Determine Screening Constant and Effective Nuclear Charge

In many atoms, each electron is said to experience less than the actual nuclear charge because of shielding or screening by the other electrons. For each electron in an atom, Slater's rules provide a value for the screening constant, denoted by σ.

The effective nuclear charge may be defined as the actual nuclear charge (Z) minus the screening effect caused by the electrons intervening between the nucleus and valence electron.

Effective nuclear charge, Z* = Z - σ Where, Z= Atomic number, σ = Shielding or screening constant.

To calculate the effective nuclear charge (Z*) we need the value of screening constant (σ) which can be calculated by using following rules.

Steps

  1. Write down the electronic configuration of the element as shown below.
    • (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) (5d)…
    • Fill the electrons according to Aufbau principle.
      • Any electrons to the right of the electron of interest do not contribute to shielding constant.
      • The shielding constant for each group is formed as the sum of the following contributions:
        • All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units except 1s group, where the other electron contributes only 0.30.
        • If the group is of the [s, p] type, an amount of 0.85 from each electron (n-1) shell and an amount of 1.00 for each electron from (n-2) and lower shell.
        • If the group is of the [d] or [f] type then an amount of 1.00 for each electron from all lying left to that orbital.
  2. For example: (a) Calculate effective nuclear charge in Nitrogen for 2p electron.
    • Electronic configuration- (1s2) (2s2, 2p3).
    • Screening constant, σ = (0.35 × 4) + (0.85 × 2) = 3.10
    • Effective nuclear charge, Z* = Z – σ = 7 – 3.10 = 3.90
  3. (b) Calculate effective nuclear charge and screening constant seen in 3p electron in Silicon.
    • Electronic configuration- (1s2) (2s2, 2p6)(3s2, 3p2).
    • σ = (0.35 × 3) + (0.85 × 8) + (1 × 2) = 9.85
    • Z* = Z – σ = 14 – 9.85 = 4.15
  4. (c) Calculate effective nuclear charge in Zinc for 4s electron & for 3d electron.
    • Electronic configuration- (1s2) (2s2, 2p6)(3s2, 3p6)(3d10)(4s2).
    • For 4s electron,
    • σ = (0.35 × 1) + (0.85 × 18) + (1 × 10) = 25.65
    • Z* = Z – σ = 30 – 25.65 = 4.35
    • For 3d electron,
    • σ = (0.35 × 9) + (1 × 18) = 21.15
    • Z* = Z – σ = 30 – 21.15 = 8.85
  5. (d) Calculate effective nuclear charge on one of 6s electron in tungsten. (At. No. =74)
    • Electronic configuration- (1s2) (2s2, 2p6)(3s2, 3p6)(4s2, 4p6) (3d10) (4f14) (5s2, 5p6)(5d4), (6s2)
    • σ = (0.35 × 1) + (0.85 × 12) + (1 × 60) = 70.55
    • Z* = Z – σ = 74 – 70.55 =3.45
Image: Wikihow

Tips

  • Read about shielding effect, screening constant, effective nuclear charge, Slater's rule, etc.
  • If there is only one electron in an orbit there will be no screening effect taking place. Again, if the number of electrons present is an odd number, then subtract one to obtain the actual quantity to be multiplied to get the screening effect.

Warnings

  • Though these rules may appear confusing, writing the proper electronic configuration will help ensure success.

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Sources and Citations

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