z effective

[Savannah Mance 4G]

I went to a late quantum review session and they showed this equation z effective which is supposed to represent the number of protons multiplied by e which is charge of proton and electrons. And then there was another equation with (z effective) x (e) = (z theoretical) - (electron electron repulsion). I have never seen this equation and I'm really confused on what it means and when and how to use it.

[Chem_Mod]

Don’t worry about this equation. Just know the atomic radius trends as you move from left to right in a row and down a column. When moving left to right in a row it’s the Z or number of protons that we care about. As you increase number of protons moving left to right in a row then atomic radius decreases. This should make sense because increased number of protons makes it so that the more positively charged nucleus can pull in its electrons closer to it. Down a column we care about shielding. Shielding from inner electrons makes it more difficult for the nucleus to pull in outer electrons which leads to increased atomic radius as you go down a column.

[Anuradha S 1F]

You can think of Z effective as the relative force (or 'effect') protons have/exert on each electron. If there are a lot of electrons surrounding the nucleus (such as Radon for example), the effect protons have on any one electron is pretty low therefore the Z effective is low. But if there are only a few electrons surrounding the nucleus (such as Lithium for example), the effect protons have on any one electron is pretty high therefore the Z effective is high.

The number of protons, number of electrons, and radius all play into the Z effective.