# Why relativistic inner core?

1. May 8, 2006

### 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?

2. May 9, 2006

### Staff: Mentor

Last edited: May 9, 2006
3. May 10, 2006

### Gokul43201

Staff Emeritus
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.

4. May 10, 2006

### 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?