# Shielding Effect and Screening Constant

## Shielding Effect or Screening Effect

The shielding effect is the reduction in the effective nuclear charge on the electron cloud, due to a difference in the attractive forces of the electrons in the nucleus. In other words, it is the reduction of attraction between the atomic nucleus and outermost electrons due to the presence of inner shell (core) electrons. So the amount by which the nuclear charge is screened i.e. decreased by the core electrons present in the shell is called **Screening Constant(S)**. The Screening (shielding) constant is greater than zero but smaller than nuclear charge (Z).

Due to screening effect, the amount of nuclear charge experienced is much less by the outgoing electron during cation formation or during the calculation of ionization potential. Hence, the screening constant(S) will have to deducted from the value of nuclear charge(Z) because, nuclear charge is not exactly situated at the point where the most loosely held electron is going to be removed from the isolated atom. So, the actual nuclear charge is not experienced by the outgoing electron present in the valence shell, rather it experiences the lesser nuclear charge. Due to this reason, nuclear charge(Z) is replaced by effective nuclear charge(Z*) in the expression of ionization potential.

The relation between Z and Z* is-

Z* = Z − S

When there are many inner shell electrons present, the atomic nucleus has less attraction from the atomic nucleus because the atomic nucleus is shielded by the electrons. Higher the number of inner electrons, greater the shielding effect. The order of increasing the shielding effect is as follows-

S orbital > p orbital > d orbital > f orbital

Hydrogen atom is the smallest atom in which one electron is present. There are no shielding electrons, therefore the effective nuclear charge on this electron is not reduced. Hence, there is no shielding effect. But when moving across a period from left to right in the periodic table, the number of electrons present in the atom increases. So, the shielding effect is also increases.

## Rules for Calculating Screening Constant(S)

Following emperical rules have been proposed by Slater in 1930 to estimate the extant of shielding-

1. The outgoing electron contributes zero to S-value as last electron considered as already removed from the valence shell or atom.

2. The remaining electrons of the valence shell(n) contributes 0.35 units per electron to the S-value.

3. The (n − 1) shell electrons contribute 0.85 units per electron to the S-value.

4. All the remaining electrons of the atom contribute one electron each to S-value.

5. The d and f sub-shells are taken as shells here.

(1s)(2s 2p)(3s 3p)(3d)(4s 4p)(4d)(4f)

### Calculate the screening constant and effective nuclear charge of the following atoms-

Li, N, Cl, Mn, Cu

**Answer**

_{3}Li: 1s^{2}2s^{1}

Screening Constant(S) = (1 x 0) + (2 x 0.85) = 1.70

Effective Nuclear Charge(Z*) = 3 − 1.70 = 1.30 units

_{7}N: 1s^{2}2s^{2}2p^{3}

Screening Constant(S) = (1 x 0) + (4 x 0.35) + (2 x 0.85) = 3.10

Effective Nuclear Charge(Z*) = 7 − 3.10 = 3.90 units

_{17}Cl: 1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}

Screening Constant(S) = (1 x 0) + (6 x 0.35) + (8 x 0.85) + (2 x 1) = 10.90

Effective Nuclear Charge(Z*) = 17 − 10.90 = 6.10 units

_{25}Mn: 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}**3d ^{5}**4s

^{2}

Screening Constant(S) = (1 x 0) + (1 x 0.35) + (5 x 0.85) + (18 x 1) = 22.60

Effective Nuclear Charge(Z*) = 25 − 22.60 = 2.40 units

_{29}Mn: 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}**3d ^{10}**4s

^{1}

Screening Constant(S) = (1 x 0) + (10 x 0.85) + (18 x 1) = 26.50

Effective Nuclear Charge(Z*) = 29 − 26.50 = 2.50 units