In a multi electron atom, the electrons of the valency shell (outermost shell) are attracted towards the nucleus and also these electrons are repelled by the electrons present in the inner shells. On account of this, the actual force of attraction between the nucleus and the valency electrons is somewhat decreased by the repulsive forces acting in opposite direction.

`text(This decrease in the force of attraction exerted by the nucleus on the valency electrons due to the presence of electrons in the inner shells, is called screening effect or shielding effect.)`

The magnitude of the screening effect depends upon the number of inner electrons i.e. higher the number of inner electrons, greater shall be the value of screening effect. The screening effect constant is represented by the symbol `sigma`. The magnitude of `sigma` is determined by the Slater's rules. The contribution of inner electrons to the magnitude of `sigma` is calculated in the following ways :

`text(For) ns or np text(orbital electrons)`

(i) Write the electronic configuration of the element in the following order and group them as,

`(1s), (2s quad 2p), (3s quad 3p), (3d), (4s quad 4p), (4d quad 4f), (5s quad 5p), (5d quad 5f), (6s quad 6p), etc.`

(ii) Electrons to the right of the (`ns`, `np`) group are not effective in shielding the `ns` or `np` electrons and contribute nothing to `sigma`.

(iii) All other electrons in the (`ns`, `np`) group contribute to the extent of `0.35` each to the screening constant (except for `1s` for which the value is `0.30`).

(iv) All the electrons in the (`n-1`)th shell contribute `0.85` each to the screening constant.

(v) All the electrons in the (`n-2`)th shell or lower contribute `1.0` each to the screening constant.

`text(For) d- or f- text(electrons)`

Rules (i) to (iii) remain the same but rules (iv) and (v) get replaced by the rule (vi).

(vi) All the electrons in the groups lying left to (`nd`, `nf`) group contribute `1.0` each to the screening effect.

See fig.

For `1s` electron `sigma = 0.3` for a `He` like atom which has `2` electrons

`Z_(eff) = Z - 0.3 = 1. 7`

For hydrogen atom, `sigma = 0` `Z_(eff) = Z`

As we move left to right in a periodic table the value of `Z_(eff)` increases by `0.65`.

Due to screening effect the valency electron experiences less attraction towards nucleus. This brings decrease in the nuclear charge (`Z`) actually present on the nucleus. The reduced nuclear charge is termed effective nuclear charge and is represented by `Z`*. It is related to actual nuclear charge (`Z`) by the following formula :

`Z`* = (`Z`-`sigma`), where `sigma` is screening constant.

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

2nd Period `U quad Be quad B quad C quad N quad O quad F quad Ne`

`Z quad 3 quad 4 quad 5 quad 6 quad 7 quad 8 quad 9 quad 10`

`s 1.7 quad 2.05 quad 2.42 quad 2.75 quad 3.1 quad 3.45 quad 3.8 quad 4.15`

`Z^(ast) = Z - sigma quad 1.3 quad 1.95 quad 2.6 quad 3.25 quad 3.9 quad 4.55 quad 5.2 quad 5.85`

In a subgroup of normal elements the magnitude of effective nuclear charge remains almost the same.

Alkali group `U quad Na quad K quad Rb quad Cs`

`Z quad 3 quad 11 quad 19 quad 37 quad 55`

`sigma quad 1.7 quad 8.8 quad 16.8 quad 34.8 quad 52.8`

`Z* = Z-sigma quad 1.3 quad 2.2 quad 2.2 quad 2.2 quad 2.2`