Effective Nuclear Charge – Definition And Calculation

What is Effective Nuclear Charge?

According to classical electrostatics, the field that arises from a spherical distribution of charge is equivalent to field generated by a single point charge at the center of the distribution. The actual charge of the nucleus is reduced by this negative charge from Z to Z_eff, where Z_eff is called the effective nuclear charge.

Z_eff depends on the values of n and ℓ because e^– in different shells and subshells approach the nucleus to different extents. This reduction from true nuclear charge by other electrons is called shielding and the effective nuclear charge is explained in terms of the shielding constant, σ.

Z* or Z_eff. = Z – σ

Rules for calculation of Screening Constant (s)

1. Write the electronic configuration of the element in order of increasing quantum numbers n and ℓ, as follows-
   (1s) (2s, 2p) (3s, 3p) (3d) (4s 4p) (4d) (4f) (and so on)
2. Electrons in groups to the right of the e^– under consideration do not shield electrons to their left. Hence contribute nothing to σ.
3. For electrons in a ns or np subshell
   1. All the other electrons in same group contribute 0.35 to the value of  for each other electron in the group.
   2. Each e^– in (n –1) groups contributes 0.85 to σ.
   3. Each e^– in (n – 2) or lower groups gives a contribution of 1.00 to σ.
4. For electrons in nd and nf subshell
   1. All other electrons in the same d-subshell/ f-subshell contribute 0.35 to σ.
   2. Each electron in groups to left contributes 1.00 to σ.