Slater's Rules

Slater's Rules are some set of empirical rules to calculate the screening constant (σ) of various electrons present in different orbitals of an atom or an ion. Once we get the value of screening constant it is easy enough to find the effective nuclear charge (Zeff).

Screening Effect and Slater's rule

    The Valence electron in a multi-electron atom is attracted by the nucleus and repelled by the electrons of inner-shells.
what values do you estimate for zeff using slater's rules?
Screening Effect
    The combined effect of this attractive and repulsive force acting on the valence electron is that the Valence - electron experiences less attraction from the nucleus. This is known as the screening effect.

Slater's Rules and its application

    Slater's rules are applicable for calculating screening constant and Zeff for atom, ions or molecules and the rules are

Slater's Rules for an electron in the nS, nP level

  1. The first to do is to write out the Electronic Configuration of Elements of the atom or the ion in the following order and grouping.
    (1S) (2S, 2P) (3S, 3P) (3d) (4S, 4P) (4d) (4f) (5S, 5P) etc. 
    It may be noted that so far as the screening effect is concerned the S and P electrons belonging to the same principal quantum shell have the same effect as advocated by Slater.
    (1S)²(2S, 2P)⁸(3S)¹

  2. An electron in a certain (nS, nP) level is screened only by electrons in the same level and by the electrons of lower energy level. Electrons lying above (nS, nP) level do not screen any (nS, nP) electron to any extent.

  3. Higher energy electrons have no screening effect on any lower energy electrons.
    Thus the screening effect of the valence electron of the Sodium atom, electronic configuration of Na atom according to slater's rule,
    (1S)² (2S, 2P)⁸ (3S)¹
    For calculation of the screening effect, Valence electron will be excluded from our Calculation.
    And for calculation of screening effect of the 2P electron of the Sodium atom, one 2P electron, and 3S electrons will be excluded from our Calculation.

  4. Electrons of an (nS, nP) level shield valence electrons in the same group by 0.35 each. This is also true for the electrons of the nd or nf that is for the electrons in the same group.

  5. Electrons belonging to one lower quantum shell, that is (n-1) shell shield the valence electrons by 0.85 each.

  6. Electrons belonging to (n-2) or still lower quantum shell shields the valence electron by 1.0 each. This means the screening effect is complete.
Slater's Rules
Slater rule for S or P electron
    Zeff of Sodium atom
    Screening Constant (σ) = (2 × 1) + (8 × 0.85) + (0 × 0.35) = 8.8
    ∴ Zeff of Sodium atom = (11 - 8.8) = 2.2

Slater's Rules for an electron in the nd, nf level

    The above rules are quite well for estimating the screening constant of S and P orbitals. However when d or f electron being shielded the (iv) and (v) rule replaced by new rules for estimation of screening constant.
    The replaced rules are, all electrons below the nd or nf level contribute 1.0 each towards the screening constant.
Slater's Rules
Slater rule for d and f  electron
    Zeff for the 4S electron of Vanadium atom
    Vanadium has atomic number 23 and the electronic configuration according to the Slater's Rules is,
    (1S)² (2S, 2P)⁸ (3S, 3P)⁸ (3d)3 (4S)² 
    We have considered only one electron of the two 4S electrons.
    ∴ Screening Constant (σ) = (2 ×1.0) + (8×1.0) + (8×0.85) + (3×0.85) + (1×0.35) = 19.7
    ∴ Zeff for Vanadium atom = (23 - 19.7) = 3.3

Slater's rules examples

  • Slater's rules for Sodium ion
    Electronic configuration of Na⁺ ion (1S)²(2S, 2P)⁸
    Screening Constant (σ) = (2 × 1) + (8 × 0.85) + (0 × 0.35) = 8.8
    Zeff for sodium ion = (11 - 8.8) = 2.2
  • Slater's rules for 2P electron of Sodium
    Electronic configuration of Na⁺¹ ion (1S)²(2S, 2P)⁸(3S)¹
    Screening Constant (σ) = (2 × 0.85) + (7 × 0.85) = 4.15
    Zeff for 2P electron of sodium = (11 - 4.15) = 6.85
  • Slater's rules for Magnesium ion
    Electronic configuration of Mg⁺² ion (1S)²(2S, 2P)⁸
    Screening Constant (σ) = (2 × 0.85) + (8 × 0.85) = 4.50
    Zeff for Magnesium ion = (12 - 4.50) = 7.50
  • Slater's rules for Potassium ion
    Electronic configuration of K⁺¹ ion (1S)²(2S, 2P)⁸(3S, 3P)⁸
    Screening Constant (σ) = (2× 1) + (8 × 0.85) + (8 × 0.35) = 11.6
    Zeff for Pottassium ion = (19 - 11.6) = 7.40
  • Slater's rules for valence electron of Fluorine
    Electronic configuration of K⁺¹ ion (1S)²(2S, 2P)⁷
    Screening Constant (σ) = (2 × 0.85) + (6 × 0.35) = 3.80
    Zeff for for valence electron of fluorine = (9 - 3.8) = 5.20
  • Slater's rules for Fluoride ion
    Electronic configuration of F⁻ ion (1S)²(2S, 2P)⁸
    Screening Constant (σ) = (2 × 0.85) + (8 × 0.35) = 4.50
    Zeff for for valence electron of fluorine = (9 - 4.50) = 4.50
  • Slater's rules for 3d electron of Vanadium
    Electronic configuration of Vanadum (1S)²(2S, 2P)⁸(3S, 3P)⁸(3d)³(4S)²
    Screening Constant (σ) = (2 ×1.0) + (8×1.0) + (8×1.0) + (2 ×0.35) = 18.70
    Zeff for for vanadium = (23 - 18.70) = 4.30
  • Slater's rules for Vanadium(II) ion
    Electronic configuration of Vanadum (1S)²(2S, 2P)⁸(3S, 3P)⁸(3d)³
    Screening Constant (σ) = (2 ×1.0) + (8×1.0) +(8×1.0) + (3×0.35)= 19.05
    Zeff for for vanadium = (23 - 19.05) = 3.95

Slater's Rules Questions Answers

  • Questions
    In the first transition series electron filling up process begins in the 3d level below a filled 4S² level. During ionization process will a 4S electron or a 3d electron be lost first? Explain with reference to chromium.
  • Answer
    Chromium has atomic number 24 and the electronic configuration according to the Slater's Rule is
    (1S)² (2S, 2P)⁸ (3S, 3P)⁸ (3d)⁵ (4S)¹
    ∴ Screening Constant (σ) for the 4S electron of Chromium atom
    = (2×1.0) + (8×1.0) + (8×0.85) + (5×0.85) + (0×0.35) = 21.05
    Thus Zeff for the 4S electron of chromium atom = (24 - 21.05) = 2.95
    ∴ Screening Constant (σ) for the 3d electron of Chromium atom
    = (2×1.0) + (8×1.0) + (8×1.0) + (3×0.85) + (4×0.35) = 19.40
    Thus Zeff for the 4S electron of chromium atom = (24 - 19.40) = 4.60
    Hence 3d electron is more tightly held than a 4S electron. So during ionisation, the 4S electron will be lost.
  • Question
    Calculate the effective nuclear charge of the hydrogen atom.
  • Answer
    The hydrogen atom has a single 1S valence electron. There is no other electron to screen it from the nuclear charge of a single proton.
    Thus, σ = 0 and Zeff = 1.0 - 0 = 1.0
    Thus hydrogen electron sees the full nuclear charge of the nucleus, that is the electron is totally exposed to the proton.
  • 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 is:
C (1S)² (2S, 2P)⁴
N (1S)² (2S, 2P)⁵
O (1S)² (2S, 2P)⁶
    In carbon, the 2P electron is screened by 1S² 2S² 2P¹ electrons while in Nitrogen and Oxygen this is done by 1S² 2S² 2P² and 1S² 2S² 2P³ electrons respectively.
Thus Zeff for Nitrogen
= Zeff for carbon + (1 nuclear charge) - Screening due to one 2P electron
= Zeff for Carbon + 1 - 0.35
= Zeff for Carbon + 0.65 and Zeff for Oxygen
= Zeff for Nitrogen + 0.65
    Thus effective nuclear charge will go up by the same amount from carbon to Nitrogen and then to Oxygen.
    For more questions answers on Slater's Rules

Screening Effect, effective nuclear charge and Slater's Rules for the Calculation of the Screening Constant with problems and their solutions

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