Between the Quantum Orbitals

[AndresKiani]

I think the reason why scientist have never been able to observe an electron between the quantum orbitals is because, electrons are possible moving as fast as light itself. We assume that electrons and light photons have many same qualities. Well why can't we assume that electrons are also moving at the speed of light?

In the de Borglie's wavelength formula w = h/mv Velocity is given as a variable, though can't we assume that since the properties of both an electron and photon can be measured with the same energy constant. "h" = 6.626 x 10 ^-34 J per S... That they may essentially have the same velocity at around 3.00 x 10^8 m/s??? The only difference maybe that the "m" mass is lighter or heavier for an electron.

Either way, I believe that electrons are never observed in between orbitals, not because they never cross over these orbitals physically. But, maybe because electrons are moving at the speed of light, and that at the speed of light it is impossible (never been done) to both observe its position and its movement. So, when we are looking at it moving from one orbital to another, we see that it "jumped" orbitals, but if we do try to observe it we always find it in either one orbital and never in between.

Let me know what you guys think...

Edited January 12, 2014 by AndresKiani

[ajb]

It is much more subtle than that.

 

We could can think about quantum mechanics in terms of path integrals and this would tell us that the electrons take all possible paths from one orbital to another. In this sense they do travel in the void between the orbitals, but we will never actually see this. We can only see the orbitals due to the absorption or emission of a photon which corresponds to the energy difference of the orbitals. These orbitals represent the eigenstates of the Hamiltonian and we will only ever see an electron in one of these orbitals.

 

The motto with quantum mechanics is "everything happens until you look at it!"

Edited January 12, 2014 by ajb

[AndresKiani]

Well put.

 

So, even though we don't observe it in between orbitals we still assume that it crosses over, but since it doesn't spend enough time their we can never really tell how it crossed over. Though because the electron is spending most of its time in the "quantized" orbitals, is the reason we can assume its there with better assurance than that it was ever in-between the orbitals.

Edited January 12, 2014 by AndresKiani

[ajb]

When the energy levels increase wouldn't that generally mean that the electron is moving faster that it would otherwise move in a lower orbital?

You could do a heuristic calculation to see this, but the notion of velocity in this example is rather a classical one and not so clear in quantum theory. I am not sure what the semi-classical heuristic calculation would really tell you.

[AndresKiani]

Lol I think you helped me understand Quantum Mechanics better than any other professor or text book, ever could, with just that statement.. Lol.

[ajb]

Your welcome. You just have to be very careful applying classical ideas to quantum systems. Sometimes it can be a useful thing to do, especial if you want to see how the results differ from the classical theory or you just want some hand-waving argument.

[AndresKiani]

Yeah.. though I like to think and give out my thought on things specially when I don't understand them as well as others, because it helps when I'm corrected I can see where I was wrong about my thought process.

[Sensei]

Lol I think you helped me understand Quantum Mechanics better than any other professor or text book, ever could, with just that statement.. Lol.

 

During measurement at macro scale we are changing state of measured object as well.

 

But this change is so meaningless small, that nobody ever think about it..

 

f.e. you want to measure temperature of water putting normal Hg thermometer to it.

Accelerated molecules of water are colliding with Hg molecules, giving Hg energy, and are loosing energy by them self.

Hg is changing volume, and we are reading new Hg volume from scale.

Hg is never returning energy that it took from water back to water!

So water permanently lost this energy - by measurement we changed state of measured object. Made water a bit colder.

 

Measurement at quantum scale is so dramatic it changes state of measured particle permanently.

[Enthalpy]

I don't really grasp what you mean by "between orbitals", since they overlap so much. And as the electron location is centered on the nucleus, it doesn't change its position when it is an orbital or an other - only its shape and size.

 

I don't understand "we don't observe the electron between orbitals". A transition is a weighed sum of both orbitals; it is as much or little observable as the initial or final orbital. The only difference of the wavefunction during the transition is that it is not stationary.

 

What shall mean: electrons crossing quickly between orbitals? Some transitions take millions of years to proceeed.

 

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It might possibly be that you imagine a point electron on an orbital. This would mislead you. An electron is a wave (though this wave has quantized properties); trapped around a nucleus, the electron in a stationary state is an orbital.

[AndresKiani]

I don't really grasp what you mean by "between orbitals", since they overlap so much. And as the electron location is centered on the nucleus, it doesn't change its position when it is an orbital or an other - only its shape and size.

 

I don't understand "we don't observe the electron between orbitals". A transition is a weighed sum of both orbitals; it is as much or little observable as the initial or final orbital. The only difference of the wavefunction during the transition is that it is not stationary.

 

What shall mean: electrons crossing quickly between orbitals? Some transitions take millions of years to proceeed.

 

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It might possibly be that you imagine a point electron on an orbital. This would mislead you. An electron is a wave (though this wave has quantized properties); trapped around a nucleus, the electron in a stationary state is an orbital.

*Let me remind you that I'm just trying to learn, so excuse me if I sound like I'm arguing, it comes off bad when your not actually sitting face to face with the other person*

 

 

Let me ask you something though... When an electron absorbs this energy, it must than be moving faster (which is what we call excited state) am I right or wrong? Causing the electron move to a higher energy orbital.. Here the electron cannot last very long because it is not a stable configuration, so it falls back down to the lower energy orbital releasing its energy..

 

I've read that this occurs almost instantaneously. If this is occurring instantaneously(absorbing and releasing energy)... Why would you say some of these transitions take millions of years?

 

So the whole process of absorbing and releasing energy is so instantaneous wouldn't that mean that the little time it spends between the two orbitals is not long at all if it spends 99 percent of its time in the quantum orbitals, and barely anytime in between, meaning within that time that we call instaneous time, it spends less than 1% of that time in between the orbitals.

Edited January 13, 2014 by AndresKiani

[ajb]

I don't really grasp what you mean by "between orbitals", since they overlap so much.

For the sake of argument here, let us assume we do not have any bands, are dealing with simple hydrogen-like atoms and we will work with the principal quantum number only.

 

I don't understand "we don't observe the electron between orbitals".

We infer from the absorption or emission of a photon that the electrons only sit in these orbitals, which for us will only be classified by energy.

 

 

It might possibly be that you imagine a point electron on an orbital. This would mislead you.

This I think is the root of a lot of misunderstanding of quantum mechanics. To some level you can think of an electron more like a point sometimes, but ultimately thinking in terms of waves is needed.

[Enthalpy]

We infer from the absorption or emission of a photon that the electrons only sit in these orbitals, which for us will only be classified by energy.

Any weighed sum of orbitals is a valid wave function for the electron. The orbitals are just the wave functions which don't evolve over time, that is which have one well-defined energy.

 

If one measures an energy - which is the case with the slow absorption or emission of a photon - then the wave function reduces, because of the measure, to the energy eigenfunctions which are the orbitals. But if one measures something else, for instance the position of the electron, then the wave function will reduce its size instead of its energy choice; then one can observe a wave function which is not an orbital.

 

Because most orbitals are separated by more energy than the usual thermal energy, electrons group to the lower energy states, so usually they have a fixed energy.

I don't really grasp what you mean by "between orbitals", since they overlap so much. And as the electron location is centered on the nucleus, it doesn't change its position when it is an orbital or an other - only its shape and size.

Orbitals have a single energy in an isolated atom; by "overlap" I mean that different orbitals of a single atom give a good presence probability to the electron at locations that are widely the same.

 

For instance the 1s orbital has its maximum density (per volume unit, not per radius unit) at the nucleus and decreases regularly with the distance; we can say arbitrarily it's positive everywhere. The 2s orbital has also its maximum density at the nucleus but decreases, goes through zero and changes its sign. Both have a significant density at the same locations - they only need that their product, summed over space, is zero, but they can overlap.

When an electron absorbs this energy, it must than be moving faster (which is what we call excited state) am I right or wrong? Causing the electron move to a higher energy orbital...

The absorbed energy puts the electron farther from the attracting nucleus as a mean distance. In the excited state, the electron's kinetic energy is smaller.

 

Orbitals don't look like planetary orbits; nice illustrations are available there (click on orbital names at left):

http://winter.group.shef.ac.uk/orbitron/

but at least for attraction versus kinetic energy, they work the same: more kinetic energy for lower orbits.

[in] a higher energy orbital.. Here the electron cannot last very long because it is not a stable configuration, so it falls back down to the lower energy orbital releasing its energy..

 

I've read that this occurs almost instantaneously.

The transition from one orbital to a other takes a measureable and measured time ranging from femtoseconds to millions of years. It depends on both orbitals. During the transition, the electron's wave function is a weighed sum of both orbitals, with proportion evolving over time. If this sum lets the electric charge wobble a lot, then the emission (or absorption) of the photon is efficient, and the transition is quick, like nanoseconds. Some sums of orbitals don't let the charge wobble, and then the emission is inefficient; this is called a "forbidden transition", which lasts very long - competing transitions generally take over.

 

An equivalent description compares some quantum numbers of two orbitals with the quantum numbers a photon can have to tell if the transition is permitted, but this is the same as checking for a dipolar wobble which is an efficient light emitter.

 

Orbitals don't wobble at all. Their shape (the position, size, shape of the electron) is constant over time, and the charge doesn't radiate.

 

External factors can influence the duration of the transition. A laser cavity shortens it. As opposed, an antiresonant cavity that forbids the emission of a photon can conserve an excited state for longer; this was used in some designs. Also, shocks among molecules reduce the time during which the photon can be emitted with a consistent phase; this time between collisions uses to be less than millions of years.

 

The duration of the transition defines the duration of the emitted light, which in turn defines the precision of its frequency or wavelength.

 

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If you measure the energy of the electron during the transition, you will find it in one orbital or in the other, because the energy measure lets it chose, so only the probability to find it as the old or new orbital evolves, and observing this probability needs several atoms or successive measures.

 

A different limit is that it takes time to measure an energy accurately.

[swansont]

 

External factors can influence the duration of the transition. A laser cavity shortens it. As opposed, an antiresonant cavity that forbids the emission of a photon can conserve an excited state for longer; this was used in some designs. Also, shocks among molecules reduce the time during which the photon can be emitted with a consistent phase; this time between collisions uses to be less than millions of years.

 

The duration of the transition defines the duration of the emitted light, which in turn defines the precision of its frequency or wavelength.

 

 

There's also the curiosity (the Quantum Zeno/Xeno Effect) that if you excite an atom and the check to see that it's excited (by seeing that it's not back in the original state), you basically reset the decay clock, and can keep it in the excited state far longer than it would naturally be there.

[ajb]

If one measures an energy - which is the case with the slow absorption or emission of a photon - then the wave function reduces, because of the measure, to the energy eigenfunctions which are the orbitals. But if one measures something else, for instance the position of the electron, then the wave function will reduce its size instead of its energy choice; then one can observe a wave function which is not an orbital.

Right, if you try to keep track of the electrons position you will completely lose its energy. If we keep track of the energy then we lose its position.

[Sensei]

Right, if you try to keep track of the electrons position you will completely lose its energy. If we keep track of the energy then we lose its position.

 

The same is with any macroscopic object - you have to stop it from moving to tell exactly where it is (with great precision f.e. 1 mm or better), and then we know that its momentum is 0 and position is exact.

Edited January 14, 2014 by Sensei