Chapter 1st:- Atomic Structure and Periodic Table
B.sc 1st year Book
(Page 12)

Screening effect or shielding effect

In the case of multi electrons atom, the valence shell electrons are attracted by the nucleus and repelled by other inner shell electrons present in that atom. The resultant effect of these attractive and repulsive forces acting on the valence shell electron reduces the net attractive force of the nucleus on it. ( Screening effect or Shielding effect )

electrons

This reduction in attractive force on valence electron is called the ‘screening effect’ or ‘shielding effect’. This screening effect becomes greater and greater as the number of inner shell electrons increases. With the decrease in the force of attraction caused by the screening effect of inner electrons, the actual nuclear charge (Z) also decreases by the quantity “o’ (or S ), which is called ‘screening constant’ (σ) or: ‘Slater constant’ (S) and the decreased nuclear charge which is denoted by ‘Z off’ or Z∗ is called effective nuclear charge.
 
 1.e. Z eff =(Z−σ)=(Z−S)
 
 Z = nuclear charge (atomic no,) and S = Slater’s constant
Thus, an effective nuclear charge may be defined as ” the actual nuclear charge (Z) minus the screening constant (σ) produced by the electrons residing between the nucleus and the outermost shell electron (valency electrons)’,

Slater’s rule for calculating Screening constant:

In order to calculate the extent of shielding in 1930 Slater proposed the following empirical rules.
(i) To calculate o-value, write out the electronic configuration of the element in the following order and groupings.

(1s); (2s,2p);.. (3s,3p); (3d);… (4s,4p); (4d);.. (4f); (5s,5p),….

(ii) Electrons in any group to the right of the ( ns,np) group contribute nothing to the shielding constant.
 
(iii) All of the electrons in the ( ns,np) group, shield the valency electron to an extent of 0.35 each, and for the 1s orbital, a value of 0.30 seems to work better.
 
(iv) All electrons in the (n−1) shell shield to an extent(max length) of 0.85 each.
 
(V) All electrons in the (n-2) or lower shells shield completely, and their contribution is 1.00 each. When the electron being shielded is in an nd or nf group, rules (ii) and (iii) are the same but rules (iv) and (v) are replaced by the rule that the contribution per electron from all electrons in the inner shell is 1.00.
 
(vi) All electrons in groups lying to the left of the ‘nd’ or ‘nf’ group contribute 1.00.
 
Thus, for an electron residing in ns or np orbital = 0.35 [Number of the remaining electrons in nth shell] +0.85 [Number of electrons in (n−1) shell] + 1.00 × [No. of electrons in the inner shells].
Slater contants, Shater-contants-sigma-values-of-each-electrons-in-different-shells
 

Calculation of σ and Zeff :

(a) For the last electron examples are:- 

$$ \left(i\right)\:For\:Na\:atom:\:\frac{\left(1s^2\right)}{2}\:\frac{\left(2s,\:2p\right)^8}{8}\:\frac{\left(3s\right)^1}{1} $$

(σ)Na = 0.35x(0) + 0.85x(8) + 1.00x(2)

= 0.00 + 6.80 + 2.00 = 8.80

therefore, 

(Zeff)Na = 11.00 – 8.80 = 2.20

$$ \left(ii\right)\:For\:Na^+\:ion\::\:\frac{1s^2}{2}\:\frac{\left(2s,2p\right)^8}{8} $$

(σ)Na+ = 0.35(7) + 0.85x(2)

= 2.45 + 1.70 = 4.15

therefore,

(Zeff)Na+=11.00-4.15

$$ \left(iii\right)\:For\:K\:atom\::\:\frac{\left(1s^2\right),\:\left(2s,2p\right)^8}{10},\frac{\left(3s,3p\right)^8}{8},\frac{\left(4s\right)^{1}}{1} $$

(σ)Na = 0.35x(0) + 0.85x(8) + 1.00x(10)

= 0.00 + 6.80 + 10.00 = 16.80
 
Thus,
 
(Zeff)K = 19.00 – 16.80 = 2.20
 
$$ \left(iv\right)\:For\:M\:in\:atom\::\:\frac{\left(1s^2\right),\:\left(2s,2p\right)^8}{10},\frac{\left(3s,3p\right)^8,\left(3d\right)^5}{13}\frac{\left(4s\right)^2}{2} $$
 
(σ)Mn = 0.35 x (1) + 0.85 x (13) + 10 x (1.00)
 
= 0.25 + 11.05 + 10.00 = 21.40
Therefore,
 
(Zeff)Mn = 25.00 – 21.40
= 3.60
 
(b) Calculation of σ and Zeff for (n-1) electron : 
 
$$ \left(i\right)\:For\:Mn\:in\:atom\::\:\frac{\left(1s^2\right),\:\left(2s,2p\right)^8\left(3s,3p\right)^8}{18},\frac{\left(3d\right)^5}{5},\frac{\left(4s\right)^2}{2} $$
 
According to slater’s rule 4s2 electrons will not contribute to the value of σ for a 3d-electron.
 
thus, 
 
Mn = 0.35 x (4) + 1.00 x (18)
 
= 1.40 + 18.00 = 19.40
Therefore,
 
(Zeff)Mn = 25.00 – 19.40 = 5.60
 
 

Related Topic | Atomic Structure and Periodic Table

Bohr’s Atomic ModelDe Broglie Hypothesis
De Broglie EquationHeisenberg uncertainty Principle
Schrodinger Wave EquationShapes of orbitals
Quantum NumbersHunds Rule
Pauli Exclusion PrincipleEnergy level diagram of Atom
Aufbau PrincipleScreening effect or shielding effect
Periodic TableMoseley Periodic law
Classification of elements 

Limitation of Slater Rule :

(i) Both s and p orbitals are grouped together for calculating the effective nuclear charge whereas the radial probability distribution curves tor a given a indicate a higher penetration or shielding effect of s as compared to p – orbital.

(ii) Penetration by higher occupied orbitals( than the one consider) Into inner orbitals is well known but even then their contribution is ignored as per Slater’s rule.

(iii) All electrons irrespective of s,ρ,d, or l orbitals at positions lower than the ( n−1) shall shield the n shell electron with an equal contribution of 1.00. This is unjustified because all orbitals are not the same so, different orbitals cannot have the same contribution to energy consideration.

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Frequently Asked Questions

The phenomena or process when the nuclear reduces our force of attraction in the balance electrons. due to the opposite charge electron present on the orbital. That is why electron-electrons repel each other in 1st orbital to the n-orbital and the nuclear force reduces here.

Check diagram of screening effect give above.

The Shielding Effect is also known as the Screening effect. In which the force of attraction of nuclear is reduced by valance electrons is called the ‘Shielding Effect’.

The nuclear force reduces by the valance electron or inner orbital electron. due to electron-electron repelling each other of the atom in the inner orbitals and outer orbitals, the extra force reduced by the nuclear is called the ‘shielding effect’.

The problems come to detect the shielding effect or screening effect in the 1915s. Then Slater proposed the following empirical rules in the 1930s.

Calculating or detecting the average value of the screening or shielding effect is called the ‘Slater Rule’. 

S is the Slater Constant.

Please Read the above on this page to check all Slater Rules.

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