[Chaste]

It is said that the electrons in heavier atoms have speed close to that of light and therefore undergo relativistic effects?

May I ask why is this so? What is it in heavier elements that caused such a change to the speed of the electron?
Is it related to the energy-mass equivalence formula?

[Borek]

It is said that the electrons in heavier atoms have speed close to that of light and therefore undergo relativistic effects?

Where "it is said"?

[Chaste]

http://www.chem.ubc.ca/courseware/320/cr00085a006.pdf

All in chapter 1 introduction.

[FeLiXe]

the idea is that the core electrons of a heavy nucleus move around it faster because there is more attractive electrostatic force to compensate

[Borek]

What I don't like about that explanation is that moving electron is a thing from corpuscular world, while electron in a molecule/atom is a standing wave.

[FeLiXe]

it seems that in may cases classical intuition goes together with quantum mechanics but I admit that i cannot say when it is the case and when it isn't
in this case it is:

motion in time independent QM corresponds to the momentum operator

a compressed wavefunction will quickly change when you move away from the nucleus which means a large derivative which means high momentum

or according to Heisenberg: a small Δx for a compressed wavefunction will lead to a large Δp

or: the virial theorem holds and 2T = -V -> strong attraction leads high kinetic energy (i.e. fast motion)

of course this is just an attempt to explain in a QM way what is really a problem of QM combined with relativity ...
well I've never worked with the Dirac equation

[Borek]

it seems that in may cases classical intuition goes together with quantum mechanics but I admit that i cannot say when it is the case and when it isn't

My intuition is identical, just this "speed" thing doesn't click. But you are most likely right that in terms of momentum it does make sense.

[Chaste]

Actually, so how do I answer quantatively the inert pair effect from elements after tin and onwards. Using the fact of relativistic effects?

these are my points:
higher energy S Atomic orbitals(AO) have penetrating power that brings it nearer to the nucleus.
outer electrons doesn't provide good screening for these S AOs
therefore electrons in the higher energy S AOs experience a greater effective nuclear charge.
In order to balance these electrostatic force of attraction, the electrons has to a higher energy which translates to higher momentum and velocity.
This change in momentum and velocity brings the velocity of the electron to a significant fraction of the speed of light
and therefore undergoes relativistic contraction, shrinking the S AO that it's in as well.
(I sound contradicting now...where the AO has already penetrated into the nucleus and still undergoes relativistic contraction?)
Therefore, making the electrons in the higher energy S AOs more stable and inert to partake in bonding.
= inert pair effect.

Please correct me. Thank you.

[FeLiXe]

by high energy, you mean high negative energy?
What do you mean by penetrating into the nucleus? the nucleus is always orders of magnitude smaller than the orbital

but besides that it sounds good I think. a core electron will move close to the speed of light and become heavier. and therefore it's orbital contracts. and then everything else contracts too, I guess

[Chaste]

by high energy, you mean high negative energy?
What do you mean by penetrating into the nucleus? the nucleus is always orders of magnitude smaller than the orbital

but besides that it sounds good I think. a core electron will move close to the speed of light and become heavier. and therefore it's orbital contracts. and then everything else contracts too, I guess

by higher energy I meant for AOs with higher N quantum numbers. We've always use that in school. now that you're mentioning negative energy, you got me thinking.

http://www.tutorvista.com/content/chemistry/chemistry-iii/atomic-structure/relative-energies.php
I'm not sure about the if it's negative or not. It's like 6s AO is definitely higher in energy than a 1s AO. The lower the energy of the AO, the more stable it is.

Alright, I'm sorry about penetrating into the nucleus bit. Higher N AOs possess penetrating power that enables it to bring itself closer to the nucleus. That's what I meant. Pardon that 'INTO' bit.

however, I'm still very unsettled regarding the penetrating power the AO has and the relativistic contraction it undergoes. It's like repetition, reilliterating the fact that it's brought closer to the nucleus.

[FeLiXe]

yes high energy typically means an outer AO
but then I don't get your point. because it should be the low energy core AOs where you have relativistic effects

[Chaste]

yes high energy typically means an outer AO
but then I don't get your point. because it should be the low energy core AOs where you have relativistic effects

http://www.fourmilab.ch/documents/golden_glow/

I think this website gives a good understanding regarding higher energy AOs experiencing relativistic effects as well. I believe the inner core do experience relativistic effects but then why does elements like thallium prefers +1 oxidation state compared to +3(unstable oxidation state) even when it's in group 13? because of the inert pair effect referring to the valence 6s electrons. These 6s electrons are in the 6s AO which is relativistically contracted and being stabilized by the strong nuclear charge.


I would further like to add, with credits from the above website(changes in italics)
higher energy S Atomic orbitals(AO) have penetrating power that brings it nearer to the nucleus.
outer electrons doesn't provide good screening for these S AOs
therefore electrons in the higher energy S AOs experience a greater effective nuclear charge.
In order to balance these electrostatic forces of attraction, the electrons have to have a sufficient energy to prevent 'falling into' the nucleus which translates to higher momentum and velocity.
This change in momentum and velocity brings the velocity of the electron to a significant fraction of the speed of light
(multiplying the Lorentz factor) Increase in speed would result in a gain in mass. (Energy-mass equivalence.since E= mc²)
and therefore undergoes relativistic contraction, shrinking the S AO that it's in as well, as electron mass and radius of atomic orbital are proportional. Thus, electrons in higher N quantum number AOs experience higher nuclear charge
Therefore, making the electrons in the higher energy S AOs more stable and inert to partake in bonding.
= inert pair effect.

Open to opinions and corrections =)

[FeLiXe]

kind of an interesting question ...
now I see what you mean: that even the outer s-orbitals have a part close to the nucleus and so they can also be affected by relativity, that make sense
but another explanation that I heard for Lanthanide contraction (which seems to be related to this) is that it is because the f-orbitals don't screen the nuclear charge well and that therefore the outer electrons are pulled in

[Chaste]

Yes, you are right to include lanthanide contraction. But that is for lower period elements whose electron configuration consists of the 4f orbitals. Whereas relativistic effects starts to take effect from tin onwards.

[FeLiXe]

alright, that's pretty cool then