finding an electron, and areas in between that have a zero probability of finding an electron. He posed the question of, how does the electron get from one of these areas to another, without crossing the space inbetween, and he admitted that he does not know or understand the answer.

Is there a definate answer to this? Or, what are the current theories to explain this? Does the electron blink out of, and back into, existance? Surely, the movement between the two areas cannot be instantanious, since that would violate the speed of light. What’s the dope on this one?

I think that all the shells cross at certain points and aren’t just spheres as depited by the Bohr model. This could this be where the transfer takes place. Here are some pictures of electron shells, and you can see how P would cross S at certain places. This is just a start, I’m sure someone will come along with an in-depth response to help us out!

Well, here is the basics. Don’t know if it will help. Your teacher doesn’t sound like a lot of help.

Electrons are always moving and orbit the nucelus in what is known as shells. They can spin in any direction, as long as they stay in their shell and the shell is the distance from the nucleus that the electron spins. The first shell i always closer to the nucleus than the electrons in the second shell. Electrons do not exist between the shells.
The shells are given names, or letters, “k,l,m,n,o,p, and q”. “K” is the one closest to the nucleus and “q” is the furthest away.

Shells do not hold the same number of electrons. The first 18 elements have rules. The k-shell holds two electrons, l-shell holds eight electrons and m-shell holds eight electrons (for the first 18 elements).

What the teacher may be referring to here is that while electrons exist in the specific shells, we can’t tell the exactly where an electron is, only an approximation (known as Quantum Theory). The electron can be found anywhere around the nucleus.

That doesn’t help a whole lot does it, after reading it? It’s 3am and I wrote that from memory. I’ll post a more clear explanation when I’m more awake.

Hasn’t this been done already in the “Ask the Alien” thread?

Teeny, tiny transporters.

This has been touched on many times in many threads, (and I’ll probably never get it), but here’s one which I started referring to a scene in the movie Mindwalk:

http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=72460&highlight=mindwalk

Maybe the question wasn’t clear So, then, let me use an incredibly simplified electron orbital that I just made up to try to make the question clearer:
X--------------X
So, then, an electron can exist at either X, but nowhere in between. So, at any given point in time, the electron can be at either side of the orbital, but never in between, or in any other position. How does this happen? How does it get from one X to the other?

This is where classical mechanics breaks down and quantum mechanics comes into play, and one of the basic concepts of quantum mechanics is that all matter has a wavelength dependent upon its mass and its velocity. You, me, a hammer, the planet Earth, and everything else in the Universe has a wavelength.

So why, then, don’t we notice? For the same reason we don’t notice atoms: Because we exist at a size well above the scale where the phenomenon becomes interesting. Our quantum effects cancel out, statistically speaking, and give us the illusion of matter and energy and a stable physical realm. It’s like how different wavelengths of sound cohere to form a tune.

At the level of electrons, however, the quantum effects come to the fore. The electrons have a wavelength, too, but a constrained one: It can only exist in a predefined number of states, defined by how energized the electron is. Each state has its own shell, so the electron’s state determines which shell it is in. It is impossible for the wavelength to exist at, say, 1.5 of a shell: It must pick 1 or 2, and it can never ever be a fraction as long as it is in orbit around a nucleus.

So, how is this accomplished? The quantum leap. When an electron changes states (by absorbing or releasing a photon), it performs a quantum leap to the next closest shell to reflect its leap to the next closest state. When an electron absorbs a photon, it jumps to the next higher state. When it emits a photon, it jumps down a rung.

Now, what is a photon? It is a quanta of electromagnetic energy. Like a photon, it has a wavelength determined by its energy level even though it is massless. (Mind-bending? Try the double-slit experiment. ;)) What’s more, it cannot split: You can never have a half of a photon, or an eighth, or two-thirds. Since electrons gain energy via photons (and lose energy the same way), electrons have no method of getting or losing anything less than a whole amount of energy.

In short, electrons are constrained as long as they are in orbit around a nucleus. The jumps are related to wave-particle duality, one of the most powerful concepts of quantum mechanics and one of the least intuitive. If you still can’t `see’ it, hang around and wait for some experts. But don’t expect it to be analogous to anything you can physically see around you: The best you can do is observe the effects.

Damned. That should read:

I tried to ask one, but my question changed the answer.

By “shell”, do you mean “energy level”, the set of electrons having the same principal quantum number n? (The numbers of electrons is the same, so I think that’s what it is…) The term “shell” seems like a simplification of the quantum-mechanical model of the atom, but it occurs occasionally in journal articles, so it must have a place.

The question about an electron going through two points without crossing the space in between might refer to a phenomenon called quantum tunneling. Basically, electrons are capable of ‘penetrating’ an energy barrier (such as travelling through space) despite their actual energy being insufficient to cross the barrier, due to the interactions between the electrons. There’s a non-technical explanation of it
here.

If you mean the ordinary movement of electrons within an atom, then, as far as I know, electrons do cross through space when traveling between points. However, the path they take cannot be known because of the Uncertainty Principle (“one cannot accurately measure the position and momentum of an electron simultaneously”).

Derleth, I’m not sure if you mean that electrons are massless, but they aren’t. Electrons have a mass of ~9.1x10^-31 kg, or about 1/1830th that of a proton. Rough estimates of the mass of an electron have been known for some time (by substituting the charge calculated by Millikan’s oil drop experiment into the charge-mass ratio obtained by observing the behavior of a stream of electrons being deflected by a magnetic field). Your post really clarified what’s meant by wave-particle duality (something I’ve never heard explained very well), though, once I thought about de Broglie wavelengths.

** Dr. Love ** what has been explained, and needs to be understoood before you try to comprehend the detailed explanations, is that you really can’t apply our big concepts of ‘here’ or ‘there’ or ‘in between’, because at the quantum level, things don’t happen like that. Failing to accept that leads to far-out theories about electrons moving faster then the speed of light and such. You just can’t think in terms of ‘a electron moves from this space to that space in x amount of time, therefore it moved faster than the speed of light.’ To suggest this would indicate that you have not erased the concepts we are all biased with in our world: the here, there, and in between notions. It just isn’t like that at the quantum level. It just isn’t like that.

It’s one of the hardest things to overcome before you can get your arms around some of the theories. It’s not a simple matter of some space or distance being 'travelled" by some object.

Actually, most electrons move much slower than light, at least in atoms and in conductors. There are instances where electrons travel close enough to the speed of light that their relativistic mass (greater than usual due to near-light speed) needs to be taken into account, such as with beta-particles, which are high-velocity electrons.

If anyone in here is studying or will be studying quantum mechanics, you’ll be comforted by something my professor said several times as he integrated and derived long, complex (well, sometimes. most of them were real… =]) equations: “This isn’t rocket science, people.”

I don’t think that the probability actually goes all the way down to zero, though–it’s close to zero, but not completely zero. Would that change the way you think about the problem?

Is it true that, when a particle undergoes a quantum leap, it instantly dissapears from one spot and reappears in another spot instantly?

That is, without transversing the space between AND without any time elapsing, thus appearing to go faster than light…effectively going infinite speed?

One particle’s state can depend on another particle’s state, and although seperated by great distances, they can instantly change states as the other does. On the surface, one might conclude that some information was relayed instantaneously between the particles, therfore something moved faster than light speed. At the quantum level, it’s flawed to think this way.

Quantum tunnelling is probably a good way to understand it, but that’s not what’s happening here. Think in terms of the wave function - there’s no such thing as a potential barrier between quantum states.

A quantum jump is an instantaneous discontinuous transition between quantum states. There is no in-between state and it takes no time for the transition to occur.

Sorry, but that is all that can be said about it. It’s a quantum phenomenon with no equivalence in classical physics.

When confronted with this reality Erwin Schrodinger said, “If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.”

And Feynman said, “I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, ’ But how can it be like that?’ because you will go ‘down the drain’ into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

Shell is the same as energy level. The term energy level replaced “shell” because shell implied electrons were in fixed circular orbits around the nucleus.

But the two are interchangeable in usage. Most college texts no longer use “shell” though it is still fairly common in high school and grade school.