Zeff is the effective nuclear charge and is calculated by the formula:
Zeff = Z - S
Z refers to the number of protons and S is the Slater's constant.
Na⁺ cation has 11 protons, the number of core electron in sodium ion are 2.
If the core electrons donates 1.00 and the valence electrons donate 0.00 then S = 2 for both the ions.
Hence, for Na⁺, Zeff = 11 - 2 = 9
F⁻ ion has 9 protons, the number of core electrons in F⁻ ion are 2. Hence, for F⁻ : Zeff = 9 - 2 = 7
Therefore, Zeff for Na⁺ and F⁻ are 9 and 7 respectively.
On the basis of Slater's rules, for s and p orbitals, the electrons in the similar shell donates 0.35 and the electrons in the n -1 shell donates 0.85.
S = (0.85 × 2) + ( 0.35 × 7)
= 4.15
Hence, according to Slater's rule,
For Na⁺, Zeff = 11 - 4.15 = 6.85
For F⁻, Zeff = 9 - 4.15 = 4.85
Thus, Zeff for Na⁺ and F⁻ calculated on the basis of Slater's rules are 6.85 and 4.85 respectively.