# Between the Quantum Orbitals

Discussion in 'Chemistry' started by AndresKiani, Jan 12, 2014.

1. ### AndresKianiRegistered Member

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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, though would also have to be relatively the same to stay at the same energy constant of "h". The "v" velocity variable change would occur slightly as the electron moves from higher orbital, causing it to move generally faster than it otherwise would in a lower energy orbital.

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...

Last edited: Jan 12, 2014

3. ### exchemistValued Senior Member

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I don't think this is right. I think you may have fallen victim to the untrue notion that electrons make the transition between stationary states "instantaneously". But they don't. The mechanism for transition, and absorption or emission of the appropriate quantum of energy as a photon, is described by the time-dependent Schodinger equation. It is a fast process but not instantaneous.

In any case, since electrons do not have zero rest mass, relativity precludes them travelling at the speed of light, doesn't it?

5. ### AndresKianiRegistered Member

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If they are not moving at the speed of light than they must be moving something rather close to the speed of the light, meaning that their quickness and randomness makes them impossible to observe. Instead we can say where they will likely be that is our best observation, and since they don't spend enough time between the orbitals we can never really say that they are there with any assurance.

A lot of the electron equations with spectroscopy involve the electron moving at speeds close to 3.00 x 10 ^ 8 m/s.

7. ### AndresKianiRegistered Member

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I'm not educated to that point as far as the time dependent formula. Please explain and how it would relate.

8. ### exchemistValued Senior Member

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There's a summary of both time-dependent and time-independent versions here: http://en.wikipedia.org/wiki/Schrödinger_equation

The time-indpependent version describes stationary states (analogous to standing waves), for example the orbitals in an atom. But the time-dependent one is the more general version and is needed to model things such as the process that occurs when an electron couples to the electric vector of a photon during absorption or stimulated emission of radiation. How it does this is the subject of fairly advanced quantum chemistry, which I studied during my degree but this was forty years ago, so I'm pretty rusty on the details. It is not a short explanation, mathematically.

9. ### exchemistValued Senior Member

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Certainly quantum indeterminacy has a lot to do with it. But I'd be very wary of claiming that electrons travel close to light speed. If they did, they would start behaving relativistically, and a different, more complicated, version of QM would then be needed to describe their behaviour. The version we generally use for atomic processes is not relativistic, which implies the speeds are not high enough for such effects to be significant.

10. ### originHeading towards oblivionValued Senior Member

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Electrons are not like little balls orbiting the nucleus in clearly defined descrete orbit. The orbital is a very fuzzy area. The highest probablility is that the elelctron will be in a certain well defined orbital but there is a nonzero probablility that the electron could be found anywhere around the atom. That of course means that the electron is sometimes between the defined orbitals. Electrons can be more accurately described as standing waves when discussing the orbitals. One of the only times the point like aspects of electrons in an atom are clearly seen is when a photon is absorbed or emitted by a single electron and the electron jumps to different orbital.

11. ### wellwisherBannedBanned

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There is a branch of chemistry called relativistic quantum chemistry. This branch is involved in effects, common to larger atoms, where the electrons can reach speeds closer to the speed of light, where relativistic effects become more important.

The color of the metal gold, which is yellow, is due to a relativistic electron effect causing a time shift to all reflected light. Another such relativistic quantum effect are the electrons ending up between the orbitals defined by the Schrödinger equation of quantum mechanics. These observed changes in orbital position are due to a relativistic electron mass increase causing the heavier electrons to get closer. This is observed in the lab and is added as an adjustment to the Schrödinger equation.

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13. ### exchemistValued Senior Member

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Broadly yes, though to be strictly accurate, the "orbital" is defined as the space an electron in that particular stationary state can occupy, so it can't be somewhere else than in that orbital. With some orbitals there are no-go places, the nodes, where the electron probability is zero. For example, in orbitals with azimuthal quantum number (l) >0, i.e. p, d, f, etc orbitals, there are nodal planes, passing through the nucleus, where the electron CANNOT be.

This has the consequence that p, d,f etc electrons are less exposed to the full nuclear charge than electrons in s orbitals (for which l=0). This affects the way the energy levels of different orbitals respond to increasing nuclear charge, as you go along the Periodic Table. Shielding and all that.

14. ### TrippyALEA IACTA ESTStaff Member

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First thing to understand: Orbitals of electrons are not like planetary orbits. Moving from an s orbital to a p orbital is not like moving from earth to mars. It's more like moving from a G to an A.
Second thing to undestand: Many of the orbitals of an atom overlap. This is (part of) what makes hybridization of orbitals possible. s orbitals overlap with all orbitals, p orbitals overlap with some of the d prbitals (specifically the ones that point along the axes eg $3d_{z^2}$ and $3d_{x^2-y^2}$ and some of the f orbitals (again, the ones that point along the axes). In fact, the fact that it's possible for orbitals to occupy the same physical space becomes important in co-ordination chemistry.
Third thing to understand: When you see images such as this one:

Which shows the shapes of all of the f orbitals, the surface your looking at isn't some kind of physical boundary. There's no Gandalf standing there with his sword and staff saying to the electron "You shall not pass!" or a sign saying "Turn back". There's nothing. The surface depicted is an artificial construct. It's a contour. It depicts some probability - usually 90% IIRC of finding an electron that is in that orbital within that space. The electrons can pass beyond that surface trivially. Representations such as this one:

Are more accurate, they represent the probability distribution as a density function, but, they're not as cool to look at, and in some regards they don't convey. An electron in any given orbit can be found nearly anywhere in the atom, it's just that the probability of finding it in some locations is far higher than the probability of finding it in other locations. There are areas where the electron can not go, where there is zero probability of it being find there. These are nodes, they're like the nodes on a guitar string, or in the youtube video I will show you.
Consider, for, example in this video showing Standing Waves on a 2D surface. Electrons orbitals are, as I recall, 3d standing waves. Electrons can only jump from standing wave to standing wave, and there is nowhere to jump to between standing waves, much like in this video. That's not a coindence either - remember, the energy of a wave is proportional to the frequency of the wave. Note that in videos such as these, the salt collects in the nodes, but an electron is more like the board that is vibrating than the salt. If you considered the volume occupied by the plane as it vibrates, then those areas where the vibration is greatest is where you're most likely to encounter the board (or electron) and the areas where the salt is collecting are the nodes, where the probability is the least.
The final thing to understand: When people talk about 'between electron orbitals' they're usually talking about the energy levels:

There is no 'between' energy levels. Either an electron has the energy to make the transition to the next level, or it does not. This is why we observe discrete lines in emission spectra (except continuum spectra):