fsci said:Why isn't the ionization energy of an electron equal to it's energy level such that:
E(electron)= -13.6(Z^2/n^2) = IP for that electron
But instead it is equal to the energy difference in energy between the atom and its ionized cation:
IP = E(A)-E(A+)
Quantum Defect said:For a hydrogen atom, this would be true (ignoring for the moment, things like the Lamb shift, etc.)
The problem with multi-electron atoms is that the "truth" is that the picture of electrons sitting in discrete energy levels given by the equation that you have above is not right. The primary problem is that electron-electron repulsions are present and are not insignificant. Imagine that you have a two-electron atom. How many electron-electron repulsions do you have to consider? You could apportion this interaction energy (50:50) to the two electrons to calculate an effective energy level for each electron. But when you ionize one electron, what happens to this interaction? The "energy level" of the remaining electron changes, too, no?
Chemists play all sorts of games to take into account the effect of electron-electron interactions. You will see things like Zeff (an effective nuclear charge) discussed. In other contexts, you will see fudge factors on "n" called a "quantum defect" -- where have I seen that before... no matter.
The ionization energy is, by definition, equal lto the energy required to ionize the atom, which is the Delta E for:
A ----> A+ + e-
fsci said:Ahhhhhhh, that makes more sense now, thanks a ton!
So if I were to calculate E(A+) for the cation using the new Zeff values for the remaining electrons I am basically accounting for the decrease in electron-electron repulsion due to one less electron? And using IP= -13.6eV (Zeff^2/n^2) for the ionized electron does not make sense because it assumes there is no change in energy in the cation even though electron-electron repulsion has decreased?
Ionization energy is the amount of energy required to remove an electron from an atom or molecule, resulting in the formation of a positively charged ion.
Ionization energy is calculated by measuring the amount of energy needed to remove one mole of electrons from one mole of gaseous atoms or molecules. This is typically measured in units of kilojoules per mole (kJ/mol).
The main factors that affect ionization energy are the size of the atom or molecule, the number of protons in the nucleus, and the electron configuration. Generally, smaller atoms with fewer electrons and a high nuclear charge will have a higher ionization energy.
As you move across a period on the periodic table, the number of protons and electrons increases, resulting in a stronger attraction between the positively charged nucleus and the negatively charged electrons. This makes it more difficult to remove an electron and therefore increases the ionization energy.
Generally, atoms with lower ionization energy are more reactive because they are more likely to lose electrons and form positively charged ions. This is why elements in the alkali metal group have low ionization energy and are highly reactive.