Anomoly in calculations/standard value for electron energy levels

Click For Summary

Discussion Overview

The discussion revolves around the calculation of electron energy levels in atoms, specifically focusing on the discrepancy between calculated ionization energy for xenon using the formula En=-13.6(Z/n)^2 and the value provided in a textbook. The scope includes theoretical calculations and conceptual clarifications regarding ionization energy.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • nSlavingBlair presents a calculation for xenon's ionization energy using the formula, resulting in -39657.6 eV, and questions the discrepancy with the textbook value of 12.127 eV.
  • One participant suggests that the textbook value refers to the ionization energy for removing the outermost electron, while the formula applies to a scenario with one electron around a fully charged core, leading to different interpretations of ionization energy.
  • Another participant argues that the formula indeed represents the energy required to completely remove an electron from the atom, citing consistency with hydrogen's ionization energy.
  • A different participant emphasizes that the formula is a simplification and notes the complexity of calculating energy levels for multi-electron atoms like helium, indicating that closed-form solutions are not always possible.
  • One participant clarifies that the equation applies to the last electron being removed, while the ionization energy pertains to the first electron removal from the atom.
  • A later reply humorously illustrates the scenario of a xenon ion with 53 electrons removed, emphasizing the context of the ionization energy discussion.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the ionization energy and the application of the energy level formula, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

The discussion highlights limitations in the application of the formula to multi-electron systems and the assumptions underlying the definitions of ionization energy, which are not fully resolved.

EnSlavingBlair
Messages
34
Reaction score
2
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
 
Physics news on Phys.org
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.
 
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
 
nSlavingBlair said:
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.
 
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.
 
That is, if you have a Xe+++++++++++++++++++++++++++++++++++++++++++++++++++++ ion :bugeye:, with 53 electrons removed and the remaining single electron in its ground state, that would be the ionization energy.
 

Similar threads

Undergrad Electromagnetic radiation, photons, quantized energy levels
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Ionization energy calculations
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Energy level of hydrogen atom - with the electron replaced by a positron
  • · Replies 3 ·
Replies
3
Views
2K
High School Ionization energy of electrons?
  • · Replies 6 ·
Replies
6
Views
6K
Graduate Electron Energies in Atoms: Fixed Values or Expectation Values?
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Why Use Nuclear Charge In Finding Energy Value of Singular Electron?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Understanding Spin-Orbit Interaction's Impact on Electron Energy Levels
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Simple Energy Levels confusion
  • · Replies 3 ·
Replies
3
Views
7K
Graduate Why KE of Annihilation Electrons Differs?
  • · Replies 11 ·
Replies
11
Views
2K
Determine energy levels of a electron in a hydrogen atom
  • · Replies 8 ·
Replies
8
Views
2K