How Do You Calculate Effective Nuclear Charge for Elements in the S Orbital?

[relativitydude]

I need to list the affective nuclear charge from least to greatest on a group of elements in the S orbital. Zeff = Z - S

So I look, at say Titanium atomic number 81 minus the electrons in the s orbital of the valance, so that's 6s^2. So is titaniums affective nuclear charge 81 - 2 = 79?

The next question asks whether various anions, K+ and Ca2+ are bigger and smaller than one another.. Can I just look at the trends in the periodic or must I calculate Zeff?

 

[chem_tr]

I recall that there is a somewhat more complex formula to calculate the effective nuclear charge, but I'm not sure.

 

[altered-gravity]

Hi,

Slater introduced the concept of "effective nuclear charge" in his try to obtain analytical and easy to integrate orbital wavefunctions. This parameter must be obtained empirically and is tabulated for each atom and shell.

In order to work in a very approximated way he developed the "Slater rules" to get acceptable Zeff values: Zeff=Z-S (but don´t forget that they´re very approximated, good ones must be obtained empirically for each wavefunction)

Theese are the rules:

Having chosen an electron, the Z eff that it "feels" is:

1- S=0 for any electron in an upper shell (value of n).

2- S=0.35 for each electron in the same shell, except if it´s 1s then 0.31.

3.- If the electron is s or p, S=0.85 for each electron in the inmediate below shell. And S=1 for the rest.

4.- If the electron is d or f, S=1 for each electron in any shell below it.

You have to sum all the S contributions and do Zeff= Z- total S

Exmpl: 1s electron of Ti: Zeff=22-1*0.35 = 21.65

4s electron of Ti: Zeff= 22 - 1*0.35 - 10*0.85 - 8*1 - 2*1 = 3.15


(Z=81 is Talium)