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# Relativistic Effects in Chemistry

Posted January 14, 2016 10:24 AM by Bayes

Atomic Orbital Contraction

Atoms can get very large and electrons in the innermost orbitals of a large atom can see a very large charge. As a result, these electrons orbit the atomic nucleus very quickly. So quickly in fact that they achieve meaningful fractions of the speed of light.

As a result, relativistic effects come into play. Chemists and Physicists discovered this soon after the formulation of quantum mechanics in the early 20th century. The result is that, for example, the 1S orbital of a Uranium atom has a smaller radius than would be expected without considering relativistic effects. In other words, relativistic effects have led to atomic orbital contraction.

I recently found a neat video that explains this concept fairly concisely and wanted to share it. Usually when we think of relativity, or at least when I do, we tend to think about astrophysics, not chemistry, and yet it plays an important role in chemistry. It's nice to see it has more of an impact in the world around us than we realize.

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Guru

Join Date: Jan 2006
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#1

### Re: Relativistic Effects in Chemistry

01/15/2016 9:31 AM

From the link it seems to me that the electron at 2/3rds C in the example would fly off at a tangent due to centrifugal force, to a higher orbit and slow down, or if the force of attraction of the atom prevents this, then why does it not drop to a lower orbit and speed up - to C (or more?).

My ignorance speaking....

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The Engineer

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#2
In reply to #1

### Re: Relativistic Effects in Chemistry

01/15/2016 9:55 AM

I think those are reasonable questions. The reason why the electron doesn't fly off (or go to a higher orbit and slow down) is because the electromagnetic force between the nucleus and the electron is very strong. A Uranium nucleus has 92 protons, so a charge of +92. That's a very, very strong positive charge from the point of view of the inner orbital electrons and makes it very difficult for the electrons to move away from the nucleus.

So then why don't the electrons just fall into the nucleus (or to a closer, faster orbit)? Well, it turns out because of the Uncertainty Principle of quantum mechanics, when you do the calculations for the structure of atoms, that atoms always have a minimum orbital distance (ground state). Another QM consequence is that the electron orbitals are discrete and limited to two electrons per orbit (1 spin up and 1 spin down).

So imagine you have just a bare Uranium (or Nitrogen or whatever) nucleus and started adding electrons one by one. The first electron would go to the 1S orbital (ground state) and so would the second one. The third electron would stop slightly farther out at the 2S orbital as would the 4th electron (remember 2 electrons per orbital). Thus the orbitals would gradually fill until you reached (in the case of Uranium) 92 electrons. On the 93 electron there would be no attractive force and it would just fly off somewhere else.

The cool thing about this post is that when you do the calculations for the inner orbitals (1S, 2S, etc.), if you don't take into account relativistic effects, you get the wrong orbital distance. In other words, electrons are moving so fast that they have measurable relativistic effects. Cool!

Guru

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#3
In reply to #2

### Re: Relativistic Effects in Chemistry

01/16/2016 8:38 AM

Thanks for your detailed reply. It answers my immediate question but at my novice level it generates so many additional questions it would be unfair of me to make demands on your time to answer them.

But as an observation of the logic of your OP it seems as though taking account of relativistic speed comes as a surprise - whereas to my simple engineering mind the conservation of momentum of a spinning object is well known where angular velocity is increased when diameter is reduced - which means the peripheral speed (the electrons in orbit) increase as well

As such when taken to an infinite point source (the diameter of the atom nucleus I guess) means the speed of the electron must approach C - where the limit of C and forces in play at that level sets the orbital distance.

No surprise there in principle (to me) only the precision of the maths to calculate it or the need to take it into account if your work involves this sort of thing.

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#5
In reply to #3

### Re: Relativistic Effects in Chemistry

01/16/2016 2:46 PM

No problem! I find the subject interesting. Because of this concept of a "ground state" orbital, you don't see that much orbital contraction in smaller atoms. Really it only shows up in very sensitive properties for small atoms. However, as atoms get larger (third row and up) this contraction becomes more and more important when calculating even basic atomic chemical properties.

But really, I just like the thought of it. Being able to precisely measure relativity using atoms rather than satellites!

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#4

### Re: Relativistic Effects in Chemistry

01/16/2016 2:16 PM

The 1s is too deep inside the Uranium atom to be involved in chemistry. The 5th, 6th, and 7th shells overlap (7s, 6d, 5f) and all contribute electrons in chemical reactions, and are affected differently by relativistic effects (different radial distribution).

The Engineer

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#6
In reply to #4

### Re: Relativistic Effects in Chemistry

01/18/2016 10:48 AM

Hi Rixter,

You bring up a good point.

I think the inner electrons can effect the orbitals of the outer electrons due to electron screening of the nucleus, but really chemistry is dominated by the outer electrons.

-R