Calculation of screening constant

Screening effect ( σ ) and effective nuclear charge (Z_eff)

1. Valence shell e^– suffer force of attraction due to nucleus and force of repulsion due to inner shell electrons.

2. The decrease in force of attraction on valence e^– due to inner shell e^– is called screening effect or shielding effect. (i.e. total repulsive force is called shielding effect.)

3. Due to screening effect valence shell e^– experiences less force of attraction exerted by nucleus. (i.e. total attraction force experienced by valence e^– is called Z_eff)

4. There is a reduction in nuclear charge due to screening effect. Reduced nuclear charge is called effective nuclear charge.

5. If nuclear charge = Z. Then effective nuclear charge = Z_eff – σ(Sigma) = Screening constant or shielding constant. So, Z_eff  =(Z-σ )

Slater’s rule to know screening constant (σ ):

(a) Screening effect (S.E.) of one e^– of the 1s is 0.30.

(b) Screening effect of ns and np (Outermost orbit) electrons is 0.35.

(c) Screening effect of (n-1) penultimate orbit s, p, d, electrons is 0.85.

(d) Screening effect of (n-2) and below all the e^– present in s, p, d, f is 1.0.

In transition series Z_eff  increases by very less amount, i.e. by 0.15 from left to right and hence atomic radii remains almost constant.From top to bottom in a group Z_eff remains constant.

Ex.       Zn = 30

 Key point:

(i) From left to right in a period Z_eff increases

(a) For normal/ Representative elements, In a period nuclear charge increases by +1, while orbit remains same, therefore in a period e^– enters in outermost shell and screening effect of outermost electron is increases. So by increasing 1 nuclear charge, Z_eff increases by 0.65 (1 – 0.35 = 0.65. That’s why in a period Z_eff increases by 0.65 and hence atomic size decreases considerably.

(b) In transition series Z increase by +1 but screening effect increases by 0.85 So Zeff is 0.15 (1-085=0.15) [Because e^– enters in (n-1) orbit which ha the value of = 0.85]

(c) For same shell shielding effect has the order as s > p > d > f (due to penetration effect)

(d) Z_eff for different ions of an element

(i)  Z_eff for different ions of an element

Ex.    N⁺ > N > N^– = Z_eff

(ii)  Z_eff of isoelectronic species

Ex.    H^– < Li⁺ < Be⁺² < Be⁺³  (2e^– species)

          N^-3 < O^-2 < F^– < Na⁺ < Mg⁺² (10 electronic species)