Why do electrons revolve so fast?

[kaushik_s]

Hi,

Recently, I was thinking why electrons move so fast that we cannot even predict their exact position?

I came up with an answer that electrons appear to move faster because their radius of revolution around the nucleus is very small compared to us.
I was thinking if we could somehow shrink ourself to the size of an atom, then the distance between the nucleus and electron would be bigger compared to us. Then, would the electrons seem to revolve slower?

Is this the reason why electrons seem to move so fast around the nucleus?

To make it more understandable I have an example:-
The Earth seems to move rather slowly around the sun to us even though it has a large velocity. I think this is because we are very small compared to its orbit's radius.
If we suddenly grew to a size so big that the solar system would appear as an atom to us, then will the Earth appear to move so fast that we will not be able to calculate its position as well?

please help me with this. If there is anything wrong with my question or answer, then please correct me. Give me suggestions on how to modify my answer.

It will be helpful if I get the answers soon. Thank you.

 

[nitsuj]

Is this the reason ['cause they're so tiny compared to us]
why electrons seem to move so fast around the nucleus?

No, they are actually moving fast.

When I run it looks like I'm running really fast, but that's just 'cause of my little kickers. I don't cover much distance over x time.

 

[kaushik_s]

HI, that's why I have given the example.
electron travels fast, but what I mean to say is, because it's orbital radius is small it seems to travel much faster then its original velocity.

 

[Steger]

Hi,

Recently, I was thinking why electrons move so fast that we cannot even predict their exact position?

I came up with an answer that electrons appear to move faster because their radius of revolution around the nucleus is very small compared to us.
I was thinking if we could somehow shrink ourself to the size of an atom, then the distance between the nucleus and electron would be bigger compared to us. Then, would the electrons seem to revolve slower?

Is this the reason why electrons seem to move so fast around the nucleus?

To make it more understandable I have an example:-
The Earth seems to move rather slowly around the sun to us even though it has a large velocity. I think this is because we are very small compared to its orbit's radius.
If we suddenly grew to a size so big that the solar system would appear as an atom to us, then will the Earth appear to move so fast that we will not be able to calculate its position as well?

please help me with this. If there is anything wrong with my question or answer, then please correct me. Give me suggestions on how to modify my answer.

It will be helpful if I get the answers soon. Thank you.

The fact that electrons don't have a set position is due to quantum mechanics, it is not that WE don't know its position it's that IT doesn't know its position. I'm afraid it has nothing to do with it "zooming around super fast". It's a fundamental aspect of the quantum world of all particles. The most common layman explanation is to point to Heisenberg's uncertainty principle but in reality this indeterminacy of both position and momentum is a general property of all waves (quantum or otherwise).

 

[kaushik_s]

Hi,
Thanks for the reply.
I did not know that.
If you don't mind can u explain how the position of an electron depends on quantum mechanics in detail.
thanks in advance.

 

[nitsuj]

HI, that's why I have given the example.
electron travels fast, but what I mean to say is, because it's orbital radius is small it seems to travel much faster then its original velocity.

Sounds fine to me, because of the qualifier "seems to". Just like I seem to be running fast because of my little kickers.

But like Steger says, position & momentum of the orbiting electron cannot be known simultaneously.

wiki has an entry on it that is easy to understand (the first paragraphs).

Below is a Max Born quote from that wiki page that I think sums it up very well;

"..To measure space coordinates and instants of time, rigid measuring rods and clocks are required. On the other hand, to measure momenta and energies, devices are necessary with movable parts to absorb the impact of the test object and to indicate the size of its momentum. Paying regard to the fact that quantum mechanics is competent for dealing with the interaction of object and apparatus, it is seen that no arrangement is possible that will fulfill both requirements simultaneously... [Max Born]"

But am not sure why Born makes a distrinction between "devices with movable parts" & measure of time/length. And goes on to mention that "devices with movable parts" is a non issue for QM calculations.

 

[kaushik_s]

Hi,
Nitsuj, thanks for the reply.
I was a little confused when I read Born's paragraph. Anyway, do you think my way of thinking is right. How can I improve it.
What do you think about Steger's reply?

 

[nitsuj]

Hi,
Nitsuj, thanks for the reply.
I was a little confused when I read Born's paragraph. Anyway, do you think my way of thinking is right. How can I improve it.
What do you think about Steger's reply?

The Max Born quote may be more clear if you look into relativity of simultaniety & how length / time are defined.

I think your thinking is fine from what I see, but I'm no authority or particularly bright so...

Speed is calculated by measuring length & time. We can get a sense of speed by noticing comparative motion. That "sense" of speed is not derived from a measure of length / time, but rather from comparative motion. As noticed when traveling in a car, the road seems to "pass by" at a higher rate than objects a farther distance away. This is just field of view & angles, and not a calculated speed.

I have a little remote control car that seems pretty fast in my room, I took it outside the other day, it's actually stupid slow. In both cases it's max speed is about 15mph.

Steger's reply is right. They answered both your questions in the first post. This is just semantics, I would preffer "the electrons position is not definitive from a physical perspective. Measuring the (exact) position makes it a definitive physical reality, but at the cost knowing the (exact) momentum."

 

[Khashishi]

Speed has an absolute scale though. The speed of light in vacuum, c, is the same for all observers, and it won't scale down when you are looking at something smaller, unless you also scale down time.

 

[nitsuj]

Speed has no "scale", it is relative. In that sense c is not a "speed", to fair it is an invariant speed, a consiquence of length/time (i.e. speed) not being absolute.

 

[Naty1]

Kaushik:
I think most of what is posted above is misleading... elementary at best.

Steger has the correct idea that an electron is a quantum mechanical entity, a wave that exhibits some particle-like behavior. If you instead think of an electron as merely a particle, you'll be baffled by it's behavior...like 'why don't electrons collapse into the nucleus'...see below...

In the following references, for example, you'll not see discussions about 'how fast the electron is moving'...[I don't think]... that's a remnant from the now outdated Bohr model of the atom with particles orbiting a nucleus...which is also discussed ...

See the first several paragraphs here: an electron is NOT a particle...it's a wave with particle like characteristics...

http://en.wikipedia.org/wiki/Atomic_orbital

further down that article I would note for you:

The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves.

The electrons retain particle like-properties such as: each wave state has the same electrical charge as the electron particle. Each wave state has a single discrete spin (spin up or spin down).

Also see the opening discussion here for a 'particle view' of the electron:

http://en.wikipedia.org/wiki/Electron

but note the Quantum Properties further down:

[What the following implies is that the older classical view of electrons, as particles with speeds, does NOT account for their observed properties...the observed properties, experimentally verified, derive from quantum [wave] theory.]

The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ(r1, r2) = −ψ(r2, r1), where the variables r1 and r2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. Bosons, such as the photon, have symmetric wave functions instead.[77]

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.

That boldface is what explains why the old Bohr model is incorrect...and underlies the Pauli exclusion principle...

 

[nitsuj]

Kaushik:
I think most of what is posted above is misleading... elementary at best.

Steger has the correct idea that an electron is a quantum mechanical entity, a wave that exhibits some particle-like behavior. If you instead think of an electron as merely a particle, you'll be baffled by it's behavior...like 'why don't electrons collapse into the nucleus'...see below...

In the following references, for example, you'll not see discussions about 'how fast the electron is moving'...[I don't think]... that's a remnant from the now outdated Bohr model of the atom with particles orbiting a nucleus...which is also discussed ...

See the first several paragraphs here: an electron is NOT a particle...it's a wave with particle like characteristics...

http://en.wikipedia.org/wiki/Atomic_orbital

further down that article I would note for you:






Also see the opening discussion here for a 'particle view' of the electron:

http://en.wikipedia.org/wiki/Electron

but note the Quantum Properties further down:

[What the following implies is that the older classical view of electrons, as particles with speeds, does NOT account for their observed properties...the observed properties, experimentally verified, derive from quantum [wave] theory.]




That boldface is what explains why the old Bohr model is incorrect...and underlies the Pauli exclusion principle...

Well call out the misleading information please. I don't think anything I posted is misleading, and always hope that if I do it'll be corrected.

Of course my response is "elementary". The op had asked if an electron is moving so fast because it's so small compared to people, and that if we were it's size would it be slower. Yea, bring up why "the old Bohr model is incorrect...and underlies the Pauli exclusion principle... " that'll clear the air on that subject.

The nuances of speed is the more urgent issue in the OP. Not the nuances of the uncertainty principle.

Though that is a nicely developed intellectual muscle you have, thanks for the demonstration.

 

[kaushik_s]

Hi,
Thanks for the reply Naty 1. It was informative.
But I think nitsuj has understood my question and idea more clearly.
As he has said, Can you please make your answer more clear so as to answer my question more directly.

Thanks in advance.

 

[Dale]

Speed has an absolute scale though. The speed of light in vacuum, c, is the same for all observers, and it won't scale down when you are looking at something smaller, unless you also scale down time.

Speed has no "scale", it is relative. In that sense c is not a "speed", to fair it is an invariant speed, a consiquence of length/time (i.e. speed) not being absolute.

Having a scale and being relative are different properties. Speed is relative (the speed of an object changes in different frames) and it also has a fixed scale (the speed of light is the same in different frames). Whether you want to call it a fixed scale or an absolute scale or just a scale is a matter of taste, but having a scale and being relative are not mutually exclusive.

 

[kaushik_s]

Hi,
can somebody please tell me weather my idea is correct or wrong.
replies at the earliest is expected.
Thank You.

 

[Dale]

I don't think it is correct. You are basically looking at angular velocity and tangential velocity and noting that even a large tangential velocity can result in a small angular velocity if the radius is astronomically large. An electrons tangential velocity can be very large, and it's angular velocity can also be very large.

 

[Naty1]

...why electrons move so fast that we cannot even predict their exact position?

Hi, can somebody please tell me weather my idea is correct or wrong.

It is not accurate as I already posted. I agree with Dalespam. The 'earth orbiting around the sun' is NOT the proper way to understand electron ORBITALS [not orbits]. That's why I mentioned the now discredited Bohr model of the atom.

I was previously thinking about replying in terms of V = wr, then decided why bother since that reinforces the original perception which I took to be about electron behavior rather than relativistic velocity considerations.

For anyone who wants to compare the OP perspective with current physics, I doubt I can do any better than the post and links I previously made.

To say what I already posted another way: We cannot predict the exact position of an electron because it does not have one. Even a slow moving free electron does not have an exact position. Even if you confine an electron in a box, you still can't measure an exact position...confinement acutally can increase the position uncertainty.

As far as the op question about

...then will the Earth appear to move so fast that we will not be able to calculate its position as well?
QUOTE

yes it will APPEAR to move faster, visually: stand right next to a train passing by and it SEEMS to be moving really fast; viewed from a mile away, not so much. But a proper experimental test of the speed from those two different locations will provide the same result of the speed.

 

[nitsuj]

Having a scale and being relative are different properties. Speed is relative (the speed of an object changes in different frames) and it also has a fixed scale (the speed of light is the same in different frames). Whether you want to call it a fixed scale or an absolute scale or just a scale is a matter of taste, but having a scale and being relative are not mutually exclusive.

Let me give the context of why I say there is no "scale" for speed. Comparatively, I think there is no "scale". Individually clearly there is a "scale". That is the scale is arbitrarily "placed".

At any time I'm okay to say I'm not moving, in effect re-coordinating my measure of length / time comparatively, in that sense the "scale" is not applicable universally.

That being said individually, as in a single FoR there is a speed "scale" of 0 - >c.

You said;
"...but having a scale and being relative are not mutually exclusive." Because "Having a scale and being relative are different properties."

That is a much much better way to put it.

Especially if "scale" is defined here as measure of proper time / length, and specifically not the calculated speed. Similar the OPs confusion regarding what speed looks like and what speed is measured. (specifically it's frequency of events or "happenings" confused with measured speed)

I did exclude the fact there is a scale of 0-c for every FoR (due to how dimensions are measured), and focused on the fact it can be applied to any object (considering relative motion).

So in that sense, from the perspective of SR, I see speed as an "appearance" when ...Universally Speaking (woo hoo RHCP!), Both from a visual & measurement perspective, but not from a proper measurement perspective.

Not specific to your post Dalespam, but telling the OP that the electron is not an object of position, and describing it as having a speed is pretty confusing. Stick to one physical reality, from there grow it into why moving so fast (having low mass) makes exact predictions probabilities. (sorry for the poor choice of words, think the meaning is still there)

 

[Dale]

Let me give the context of why I say there is no "scale" for speed. Comparatively, I think there is no "scale". Individually clearly there is a "scale". That is the scale is arbitrarily "placed".

At any time I'm okay to say I'm not moving, in effect re-coordinating my measure of length / time comparatively, in that sense the "scale" is not applicable universally.

That being said individually, as in a single FoR there is a speed "scale" of 0 - >c.

OK, I can see that.

Not specific to your post Dalespam, but telling the OP that the electron is not an object of position, and describing it as having a speed is pretty confusing. Stick to one physical reality, from there grow it into why moving so fast (having low mass) makes exact predictions probabilities. (sorry for the poor choice of words, think the meaning is still there)

You can measure all sorts of properties about an electron, speed, position, distance, angular velocity, ... (all relative to the nucleus). For each one of those properties you can construct an operator and apply it to the wavefunction to get an expectation. The HUP limits the uncertainty in certain pairs of these operators, but doesn't mean that we cannot get expectation values for them. In certain orbitals the expectation value of the speed can be quite high. There is nothing contradictory in saying that and also saying that the uncertainty in the position is quite high.

 

[nitsuj]

OK, I can see that.

You can measure all sorts of properties about an electron, speed, position, distance, angular velocity, ... (all relative to the nucleus). For each one of those properties you can construct an operator and apply it to the wavefunction to get an expectation. The HUP limits the uncertainty in certain pairs of these operators, but doesn't mean that we cannot get expectation values for them. In certain orbitals the expectation value of the speed can be quite high. There is nothing contradictory in saying that and also saying that the uncertainty in the position is quite high.

I am starting to wonder why physics discounts the dichotomy of appearance between a wave & a particle. In what sense is it not a point particle, that appears as a wave when "stretched" across a distance when in motion, in effect changing dimensional shape into something measured as space like, where the position of the "end" of the wave is simultaneous with the position of the "front" of the wave. Going even more arbitrary, a particle looks like a wave if the time "component" is "removed".

Why is the way we measure time / length carried over into observations of particle(time)/waves(length) when the technique is accurate but lacks a determinate prediction?

I ask this because the measure of time / length is defined by c, but [STRIKE]fails[/STRIKE] works differently in microscopic observations. This makes me wonder if c is the "probability". More clear if I throw it in a postulate, the one way speed of c (keep in mind time/length is defined by c) is a probability calculated by whatever and is an accurate prediction of the probability, and it's always the same. the two way speed is exact for the same reasoning as the mechanics of "entanglement".

I'll have to check out Naty1's links, I'd guess it'd cover these elementary misunderstandings of mine.