Understanding Relativistic Inner Core Electrons in Heavier Elements

[quetzalcoatl9]

Can anyone please explain why the inner core electrons for heavier elements would have relativistic momenta? I have not seen this clearly explained before.

My thinking is: given the stronger coloumbic interaction with the nucleus (and e-e repulsion with the higher energy shells) that the spatial regions that these electrons can occupy for a given energy is limited, in order for the electrons to exist in these regions they must have a certain minima (quanitized) energy - the remainder of which is kinetic.

is this right?

 

[Astronuc]

Presumably its related to the high binding energy (due to Coulomb attraction) which is on the order of 100+ keV as compared to the 511 keV rest mass of the electron.

See - http://xdb.lbl.gov/Section1/Table_1-2.pdf (Thanks to Gokul who dug up this one)

http://www.csrri.iit.edu/periodic-table.html

 

[Gokul43201]

The Bohr calculation (although not good for accuracy, but still good enough for an OoM estimate perhaps) throws some light: v_n ~~\alpha~~ z/n.

Alternatively, you could think of this in terms of the higher (in magnitude) potential energy and the virial theorem.

 

[quetzalcoatl9]

thanks guys, the Bohr velocity makes sense to me, the virial theorem as well

could the HUP also be used to show this somehow - that since the core electrons are restricted (probabilistically) to certain spatial regions, that the uncertainty in the momentum will go up?