super heavy elements

[johnct]

I have read recently that it is believed that special relativity comes into play in very large atoms, because the "orbital speed" of electrons gets close to the speed of light. I have not thought of electrons in orbit since grammar school, their positions (as particles) being a kind of a smear of probabilities within a given orbital and the corresponding waves as standing closed cycle waves with discreet wavelengths fitting within the cycles. By what is meant orbital speed?

 

I am a new member. If it is possible to include my email in the reply, it would be appreciated. By the way, this is the only website including physics which I could find that was at all possible to register for. Either the image verifications were illegible, or I got rejected as a spammer, or the verification application instructions made zero sense.

 

John

[fiveworlds]

Hi John, generally we use google/yahoo etc for these types of questions a quick search of orbital speed gives this Wikipedia page https://en.wikipedia.org/wiki/Orbital_speed

 

The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body.

 

The barycenter being the center of mass of the atom.

[swansont]

I have read recently that it is believed that special relativity comes into play in very large atoms, because the "orbital speed" of electrons gets close to the speed of light. I have not thought of electrons in orbit since grammar school, their positions (as particles) being a kind of a smear of probabilities within a given orbital and the corresponding waves as standing closed cycle waves with discreet wavelengths fitting within the cycles. By what is meant orbital speed?

 

I am a new member. If it is possible to include my email in the reply, it would be appreciated. By the way, this is the only website including physics which I could find that was at all possible to register for. Either the image verifications were illegible, or I got rejected as a spammer, or the verification application instructions made zero sense.

 

John

 

What you are likely to find (and what I've found the times I have followed up on this) is that phrase "orbital speed" is used in pop-sci descriptions of the phenomena (possibly along with suggestions that the mass has changed), but when you go to the primary literature they generally discuss the energy, because that's what's in the QM. What's happening is that the kinetic energy is not what is described classically, because the energy high enough that the relativistic solution for the orbital differs from the classical one. That happens at a few percent of the mass energy (depending on what you mean by "significant") The mass energy of the electron is 511 keV, so kinetic energies of several keV would give rise to such effects. Ionization energy for inner electrons of really heavy atoms can approach 100 keV. http://hyperphysics.phy-astr.gsu.edu/hbase/tables/kxray.html#c1and the KE is that same magnitude (Though I may be forgetting a factor of 2, but that doesn't change the concept)

 

The speed calculations take the kinetic energy and solve for a speed, but that's kinda dicey physics when you're discussing QM. There's always a momentum uncertainty, so the speed cannot be precisely known.

[Eise]

Maybe this helps a little?

What Gives Gold that Mellow Glow?

Color of gold and caesium

[swansont]

What Gives Gold that Mellow Glow?

That's a site written by a computer scientist, and suffers from the very pop-sci foibles I mentioned earlier.