Content

• Steps
• Tips
• Warnings

As you know, in many atoms, each electron is affected by an attractive force somewhat less than the true charge of the nucleus, which is due to the effect of the screening exerted by other electrons of the atom. By applying Slater's rule, we can calculate the screening constant, denoted by the letter σ, for each electron in the atom.

The effective charge of a nucleus can be defined as the difference between the true charge of the nucleus (Z) and the screening effect of electrons rotating between the nucleus and the valence electron.

The effective charge of the nucleus is calculated by the formula Z * = Z - σ where, Z = atomic number, σ = screening constant.

In order to calculate the effective nuclear charge (Z *), we need the value of the screening constant (σ), which can be obtained using the following rules.

Steps

1. 1 Record the electronic configuration of the item as shown below.
   • (1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) (5d) ...
   • Arrange the electrons according to the Klechkovsky rule.
     • Any electrons to the right of the electron of interest have no effect on the screening constant.
     • The shielding constant for each group is calculated as the sum of the following components:
       • All other electrons in the same group with the electron of interest to us screen 0.35 nuclear charge units. An exception is the 1s group, where one electron is counted only as 0.30.
       • In the case of a group belonging to the [s, p] type, take 0.85 units for each electron (n-1) of the shell and 1.00 unit for each electron (n-2) and the following shells.
       • In the case of a group belonging to the [d] or [f] type, take 1.00 unit for each electron to the left of this orbital.
2. 2 For example: (a) Calculate the effective nuclear charge for 2p in the nitrogen atom.
   • Electronic configuration - (1s) (2s, 2p).
   • Shielding constant, σ = (0.35 × 4) + (0.85 × 2) = 3.10
   • Effective nuclear charge, Z * = Z - σ = 7 - 3.10 = 3.90
3. 3 (b) Calculate the effective nuclear charge and screening constant for a 3p electron in a silicon atom.
   • Electronic configuration - (1s) (2s, 2p) (3s, 3p).
   • σ = (0,35 × 3) + (0,85 × 8) + (1 × 2) = 9,85
   • Z * = Z - σ = 14 - 9.85 = 4.15
4. 4 (c) Calculate the effective nuclear charge for the 4s electron and for the 3d electron in the zinc atom.
   • Electronic configuration - (1s) (2s, 2p) (3s, 3p) (3d) (4s).
   • For a 4s electron,
   • σ = (0,35 × 1) + (0,85 × 18) + (1 × 10) = 25,65
   • Z * = Z - σ = 30 - 25.65 = 4.35
   • For a 3d electron,
   • σ = (0,35 × 9) + (1 × 18) = 21,15
   • Z * = Z - σ = 30 - 21.15 = 8.85
5. 5 (d) Calculate the effective nuclear charge for one of the 6s electrons of tungsten (Atomic number = 74)
   • Electronic configuration - (1s) (2s, 2p) (3s, 3p) (4s, 4p) (3d) (4f) (5s, 5p) (5d), (6s)
   • σ = (0,35 × 1) + (0,85 × 12) + (1 × 60) = 70,55
   • Z * = Z - σ = 74 - 70.55 = 3.45

Tips

• Read more about the shielding effect, shielding constant, effective nuclear charge, Slater's rule and other chemical quantities.
• If there is only one electron in the orbital, then there is no screening effect. In case an atom contains an odd number of electrons, the number must be reduced by one before you multiply it by the appropriate number to get the actual shielding effect.

Warnings

• While all of these rules may seem daunting to you, writing the correct electronic configuration will help you succeed.