Shielding or Screening Effect

There are many observable patterns in the physical and chemical properties of elements as we descend in a group or move across a period in the Periodic Table. The term periodicity is used to indicate that some characteristic properties occur in the periodic table after definite intervals, with a varying (gradual increase or decrease) magnitude. The periodic recurrence of elements having similar properties after regular intervals is called periodicity. In this article, we shall study a very important factor called screening effect or shielding effect which influences periodic properties.

Atomic Properties:

Properties such as atomic and ionic radii, ionization enthalpy, electron gain enthalpy, valency, screening effect, effective nuclear charge, and electronegativities are the properties of individual atoms. These properties are directly dependent on their electronic configuration.
Properties such as melting point, boiling point, the heat of fusion, heat of vaporization, density, atomic volume, etc., are collective properties of a group of atoms. These properties are indirectly dependent on their electronic configuration.
All such properties which are directly or indirectly dependent on the electronic configuration of the elements are called atomic properties.

Cause of Periodicity:

The physical and chemical properties of an element depend upon the distribution of electrons in the various shells of an atom. The distribution of electrons in the outermost shell is called the valence shell of an atom. This distribution of electrons in the outermost shell is important because it influences the physical and chemical properties of that element. In a particular group, all elements show a similar electronic distribution in the valence shell and hence they show similar physical and chemical properties. The following table gives the electronic distribution of the halogen family (Group – 17). We can observe the characteristic configuration of the ns2np5 valence shell. All these elements have similar properties with definite gradation (increase or decrease).

Period	Element	Symbol	Atomic Number	Electronic Configuration
2	F	F	9	[He]2s22p5
3	Chlorine	Cl	17	[Ne]3s23p5
4	Bromine	Br	35	[Ar]3d104s24p5
5	Iodine	I	53	[Kr]4d105s25p5
6	Astatine	At	85	[Xe]4f145d106s26p5

Thus the elements with similar configuration recur at regular intervals in the periodic table, the similar properties also recur in the periodic table. Thus the distribution of electrons in the outermost (valence) shell is the cause of periodicity.

In a period due to the gradual change in electronic configuration across the period from member to member, there is a gradual change in periodic property across the period. These properties include screening effect, atomic number, atomic radii, ionic radii, ionization enthalpy, electron gain enthalpy (electron affinity), electronegativity,  etc. They follow the general trend of periodicity.

In a group, valence shell configuration is the same, hence chemical properties in a group remain the same. There is a gradual change in physical properties due to an increase in atomic size which is due to the start of a new energy level.

Screening or Shielding Effect:

This effect is observed in an atom having more electrons and particularly more electron shells. The electrons in the valence shell are attracted by the positively charged nucleus. While there is repulsion between the valence electrons and the electrons present in the inner shells. Due to this, there is a decrease in the force of attraction between the electrons in the valence shell and the nucleus. This effect is known as the screening effect. The magnitude of the screening effect depends on the number of electrons in the inner shells.

The decrease in the force of attraction exerted by the nucleus on the valency electron due to the presence of electrons in the inner orbit is called screening effect or shielding effect.

Screening Effect Constant (Slater’s Rule):

Screening effect constant is denoted by letter σ. To find screening effect constant following steps should be followed.

Step 1: 

Write the electron configuration of the atom in the  form: (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) . . .

Step 2: 

Identify the electron of interest (ns, np), and ignore all electrons in higher groups (to the right in the list from Step 1). These do not shield electrons in lower groups and hence do not contribute to screening effect constant.

Step 3: (For the shielding experienced by s- or p- electron):

All other electrons in the (ns, np) group contribute shielding to the extent of 0.35 each to the screening constant. note that for 1s this value is 0.30.

All the electrons in the (n – 1)th shell contribute 0.85 each to the screening effect constant.

All the electrons in the (n – 2)th shell contribute 1.0 each to the screening effect constant.

Step 3: (For the shielding experienced by d- or f- electron):

all other electrons in the (ns, np) group contribute shielding to the extent of 0.35 each to the screening constant. note that for 1s this value is 0.30.

All the electrons in a group lying left of (nd, nf) group contribute 1.0 each to the screening effect.

Examples of calculation of screening effect constant:

Screening Effect Down the Group (Alkali Metals):

Elements	Atomic number	Electronic configuration	Detailed Electronic configuration	Calculation	Screening effect constant
Lithium (L)	3	2, 1	1s2,2s1	2 x 0.85	1.7
Sodium (Na)	11	2, 8, 1	1s2,2s22p6,3s1	8 x 0.85 + 2 x 1	8.8
Potassium (K)	19	2,8, 8, 1	1s2,2s22p6,3s23p6,4s1	8 x 0.85 + 8 x 1 + 2 x 1	16.8
Rubidium (Rb)	37	2, 6. 18, 8, 1	1s2,2s22p6,3s23p63d10,4s24p6, 5s1	8 x 0.85 + 18 x 1 + 8 x 1 + 2x 1	34.8
Caesium (Cs)	55	2, 8,18,18, 8,1	1s2,2s22p6,3s23p63d10,4s24p64d10, 5s25p6,6s1	8 x 0.85 + 18 x 1 + 18 x 1 + 8 x 1 + 2x 1	52.8

We can see that as we move down the group screening effect increases.

Screening Effect Across the Period (Second Period):

Elements	Atomic number	Electronic configuration	Detailed Electronic configuration	Calculation	Screening effect constant
Lithium (L)	3	2, 1	1s2,2s1	2 x 0.85	1.7
Beryllium (Be)	4	2, 2	1s2,2s2	2 x 0.85 + 1 x 0.35	2.05
Boron (B)	5	2,3	1s2,2s22p1	2 x 0.85 + 2 x 0.35	2.40
Carbon (C)	6	2, 4	1s2,2s22p2	2 x 0.85 + 2 x 0.35 + 1 x 0.35	2.75
Nitrogen (N)	7	2, 5	1s2,2s22p3	2 x 0.85 + 2 x 0.35 + 2 x 0.35	3.10
Oxygen (O)	8	2, 6	1s2,2s22p4	2 x 0.85 + 2 x 0.35 + 3 x 0.35	3.45
Fluorine (F)	9	2, 7	1s2,2s22p5	2 x 0.85 + 2 x 0.35 + 4 x 0.35	3.80
Neon (N1)	10	2, 8	1s2,2s22p6	2 x 0.85 + 2 x 0.35 + 5 x 0.35	4.15

We can see that as we move across the period from left to right there is increase in screening effect but there is no major changein the  screening effect as observed down the group in the periodic table.

Thus as the atomic number increases, the magnitude of the screening effect constant in case of s- and p- block elements increases in a period as well as in a group.

Calculation of screening effect constant for electron 3s orbital of bromine:

Atomic number of bromine is 35, its electronic configuration is 2, 8, 18, 7

The detailed configuration is  Br: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵

Br: (1s²)(2s²,2p⁶)(3s²,3p⁶)(3d¹⁰)(4s²,4p⁵)

Ignore the group to the right of the 3s electrons. These do not contribute to the shielding constant.

Screening effect constant = σ = 0.35 x 1 + 0.85 x 8 + 1 x 2 = 9.15

Calculation of screening effect constant for electron 3p orbital of bromine:

Ignore the group to the right of the 3p electrons. These do not contribute to the shielding constant.

Screening effect constant = σ = 0.35 x 5 + 0.35 x 2 + 0.85 x 8 + 1 x 2 = 11.25

Calculation of screening effect constant for electron 3d orbital of bromine: 

Ignore the group to the right of the 3d electrons. These do not contribute to the shielding constant.

Screening effect constant = σ = 0.35 x 9 + 1 x 8 + 1 x 8 + 1 x 2 = 21.15

Note: From above example we can see that for same main energy level screening effect constant for s- orbital is the least and for d- orbital it is the highest. So order for same main energy level is s < p < d< f.

Calculation of screening effect constant for electron 4s orbital of zinc: 

Atomic number of zinc is 30, its electronic configuration is 2, 8, 18, 7

The detailed configuration is  Zn 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰

Zn: (1s²)(2s²,2p⁶)(3s²,3p⁶)(3d¹⁰)(4s²)

Screening effect constant = σ = 0.35 x 1 + 0.85 x 18 + 1 x 8 + 1 x 2 = 25.65

Calculation of screening effect constant for electron 3d orbital of zinc: 

Br: (1s²)(2s²,2p⁶)(3s²,3p⁶)(3d¹⁰)(4s²)

Ignore the group to the right of the 3d electrons. These do not contribute to the shielding constant.

Screening effect constant = σ = 0.35 x 9 + 1 x 8 + 1 x 8 + 1 x 2 = 21.15

Note: The electrons in different orbitals are affected differently by the same nuclear charge dep[ending upon their proximity to the nucleus.

Effective Nuclear Charge:

Due to the screening effect, there is a decrease in the force of attraction on the electron in the valence shell towards the nucleus. Thus there is a decrease in the effect of nuclear charge. This reduced nuclear charge is called effective nuclear charge is denoted by  ‘Z_eff‘. The effective nuclear charge is the difference between the actual nuclear charge and the screening effect constant.charge.  Z_eff = Z – σ.

Let us consider the variation of effective nuclear charge across period:

Second Period Elements:

Elements	Atomic Number (Z)	Screening effect Constant (σ)	Effective Nuclear charge Zeff = Z – σ
Lithium (Li)	3	1.7	1.3
Beryllium (be)	4	2.05	1.95
Boron (B)	5	2.40	2.60
Carbon (C)	6	2.75	3.25
Nitrogen (N)	7	3.10	3.90
Oxygen (O)	8	3.45	4.55
Fluorine (F)	9	3.80	5.20
Neon (N)	10	4.15	5.85

It is observed that the magnitude of effective nuclear charge increases in a period when we move from left to right.

Group – 1 (Alkali Metals):

Elements	Atomic Number (Z)	Screening effect Constant (σ)	Effective Nuclear charge Zeff = Z – σ
Lithium (L)	3	1.7	1.3
Sodium (Na)	11	8.8	2.2
Potassium (K)	19	16.8	2.2
Rubidium (Rb)	37	34.8	2.2
Caesium (Cs)	55	52.8	2.2

Group – 2 (Alkaline Earth Metals):

Elements	Atomic Number (Z)	Screening effect Constant (σ)	Effective Nuclear charge Zeff = Z – σ
Beryllium (B)	4	2.05	1.95
Magnesium (Mg)	12	9.15	2.85
Calcium (Ca)	20	17.15	2.85
Strontium (Sr)	38	35.15	2.85
Barium (Ba)	56	53.15	2.85

It is observed that in a subgroup of normal elements the magnitude of effective nuclear charge remains almost the same.