Q & A: Speedy Electron

How long does it take an electron to orbit the nucleus of a hydrogen atom?
- Dana Bahr (age 49)
Sch Dist 885, Albertville,MN,US

Hi Dana,

That’s a great question, and the answer may surprise you.

The picture we often have of electrons as small objects circling a nucleus in well defined "orbits" is actually quite wrong. The electrons really aren’t at any particular place. However, we CAN figure out the volume of space where we are likely to find a given electron if we look, since that ’measurement’ somehow causes the electron to be found in a small region. For example, the electron in a hydrogen atom likes to occupy a spherical volume surrounding the proton. If you think of the proton as a grain of salt, then the electron is about equally likely to be anywhere inside a ten foot radius sphere surrounding this grain, kind of like a cloud.

The weird thing about that cloud is that its spread in space is related to the spread of possible momenta (or velocities) of the electron. So here’s the key point, which we won’t pretend to explain here. The more squashed in the cloud gets, the more spread out the range of momenta has to get. That’s called Heisenberg’s uncertainty principle. Big momenta mean big kinetic energies. So the cloud can lower its potential energy by squishing in closer to the nucleus, but when it squishes in too far its kinetic energy goes up more than its potential energy goes down. So it settles at a happy medium, and that gives the cloud and thus the atom its size.

We’ve actually already answered a very similar question: try checking out Why do Electrons Move? for some more details -Tamara

(published on 10/22/2007)

what is in between the nucleus and the electron?
- Narmeen (age 16)
London

There's really nothing else special in there. The electron cloud itself can wash right through the nucleus (for any technical readers: if it's in an S state) , so there doesn't have to be any space in between them.  Even if the electron is in some state where it isn't near the nucleus, there's nothing special in between. There is an electric field, which you could say means that there are virtual photons in there- but really it's no different from the electric field around an ordinary battery, no matter what name you call it.

Mike W.

(published on 11/14/06)

Please note that I'm not trying to be argumentative. Rather, I'm trying to understand. [answer #1, paragraph 2 (Tamara] Paraphrasing, 'Electrons exist as sort of a cloud. If the proton was the size of a grain of salt, then the electron cloud would be at a 10' radius.' I think this contradicts 'if you probe, you'll find the electron somewhere in that region', i.e., are we back to the orbital model or was the word "cloud" accidentally left out ('...find the electron *cloud* somewhere in that region')? [answer #1, paragraph 3 (Tamara)] "the cloud can lower its potential energy by squishing in closer to the nucleus, but when it squishes in too far ***its kinetic energy goes up more than its potential energy goes down.*** So it settles at a happy medium, with the lowest possible energy..." How is the statement (within asterisks) reconciled with energy conservations laws? Where is the additional kinetic energy acquired from, if not from an equivalent reduction in potential energy? [follow up answer #1 (Mike)] Paraphrasing, 'the electron isn't going anywhere at all. However, ***the cloud has the potential to show movement in any direction*** if something comes along to 'measure' that movement.' I'm trying to reconcile that statement with [answer #1, paragraph 3] regarding the kinetic energy of an electron. If it isn't going anywhere yet has KE (0.5mvv), then is the electron *cloud* spinning (presumably uniformly)? The last 2 sentences of [follow up answer #5 (Mike)] seem to suggest this interpretation. [follow up answer #3 (Mike)] "The extra energy will radiate away as an electromagnetic field." My understanding is that an electric field is exhibited by charges, just as a gravitational field is exhibited by mass. The quoted statement implies that the electric field of a charge could be spent until it's gone. Or should I understand the quoted statement as 'the extra [KE] will radiate a stronger electric field'? But even that doesn't make sense since it implies that there are physically more charges present xor contradicts that charges are quantized. Please elaborate. Best Regards, Noel
- Noel Khan (age 31)
Victorville, CA

Noel- It's great you're trying to make sense of this. Before going further, I should say that I'm responsible for the passages you are concerned about, not Tamara.

point one: Yes, to be more precise what's left is a new cloud, more localized than the first one. Good point.

point two. Once again I wrote a little sloppily. The only way the cloud can squish in more is if something does work to squeeze it in. Otherwise, as you say, energy wouldn't be conserved.

point three: No, in the simple case of low-energy hydrogen the cloud isn't spinning at all. (Higher energy states can spin.) The kinetic energy term actually comes from the range of possible radial velocities implicit in the electronic state. However, this cloud is not changing in time. Imagine a classical standing wave, say on a string. The wave is a mixture of waves traveling left and right but overall does not move. The electron wave is a little similar, but in 3-d. I know this sounds very mysterious.

point 4: Electromagnetic waves are a subset of electromagnetic fields, just ones that actually carry energy around. There's energy in the static field from a charge, but it isn't going anywhere.

I hope this helps.

Mike W.

(published on 10/10/09)

Original question on this page asked "__How long__ does it take an electron to orbit ..." So, how long DOES it take? I don't see that answered here in a simple number or range.
- r.s. (age 48)
Canada

We didn't say how long an electron takes to orbit an atom because, except in very special cases, an electron doesn't orbit an atom. In the typical case people start with, a single electron in one of the two low-energy states around a proton, the electron is always all around the nucleus and its spread of positions is unchanging in time.

You could make an electron state that looks more like a small blob actually orbiting the nucleus, but it would have to be a combination of states with different energies and those energies would have to be near the value at which the electron would escape from the nucleus. The time that packet would take to make an orbit would depend on what ingredient single-energy states went into it. There's no maximum time, but the minimum time would be about 10^-14 seconds. If you'd settle for a big blob that doesn't quite resemble an orbiting object but does rotate around the atom, the minimum rotation time is about 4.055*10^-16 s for a hydrogen atom. That would be a combination of 1s and 2p states.

Mike W.

p.s. Those orbits won't last very long, since they radiate electromagnetic energy in about a billionth of a second.

(published on 02/12/11)

To follow up on Dana Bahr’s question; What is the electron really doing in relation to its’ nucleus
- Brian Matt
American Gnostic sch, Yelm, WA

That's a loaded question...to give you a detailed answer would take several text-books on quantum mechanics, but to give you a sketchy picture is pretty easy (so that's what I'll do):

The picture we sometimes see of electrons making orderly circular orbits around a nucleus (like little planets in a micro solar system) is clearly wrong, nevertheless it helps picture part of what is going on. We know the electron and the nucleus are attracted to each other by the electromagnetic force, and are somehow "bound together" (just like the earth and the moon are).

The thing that is a little harder to visualize is the way the electron "orbits" the nucleus. The mathematics of quantum mechanics, (which allows us to study atoms the same way that Newton's F=ma allows us to study big objects), tells us that the electron is more like a cloud that surrounds the nucleus. In other words, the position of the electron is not at all well defined (like a little planet) but rather it is smeared out over a large volume all around the nucleus. Picture the nucleus as a tiny grain of sand that lives at the middle of a puff of smoke, which is the electron.

The shape of the electron "cloud" or "smoke" depends on how many other electrons are caught by the nucleus, how much energy the electron has, and other more subtle things as well. Sometimes the cloud will be spherical, sometimes it will be shaped like a doughnut, sometimes like a dumbbell etc.

If you look in a high-school chemistry book, or a college level modern-physics book you can find out more.

MS

(republished on 07/21/06)