# Slater’s rule shielding

### Slater’s rule shielding constant

Slater’s rules are empirical rules to calculate the shielding constant of various electrons present in different orbitals of an atom or an ion.

The valence electrons for a multi-electron atom attracted by the nucleus of an atom and repelled by the electrons from inner-shells.

This attractive and repulsive force acting on the valence electrons experience less attraction from the nucleus of an atom. Larger the number of inner electrons, lesser will be the attraction between the nucleus and outer electrons.

The inner electrons which shielded the force of attraction between the nucleus and valence electron are known shielding electrons and the effect is known as the shielding effect or screening effect.

Thus the nuclear charge of an atom or ion is less than the actual nuclear charge and can easily be calculated by the following equation.

∴ Effective nuclear charge = Z – σ

where σ = shielding constant.

### How do you find an effective nuclear charge using Slater’s rule?

Effective nuclear change means the net positive charge which affects the attraction of outer electrons from the nucleus of polyelectronic atom. The term effective is used because the shielding electrons prevent the attraction of outer orbital electrons of an atom.

Slater’s rules are applicable for calculating the value shielding constant and effective nuclear charge of an electron in an atom or ion.

#### S and P valence electrons

1. The first we write the electron configuration of elements of the atom or ion in the following order and grouping.
(1S) (2S, 2P) (3S, 3P) (3d) (4S, 4P) (4d) (4f) (5S, 5P) etc.
The shielding effect concerned the nS and nP electron belonging to the same principal quantum level have the same effect advocated by Slater.
(1S)²(2S, 2P)⁸(3S)¹
2. Electron in a certain nS, nP level is screened only by electrons at the same level and by the electrons of lower energy levels of an atom, or ion.
Electrons lying above nS, nP level do not shield any nS, nP electron to any extent.
3. Electrons of higher energy levels did not shield the lower-energy level of an atom. For calculating the value screening constant of the valence electron of a sodium atom, the electronic configuration of the sodium atom
(1S)² (2S, 2P)⁸ (3S)¹.
The value of the shielding constant for the 3P-electrons, the valence electron or 3S electron will be excluded from our calculation.
4. Electrons lying nS and nP atomic level shield a valence electron in the same group by 0.35 each. This rule also true for the electrons of the nd or nf atomic level of atom or ion.
5. Electrons belonging to one lower quantum level, that is (n-1) level shield the valence electron by 0.85 each.
6. Electrons belonging to (n-2) or still lower quantum shell shields the valence electron by 1.0 each.

#### Screening constant for sodium atom

= (2 × 1) + (8 × 0.85) + (0 × 0.35)
= 8.8.

Thus Z effective of sodium atom = (11 – 8.8)
= 2.2

Question
Comment on the variation in effective nuclear charge for a 2P electron from carbon to oxygen.

Electronic distribution according to the Slater’s rule

Carbon
(1S)² (2S, 2P)⁴

Nitrogen
(1S)² (2S, 2P)⁵

Oxygen
(1S)² (2S, 2P)⁶

In carbon atom, the 2P electron shield by 1S² 2S² 2P¹ electrons while in nitrogen and oxygen this is done by 1S² 2S² 2P² and 1S² 2S² 2P³ electrons respectively.

Zeff of nitrogen = Zeff of carbon + (1 nuclear charge) – shielding due to one 2P electron

Zeff of nitrogen = Zeff of carbon + 1 – 0.35

= Zeff of carbon + 0.65 and Zeff of oxygen

= Zeff of nitrogen + 0.65

The effective nuclear charge will go up by the same amount from carbon to nitrogen and then to oxygen.

#### d and f sublevels of atoms and ions

Previous rules are quite well for estimating the screening constant of S and P orbitals. However when shielding by d subshell or f subshell the four and five rule replaced by new rules for the estimation of screening constant.

The new rules are, all electrons below the nd subshell or nf-subshell contribute 1.0 each towards the screening constant.

#### 4s and 3d subshell of an atom

Vanadium has atomic number 23 and the electronic configuration according to the Slater’s rules

(1S)² (2S, 2P)⁸ (3S, 3P)⁸ (3d)3 (4S)²

∴ Screening constant for 4S electron of vanadium
= (2 ×1.0) + (8×1.0) + (8×0.85) + (3×0.85) + (1×0.35)
= 19.7

Thus the effective nuclear charge for 4S electron of vanadium

(23 – 19.7)
= 3.3

Screening constant for 3d electron of vanadium
= (2 ×1.0) + (8×1.0) + (8×1.0) + (2 ×0.35)
= 18.70

The effective nuclear charge for 3d electron of vanadium
= (23 – 18.70)
= 4.30

#### Why 3d subshell has more energy than 4S?

In the first transition series electron filling up process begins in the 3d energy level below a filled 4S energy level. During the ionization process, 4S electron will be lost first. We can explain this with the reference to chromium.

Chromium has atomic number 24 and the electronic configuration

(1S)² (2S, 2P)⁸ (3S, 3P)⁸ (3d)⁵ (4S)¹

∴ Screening constant for 4S electron of chromium
= (2×1.0) + (8×1.0) + (8×0.85) + (5×0.85) + (0×0.35)
= 21.05

Thus the effective nuclear charge for 4S electron of chromium atom

= (24 – 21.05)
= 2.95

∴ Screening constant for 3d electron of chromium atom

= (2×1.0) + (8×1.0) + (8×1.0) + (3×0.85) + (4×0.35)
= 19.40

Effective nuclear charge for 4S electron of chromium atom

= (24 – 19.40)
= 4.60

Shielding of 3d subshell electron lower than 4S subshell. From this study, it is clearly indicated that 3d electron more tightly bound within the nucleus than 4S electron.

Thus during the ionization less tightly bound electron losses first. So during the ionization process, 4S electron of energy level loses first than the 3S energy level.

#### Slater’s rule practice problems

1 Slater's rule practice Set

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#### Slater's rules for effective nuclear charge

Effective nuclear charge of sodium ion

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what is the effective nuclear charge of fluorine ion

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Effective nuclear charge of magnesium ion

5 / 7

what is the effective nuclear charge of fluorine

6 / 7

Effective nuclear charge of potassium ion

7 / 7

Effective nuclear charge of the hydrogen atom