Understanding Relativistic Inner Core Electrons in Heavier Elements

In summary, the reason why inner core electrons for heavier elements have relativistic momenta is due to the stronger Coulomb interaction with the nucleus and the limited spatial regions they can occupy. This requires them to have a certain minimum energy, with the remainder being kinetic energy. This is also related to the high binding energy of these electrons. The Bohr calculation and the virial theorem can provide estimates for their velocities. Additionally, the Heisenberg Uncertainty Principle can also be used to show that the uncertainty in momentum increases due to the limited spatial regions the core electrons can occupy.
  • #1
quetzalcoatl9
538
1
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?
 
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  • #3
The Bohr calculation (although not good for accuracy, but still good enough for an OoM estimate perhaps) throws some light: [itex]v_n ~~\alpha~~ z/n [/itex].

Alternatively, you could think of this in terms of the higher (in magnitude) potential energy and the virial theorem.
 
  • #4
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?
 

Related to Understanding Relativistic Inner Core Electrons in Heavier Elements

1. Why is the inner core of the Earth considered relativistic?

The inner core of the Earth is considered relativistic because it experiences extreme pressures, reaching up to 360 GPa, which causes the atoms to be squeezed closer together and increases their velocities. This leads to relativistic effects, such as time dilation and length contraction, which are significant at these high pressures.

2. How does the relativistic nature of the inner core affect the Earth?

The relativistic nature of the inner core affects the Earth in several ways. It contributes to the Earth's magnetic field, as the high pressures and temperatures cause the iron atoms in the inner core to align and create a magnetic field. It also affects the Earth's heat budget, as the high temperatures in the inner core contribute to the convection of heat in the Earth's mantle.

3. What is the evidence for the inner core being relativistic?

One of the main pieces of evidence for the inner core being relativistic is the observation of seismic waves passing through the inner core. These waves travel at different speeds, depending on the direction they are traveling and the type of wave. This can only be explained by the inner core experiencing relativistic effects, such as anisotropy and shear wave splitting.

4. How does the relativistic inner core affect our understanding of the Earth's formation?

The relativistic inner core provides insight into the Earth's formation by revealing information about the Earth's early history. The high pressures and temperatures in the inner core suggest that the Earth's core formed through differentiation, where the heavier elements sank to the center and the lighter elements rose to the surface. This helps us understand the Earth's evolution and how it developed into its current state.

5. Can the relativistic inner core be used to study other planets?

Yes, the relativistic inner core can be used to study other planets. By understanding the inner core of the Earth, scientists can apply this knowledge to other planets with similar properties, such as size, mass, and composition. This can help us understand the formation and evolution of other planets in our solar system and beyond.

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