What is the calculation for effective nuclear charge using Slater's Rules?

[Yh Hoo]

I have come across the Slater's Rules that is used to calculate the numerical value of effective nuclear charge of elements.
Can somebody please show to me the calculation of effective nuclear charge of atoms of element down the group 2 by using the Slater's rule??
I calculate by using the information from http://en.wikipedia.org/wiki/Slater's_rules.
many books mention that increment in atomic radius down the group 2 is caused by the decreasing effective nuclear charge. is it true? Thanks for your help and i really need all your help.

 

[JohnRC]

Firstly, I am not sure that Slater's rules as presented in the wikipedia article are a correct interpretation. However , let us suppose that they are.

I calculate effective nuclear charges of 1.95, 2.85, 2.85, 2.85, and 2.85 for Be, Mg, Ca, Sr, and Ba respectively.

The increase in atomic radius is not the result of a decreasing effective nuclear charge. It is mostly the result of an increasing principal quantum number for the outermost electrons, and the increase in atomic radius is lessened by the increasing effective nuclear charge.

 

[Yh Hoo]

I calculate effective nuclear charges of 1.95, 2.85, 2.85, 2.85, and 2.85 for Be, Mg, Ca, Sr, and Ba respectively.

I calculated the same thing also. If our calculation are correct ,that means the effective nuclear charge is increasing and then go to constant. But many books wrote that the effective nuclear charge is decreasing down the group.
Or could you please share with me your knowledge and understanding on Slater's rule ?? Thanks a lot.

 

[JohnRC]

Slater's rules were designed for the specific purpose of trying to calculate molecular structures and chemical bonds in a simplistic model where only valence electrons were considered, with single electron wave functions, and "hydrogen-like orbitals" -- that is,

psi(3px) = x * exp(-alpha*r) rather than the truly hydrogen-like (b – x) * exp(-alpha*r)

They were also "tuned" for energy -- ionization potentials and bond strengths -- rather than atom size.

There is another method that is used for obtaining effective nuclear charge. It involves a close examination of the atomic spectrum of an element and identifying particular groups of lines as "Rydberg series". If this method is used, you can arrive at a significantly different pattern for effective nuclear charge.