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What is Slater's rule in chemistry?

Published in Slater's Rules 3 mins read

Slater's rules are a set of empirical guidelines used in chemistry to estimate the effective nuclear charge experienced by an electron in a multi-electron atom.

Understanding Effective Nuclear Charge

The effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a polyelectronic atom. Because of shielding effects, the effective nuclear charge is always less than the actual nuclear charge (Z).

Slater's rules provide a way to calculate this Zeff. According to Slater, the Zeff acting on a given electron is calculated by subtracting the screening constant (S) from the atomic number Z (nuclear charge):

Zeff = Z - S

Where:

  • Zeff is the effective nuclear charge.
  • Z is the atomic number (number of protons in the nucleus).
  • S is the screening constant, also known as the shielding constant. This represents the shielding effect of the other electrons in the atom.

How to Determine the Screening Constant (S) Using Slater's Rules

Slater's rules outline a series of steps to determine the value of S for a specific electron:

  1. Write the electron configuration: Group the electrons as follows:

    (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) ...

  2. Electrons to the right: Electrons in groups to the right of the electron of interest do not contribute to the screening constant.

  3. Electrons within the same group:

    • Each other electron in the same (ns, np) group contributes 0.35 to S.
    • Each other electron in the same (nd) or (nf) group contributes 0.35 to S.

  4. Electrons to the left:

    • If the electron of interest is an (ns) or (np) electron:
      • Each electron in the (n-1) shell contributes 0.85 to S.
      • Each electron in the (n-2) or lower shells contributes 1.00 to S.
    • If the electron of interest is an (nd) or (nf) electron:
      • Each electron in a group to the left contributes 1.00 to S.

Example: Calculating Zeff for a 3p electron in Chlorine (Cl)

Chlorine (Cl) has an atomic number (Z) of 17. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁵.

  1. Group the electrons: (1s²) (2s², 2p⁶) (3s², 3p⁵)

  2. We are interested in a 3p electron, so we focus on the (3s², 3p⁵) group.

  3. Screening Constant (S) Calculation:

    • Electrons to the right: None.
    • Electrons in the same group (3s², 3p⁵): There are 6 other electrons (2 in 3s and 4 in 3p). Each contributes 0.35. So, 6 * 0.35 = 2.10.
    • Electrons in the (n-1) shell (2s², 2p⁶): There are 8 electrons. Each contributes 0.85. So, 8 * 0.85 = 6.80.
    • Electrons in lower shells (1s²): There are 2 electrons. Each contributes 1.00. So, 2 * 1.00 = 2.00.

    Therefore, S = 2.10 + 6.80 + 2.00 = 10.90

  4. Effective Nuclear Charge (Zeff) Calculation:

    Zeff = Z - S = 17 - 10.90 = 6.10

Therefore, the effective nuclear charge experienced by a 3p electron in Chlorine is approximately 6.10.

Significance of Slater's Rules

Slater's rules, though a simplification, are valuable for:

  • Providing a basic understanding of electron shielding.
  • Estimating relative atomic and ionic sizes.
  • Explaining trends in ionization energies.
  • Offering a conceptual framework for understanding chemical reactivity.

While more sophisticated computational methods exist for calculating effective nuclear charge, Slater's rules offer a quick and insightful approach.

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