Finite Size vs Point Size Hydrogen like Atoms

[photomagnetic]

Ok my question:
what is the difference between the binding energies of these 2 types of atoms, conceptual wise, which one is greater?

I am assuming based on the easy calculations of the potential energy of the finite size atom ( inside and outside)
There is a difference between the potential energies of those 2 regions, and just because of that difference. It's easier to ionize the atom.
Am I correct?

Thank You

 

[Vanadium 50]

I don't know what you mean by "point sized atoms", since they do not exist in either theory or in nature, but the Rydberg constant is inversely proportional to the Bohr radius.

 

[blue_leaf77]

what is the difference between the binding energies of these 2 types of atoms, conceptual wise, which one is greater?

Unfortunately there is no answer to your question because the two types of atom you are considering are not present to begin with.

 

[jtbell]

I am assuming based on the easy calculations of the potential energy of the finite size atom ( inside and outside)
There is a difference between the potential energies of those 2 regions,

How do you distinguish "inside" versus "outside" for e.g. the ground state of hydrogen, for which the electron probability density as a function of r looks like the right-hand graph below? Do you mean "r large enough that the probability density is negligible"? (It never actually reaches zero.)

(source: http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html)

Both the potential and kinetic energies of the electron must also be described using probability distributions. Their sum is of course a fixed number: -13.6 eV for the ground state of hydrogen.