Shielding electrons and Slater's rules

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What is the Slater's rules for shielding electrons?

A study of valence electrons for a multi-electron atom attracted by the nucleus of an atom and repelled by the electrons from inner-shells.
Shielding effect and Slater's rules
Shielding electrons and Slater's rules
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.

To study shielding electron, Slater's set some empirical rules to calculate the shielding or screening of various electrons present in different orbitals of an atom or an ion.

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 to calculate the effective atomic number?

This article is an important article for school and college-level courses in different schools and universities.

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.

nS and nP level electron of an atom or ion

  1. The first we write the electronic 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.
Shielding effect in nS, nP subshell of an atom
Shielding effect in nS, nP subshell

Screening constant for sodium atom
= (2 × 1) + (8 × 0.85) + (0 × 0.35)
= 8.8.

∴ Z effective of sodium atom = (11 - 8.8)
= 2.2.
Question
How to calculate the effective nuclear charge of the hydrogen atom?

Answer
The hydrogen atom has a single 1S valence electron. There are no other electrons to shield it from the nuclear charge of a single proton.

∴ Shielding constant = 0
Zeff = 1.0 - 0 = 1.0.

Thus hydrogen electron sees the full nuclear charge of the nucleus and the electron totally exposed to the proton.

Sodium, potassium, and magnesium ion

Electronic configuration of sodium ion or Na⁺
(1S)²(2S, 2P)⁸.

Screening constant of sodium ion
= (2 × 0.85) + (8 × 0.35)
= 4.5.

Effective nuclear charge of sodium ion
= (11 - 4.5)
= 4.5.

Electronic configuration of potassium ion
(1S)²(2S, 2P)⁸(3S, 3P)⁸.

Screening constant of potassium ion or K⁺
= (2× 1) + (8 × 0.85) + (8 × 0.35)
= 11.6.

Effective nuclear charge of potassium ion
= (19 - 11.6)
= 7.40.

Electronic configuration of magnesium ion or Mg⁺²
(1S)²(2S, 2P)⁸

Screening constant of magnesium ion
= (2 × 0.85) + (8 × 0.85)
= 4.50.

Effective nuclear charge of Magnesium ion
= (12 - 4.50)
= 7.50.

Valence electron of fluorine and fluoride ion

Electronic configuration of fluorine atom
(1S)²(2S, 2P)⁷

Screening constant (σ) of fluorine atom
= (2 × 0.85) + (6 × 0.35)
= 3.80.

Effective nuclear charge for valence electron of fluorine
= (9 - 3.8)
= 5.20.

Electronic configuration of fluoride ion
(1S)²(2S, 2P)⁸

Screening constant (σ) of  fluoride ion
= (2 × 0.85) + (8 × 0.35)
= 4.50.

Effective nuclear charge of fluoride ion
= (9 - 4.50)
= 4.50.
Question
Comment on the variation in effective nuclear charge for a 2P electron from carbon to oxygen.

Answer
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.

Chemistry articles for school-college courses

nd, nf-sublevel of an atom or ion

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.
Shielding effect in nd, nf subshell of an atom
Shielding effect in nd, nf subshell

4S and 3d electron of the vanadium 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.

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

d-subshell of vanadium(II) ion

Electronic configuration of vanadium ion
(1S)²(2S, 2P)⁸(3S, 3P)⁸(3d)³

Screening constant (σ)  of vanadium(II) ion
= (2 ×1.0) + (8×1.0) +(8×1.0) + (3×0.35)
= 19.05.

Effective nuclear charge of vanadium(II) ion
= (23 - 19.05)
= 3.95.

Why the electron of the 4S energy level lost first?

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.

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.

Shielding effect and Slater's rules, shielding electrons of s, p, and d energy level and hydrogen for the study of school, college-level courses

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