Speed of electrons in an atom

[The Gregorian]

I'm going to see if I can do this, intentionally without making the suggestion myself:

First: Relative to the speed of light, about how fast do electrons travel? Obviously, this will very depending on the element and which group of electrons.. but, if you were to generalize.

 

[Muad Dib]

Bah, there's an equation somewhere that works it out (drift velocity?) But I cant be bothered finding it, so searched your question in google:

For example, the drift speed through a copper wire of cross-sectional area 3.00 x 10-6 m2, with a current of 10 A will be approximately 2.5 x 10-4 m/s or about a quarter of a milimeter per second.

Just google the question yourself and find all the relevant answers

Ninja edit: Look for "drift velocity" on wikipedia

 

[Wedjat]

Obviously, this will very depending on the element and which group of electrons.

Will it?
Are you assuming electrons to be only particles?
That they travel at any given speed is debatable, things don't work the same way on that scale. Example, at what speed does an electron travel if it is quantum tunneling through the nucleus of it's atom. Is it even traveling?

 

[Cabal]

I'm going to see if I can do this, intentionally without making the suggestion myself:

First: Relative to the speed of light, about how fast do electrons travel? Obviously, this will very depending on the element and which group of electrons.. but, if you were to generalize.

I don't know if you can consider them as moving as such. They aren't exactly orbiting the nucleus.

 

[PhilosophicalBluster]

I don't know if you can consider them as moving as such. They aren't exactly orbiting the nucleus.

An electron's movement within an orbital is random?

 

[Cabal]

An electron's movement within an orbital is random?

Not random as such - nondeterministic would be a better way of describing it.

As an example, the electron ground state of the hydrogen atom is the s-orbital. It's spherical in shape - this orbital essentially dictates the volume in which the electron is likely to found. However, it's a probabilistic construct only, you can't exactly track where they are - only where they are likely to be found.

 

[PhilosophicalBluster]

Not random as such - nondeterministic would be a better way of describing it.

As an example, the electron ground state of the hydrogen atom is the s-orbital. It's spherical in shape - this orbital essentially dictates the volume in which the electron is likely to found. However, it's a probabilistic construct only, you can't exactly track where they are - only where they are likely to be found.

Right, because of Heisenberg's uncertainty principle, but you would think that even though you are unable to determine the exact place where the electron is found, they would follow some sort of orbit, even if it is constantly changing. What I mean to say is that although you can't figure out exactly where it is, it probably doesn't just go around in small circles in empty space in the top left part of the orbital. The positive nucleus must act on its movement in some way. Right?

 

[thaumaturgy]

Right, because of Heisenberg's uncertainty principle, but you would think that even though you are unable to determine the exact place where the electron is found, they would follow some sort of orbit, even if it is constantly changing. What I mean to say is that although you can't figure out exactly where it is, it probably doesn't just go around in small circles in empty space in the top left part of the orbital. The positive nucleus must act on its movement in some way. Right?

The shapes of the electron's orbitals are derived from the square of the wave function describing the electron. As such they are regions of likelihood of finding the electron.

This is where I get a bit confused myself; I am always unsure how to proceed with "wave-particle duality" things.

If the de Broglie relationship is followed:

lambda = h/p

where
lambda = wavelength of the electron
h = planck's constant
p = momentum (mv)

then for a given electron of known wavelength we should be able to calculate a speed, which, as I understand it, is one of the ways De Broglie developed the equation in the first place based on the size of the electrons "orbit" being some integer multiple of the wavelength of the electron (owing to the idea of wave-particle duality).

But if the electron is actually merely in a "most likely region" (not necessarily "spherical", such as something like a p-orbital or d-orbital) and not the planetary Bohr type model, how does that affect the de Broglie calculation? Would De Broglie have come to the right conclusion without the assumption of a given "planetary type orbit" for the electron?

 

[The Gregorian]

Bah, there's an equation somewhere that works it out (drift velocity?) But I cant be bothered finding it, so searched your question in google:

Just google the question yourself and find all the relevant answers

Ninja edit: Look for "drift velocity" on wikipedia

... perhaps the title "Speed of electrons in an atom" was unclear. I'm not talking about electron's speed moving from one atom to another (as in an electrical wire). But, the speed at which electrons orbit around an atom.

Whatever the path of the orbit, most would agree that the electrons aren't sitting stationary.

The shapes of the electron's orbitals are derived from the square of the wave function describing the electron.

Rather, "we describe an electron's orbitals by the square of the wave function describing the electron." Math doesn't cause the electron to move, we base our math on the electron's observed movement.

I don't like mathemagicians hijacking science.

 

[Cabal]

Rather, "we describe an electron's orbitals by the square of the wave function describing the electron." Math doesn't cause the electron to move, we base our math on the electron's observed movement.

I don't like mathemagicians hijacking science.

You can still base the math on the Hamiltonian of the system and if done correctly, it will give out the forms of the orbitals. So you don't need to observe the movement to get the orbitals out. And no-one claimed that the math was causative.

Also, it's a probability region. It's not exactly "observed movement".

 

[Wiccan_Child]

I'm going to see if I can do this, intentionally without making the suggestion myself:

First: Relative to the speed of light, about how fast do electrons travel? Obviously, this will very depending on the element and which group of electrons.. but, if you were to generalize.

They don't move. They just sit there, cloud-like, in their 'orbital' until promoted or demoted. Their clouds sometimes wobble, giving rise to the Van der Waals force, but that's about it.
Their speed has nothing to do with element, or with 'group of electrons' (whatever that means).

They can move outside an atom, but their velocity could be anything from zero to lightspeed.

 

[canphys]

Hi,

The question, "how fast are electrons in atoms?" is a little ill-formed. In order to determine a particle's speed, you need to know how its position changes with time. The problem is that, as others have said, the uncertainty principle prevents you from simultaneously tracking how the position of a particle changes over time, which you would have to do in order to talk about its speed. Instead we describe the electrons as being spread out over space in clouds called orbitals. So asking "how fast is an electron" is sort of like asking "how fast is the ocean"; the question doesn't really make sense.

Since you mentioned the speed of light, you probably are thinking of some sort of application to relativity. In this case, a better question that you might ask is, "how much momentum do electrons in atoms have"? Momentum is well-defined in quantum mechanics, and given a wavefunction its expected ("average") value could in principle be calculated, but exactly what it is depends on the atom in question. I believe (don't quote me, though) that the outer electrons in atoms with more than about 30 electrons total have momenta high enough that relativity becomes important.

I should point out that you can't just naiively apply the formulas of special relativity on scales this tiny, though. Properly, you would need to use quantum field theory to describe such cases, which I'm afraid is mathematically a bit beyond my sophistication.

I should also point out that in some ways relativity is important even for very small atoms. Consider helium, which consists of two electrons orbiting a nucleus of two neutrons and two protons. Neutrons, protons, and electrons at rest have masses of 1.007276470, 1.008665012, and 0.00054858026 atomic mass units, respectively. Simply adding together the rest masses of two neutrons, two protons, and two electrons would give us 4.0322980 AMU, but the actual mass of helium is 4.00260 AMU. This is because the particles in helium are bound within wells of potential energy, and therefore have less energy than they would have if free. Special relativity tells us that mass and energy are equivalent, so this lower energy results in lower mass. So relativity (special relativity, at least) is not just an abstract theory of spacemen moving at impossible speeds; it explains the properties of everyday materials all around us. It is in part because of this wide applicability that special relativity enjoys such firm belief among physicists.

 

[The Gregorian]

The question, "how fast are electrons in atoms?" is a little ill-formed. In order to determine a particle's speed, you need to know how its position changes with time. The problem is that, as others have said, the uncertainty principle prevents you from simultaneously tracking how the position of a particle changes over time, which you would have to do in order to talk about its speed. Instead we describe the electrons as being spread out over space in clouds called orbitals. So asking "how fast is an electron" is sort of like asking "how fast is the ocean"; the question doesn't really make sense.

So, people have universally given up the concept that electrons "move?" They simply sit idle somewhere in the field as the protons/neutrons just sit in the nucleus. Oh well... without electrons moving in an atom, my illustration doesn't work.

I'm curious... what lead people away from the old model of electrons actually orbiting?

I should also point out that in some ways relativity is important even for very small atoms. Consider helium, which consists of two electrons orbiting a nucleus of two neutrons and two protons. Neutrons, protons, and electrons at rest have masses of 1.007276470, 1.008665012, and 0.00054858026 atomic mass units, respectively. Simply adding together the rest masses of two neutrons, two protons, and two electrons would give us 4.0322980 AMU, but the actual mass of helium is 4.00260 AMU. This is because the particles in helium are bound within wells of potential energy, and therefore have less energy than they would have if free. Special relativity tells us that mass and energy are equivalent, so this lower energy results in lower mass. So relativity (special relativity, at least) is not just an abstract theory of spacemen moving at impossible speeds; it explains the properties of everyday materials all around us. It is in part because of this wide applicability that special relativity enjoys such firm belief among physicists.

Energy and mass being correlatory is perfectly logical and observable. The idea that photons move through space while experiencing time as "stopped" due to a universal speed limit.... isn't. The concept of time dilation is purely based on "Well, we couldn't observe a universal constant of aether, therefore I suggest a new universal constant that makes less sense. And I'll attach it to a few realistic observations so that I can prove time dilation by proving that mass is energy."

 

[canphys]

Hi again,
It's not so much that we've given up on the idea that electrons "move" as that we've given up on the idea that electrons are particles. In a classical world, we could in principle measure where something is and how fast it is going to infinite accuracy. This would allow us to describe how that thing's position changes with time, and thus draw a nice trajectory for the particle. But the uncertainty principle tells us that the more accurately we measure position, the less accurately we can know momentum, and vice versa. This means that if I figure out where a particle is sitting right now (position), I can't have any idea about where it will be a few moments later (momentum). So we can't really draw trajectories for quantum particles.

What we can know is how probable it is that a measuring device will find the electron at a particular point in space. These "clouds" of probability are the orbitals we've been describing. If we try to measure the electron's position somewhere in the cloud, we have a certain chance (given by the wavefunction) of finding the electron. The problem is that this improvement in our knowledge of position results in great uncertainty in momentum, so a few moments later we'll have no idea where the electron went. You could think of it as the measuring device having momentarily transformed the electron from a cloud into a particle, but only momentarily. The gist of this is: sometimes it's fruitful to describe electrons as "particles" with "speed", but other times it isn't, and when the electrons are in atoms is one of the latter times.

We consider this model to be superior to the simple "pointlike electron orbiting a nucleus" model for a variety of reasons. Firstly, the quantum model gives much better predictions (of atomic binding energies and spectra), and is more in line with our wider understanding of nature. Secondly, the pointlike electron model imples that electrons are little spheres of charge, which combined with the fact that electrons have angular momentum would mean that they would have to be constantly rotating at speeds much greater than that of light. Thirdly, the quantum model is a necessary consequence of the uncertainty principle, which is an extremely firmly established principle of physics. Finally, experiments on free electrons, which involve such things as firing them through double slits, reveal that they have wave-like properties such as self-interference. There are almost certainly many more reasons, but this is all I can think of off the top of my head.

I'm not sure how time dilation came into this, to be honest, but it is also a firmly established physical phenomenon. It has both been directly observed, in experiments involving atomic clocks on planes, GPS satellites, muon decay, and particle accelerators, and is indirectly a necessary consequence of the postulates of relativity. Since mass-energy equivalence stems from these same postulates, accepting one but not the other is logically problematic.

If you think that belief in time dilation is unwarranted, I respect that belief and don't wish to get into a shouting match about it. However, I am a little curious about what it is that you find so unacceptable about this idea. What is it that you think time dilation is, precisely? Thanks for the time.

 

[Wiccan_Child]

So, people have universally given up the concept that electrons "move?" They simply sit idle somewhere in the field as the protons/neutrons just sit in the nucleus.

They move, but not in the nice 'whizzing round the atom' idea most people have. They generally just sit there as clouds of probabilty.

I'm curious... what lead people away from the old model of electrons actually orbiting?

Quantum mechanics.

Energy and mass being correlatory is perfectly logical and observable. The idea that photons move through space while experiencing time as "stopped" due to a universal speed limit.... isn't. The concept of time dilation is purely based on "Well, we couldn't observe a universal constant of aether, therefore I suggest a new universal constant that makes less sense. And I'll attach it to a few realistic observations so that I can prove time dilation by proving that mass is energy."

Time dilation is a direct consequence of special relativity. To reject time dilation, but accept mass-energy equivalence, is... silly. You may as well accept that gravity makes the Earth go round the Sun, but not that the Moon goes round the Earth.

 

[The Gregorian]

We consider this model to be superior to the simple "pointlike electron orbiting a nucleus" model for a variety of reasons. Firstly, the quantum model gives much better predictions (of atomic binding energies and spectra), and is more in line with our wider understanding of nature. Secondly, the pointlike electron model imples that electrons are little spheres of charge, which combined with the fact that electrons have angular momentum would mean that they would have to be constantly rotating at speeds much greater than that of light. Thirdly, the quantum model is a necessary consequence of the uncertainty principle, which is an extremely firmly established principle of physics. Finally, experiments on free electrons, which involve such things as firing them through double slits, reveal that they have wave-like properties such as self-interference. There are almost certainly many more reasons, but this is all I can think of off the top of my head.

I see, my understanding of electrons and their functions are entirely based on the old model, so I don't have a footing to knowledgably discuss the new explanation. It seems that electrons are treated more as direct energy than matter. Having features of both a particle and a wave similar to photons... makes sense. But I haven't studied these ideas, and from the looks of it, these ideas are still in development.

I'm not sure how time dilation came into this, to be honest, but it is also a firmly established physical phenomenon. It has both been directly observed, in experiments involving atomic clocks on planes, GPS satellites, muon decay, and particle accelerators, and is indirectly a necessary consequence of the postulates of relativity.

Indeed, we've seen the rate of atomic decay alter at high speeds (which explains the cesium clocks and muons... That doesn't mean the fabric of time has been altered... only that the atomic decay has slowed. Specifically, the Hafele–Keating experiment was just plain horribly done. And, yes, GPS satellites are accurate due to relativistic math, that doesn't prove the theory behind the math. But, what's been done in particle accelerators that indicate time dilation? I know they're looking for dark matter, extra dimensions, different forms of energy... but nothing that would indicate time dilation. Are you just referring to the fact that the closer to C the particles get, the more energy it takes to increase it's speed? Or is there actual evidence of time dilation?

Since mass-energy equivalence stems from these same postulates, accepting one but not the other is logically problematic.

I assume you're familiar with American Politics? Legislators write a nice, pretty bill that would help the population... But they attach parasite legislation onto the main bill in order to fatten their pocket. This parasite legislation becomes part of the original bill, and the house/congress must vote the whole thing up or down. Special relativity's the same way. The math's more accurate than Newton's and the concept the relationship between matter and energy was quite well done. ... But, the relationship between space and time was not.

What is it that you think time dilation is, precisely? Thanks for the time.

A universal constant. ... And the only universal constant that's proven to be constant is that universal constants are consistently wrong.

 

[Wiccan_Child]

A universal constant. ... And the only universal constant that's proven to be constant is that universal constants are consistently wrong.

Time dilation is where an observer sees a moving clock tick slower than the observer's personal watch. The only universal constant in special relativity is c. Indeed, the whole point is that time isn't constant.

 

[ArnautDaniel]

The "speed" of an electron goes anywhere from zero to whatever.

Yes, electrons can have a zero velocity (relative to the nucleus) and still be stably part of an atom.

Of course, quantum mechanically speaking, "speed" isn't exactly clearly defined.

 

[The Gregorian]

Time dilation is where an observer sees a moving clock tick slower than the observer's personal watch. The only universal constant in special relativity is c. Indeed, the whole point is that time isn't constant.

Time isn't a constant because it's not a "thing." It's an observation. I'm fine with the suggestion that certain things give the optical illusion of a clock moving relative to you moving faster or slower... or the temporal illusion that time seems to speed up or slow down. However, regardless of how long it seems to take to get from one point in history to another... reality happens, and it's always changing. An object can't move through space while paused in time (contrary to what einstein would have you believe about photons).

The simple fact that it moves shows that it "is currently in a place it didn't used to be." No matter what it "thinks" is happening... that's time moving. A rate of change in position can not alter the fact that time flows... whether you're moving at a rate of 186,000 miles/second or 88 MPH with 1.21 gigawatts powering your flux capacitor. Your body can experience reactions on a cellular or even atomic level... but whatever happens can not change "time" ... not because it's a "thing that flows constantly" ... but because it's not a "thing" at all. It's only an explanation for what point in history we're in.

Take the "clock on a jet" experiments, for example... at the end of a flight that lasted a certain amount of time... they came back with their clocks off by a bit. The fact that the clocks are off proves nothing more or less than the "clocks were off."

... if time is a substance one can alter... bring me a jar of time. I'll give you $20.

 

[canphys]

Re: electrons in atoms
The ideas involved here are indeed very strange (they seem a bit less so in their mathematical forms, but nevertheless are rather odd) but they actually were mostly worked out by the 30's. Contemporary quantum physics generally studies much smaller length scales.

Re: SR and particle accelerators
An accelerator is basically a machine that blasts subatomic particles around a track really, really fast (you probably knew that, but I'm just giving some background in case). In more powerful accelerators, the particles being blasted can reach speeds approaching that of light. These accelerators demonstrate the predictions of special relativity in three ways (that I can think of immediately):

1. The energy required to accelerate the particles increases with speed, which is not predicted by Newton (as you mentioned).
2. Some such accelerators work by flipping the direction of the electric field as particles move through a circular track. This works fine at lower speeds, but near the speed of light the particles begin to experience length contraction and time dilation. To account for this the shape of the track (because of length contraction) and the time between current flips (because of time dilation) must be changed at high speeds in ways special relativity predicts accurately.
3. Some particles are unstable: after a certain (usually very short) amount of time they transform into energy. The average "lifetime", as it is called, of such particles is generally very well known. When such particles are brought to speeds near that of light in particle accelerators, their lifetimes (in our frame of reference) become longer. The new lifetime is exactly that predicted by special relativity.

You mention that you accept caesium decays are slowed at high speeds. I wonder if the problem here is that we're using different definitions of the word, "time"? Perhaps you are imagining time as a sort of constant beat through the universe that objects conform to, more fundamental than clocks.

Special relativity doesn't really talk about time in this sense, which can't be detected anyway. What time dilation means is that events in moving reference frames happen more closely together (in time) than events in stationary ones (by "stationary frame" I mean "the frame of the observer"). You could, I suppose, think of this not as time slowing down but as events slowing down, but the important thing is that *all* events will slow down *exactly as if time had slowed down*. Since all events have slowed down, and the only way to measure the passage of time is by the frequency of events, this is equivalent from a physical point of view to time itself having slowed down.

So the clock on the plane does slow down, but so does the heartbeat of the pilot, so does the combustion of the engine fuel, and so do the thoughts of the passengers. Any experiment performed on the plane seems like it is going more slowly than usual to the people on the ground (the reverse is true for the people on the plane: the people on the ground seem to be going more slowly, until the plane slows down and the reference frames realign).

You might imagine that there is some sort of absolute time, separate from the frequencies of events in the universe. Such a time might exist, for instance in the minds of supernatural beings, but noone in the natural universe will ever notice. The same is true of the aether: sure, it could be there for the angels to see, but we'll never know. This is what physicists mean when they deny the existence of something. In this sense, absolute time does not exist.