Anomoly in calculations/standard value for electron energy levels

[EnSlavingBlair]

The energy levels of an atom are found by En=-13.6(Z/n)^2.

Using this equation for xenon's ionization energy (Z=54) gets E=-39657.6eV. However in the Modern Physics ed3 textbook by Serway/Moses/Moyer on pg232 it has the ionization energy for xenon to be 12.127eV.

Does anyone know what's going on and why the values are different?

Cheers,
nSlavingBlair

 

[xepma]

Looks to me that the ionization energy mentioned by Serway/Moses refers to ionizing the atom by removing one electron (the outermost of the 54 in total). Total charge of the ionization is +e, and this will cost you ~12 ev.

On the other hand, the way you use the formula is the case where you have one electron encircling the Z=54 core. So before removing the electron you would have a charge of +53e, and after extracting the electron (at a cost of ~40.000 ev) you end up with a bare core containing +54e.

So you are more or less comparing apples and pineapples here.

 

[EnSlavingBlair]

Really? Because I learned that the energy that relates to each level by the aforementioned equation was the energy required to remove an electron from that energy state and out of the atom completely, hence ionizing the atom.

For hydrogen they are the same, the book says 13.595eV and using the equation that is what you get to 3 sig figs.

also I miss quoted the page before, it's on page 323, not 232

 

[vanesch]

The energy levels of an atom are found by En=-13.6(Z/n)^2.

This is a strong over simplification. xempa is right.
In fact, it isn't even possible to give a closed-form solution for the energy levels of helium and one needs to resort to approximations or numerical techniques, so go figure.

 

[Vanadium 50]

The equation you gave is for removing the last electron from an atom. The ionization energy is the energy for removing the first electron from an atom.

 

[jtbell]

That is, if you have a Xe+++++++++++++++++++++++++++++++++++++++++++++++++++++ ion , with 53 electrons removed and the remaining single electron in its ground state, that would be the ionization energy.