Question

Calculate the screening constant and effective nuclear charge of 4s and 3d electrons of Zn?

Answer 1

As we know that screening constant is the summation of contribution of each electron in screening from the force of the nucleus according to Slater's Rule. The contribution of electrons of each orbital is different and its values are provided by Slater’s Rule. Also effective nuclear charge can be defined as the net attraction or net positive charge experienced by an electron in a multi-electron atom.
Formula used:
Effective nuclear charge (${{Z}_{eff}}=Z-\sigma$ )
where,
Z = Atomic number of an atom
$\sigma$= Screening constant

Complete answer:
Let us first discuss about screening constant and effective nuclear charge:-
-Screening constant (denoted by $\sigma$ ) can be described as the measure of screening of electrons from the force of the nucleus. It is the effect of the electron with respect to its position in the atom whereas effective nuclear charge is the net attraction or net positive charge experienced by an electron in a multi-electron atom.
-Slater’s rule tells us about the contribution made by every electron in the screening of other electrons. These values are as follows:-
(A) For ‘s’ or ‘p’ sub-shell:-
Electrons present in outermost shell: 0.35
Electrons present in ${{(n-1)}^{th}}$ shell: 0.85
Electrons present in remaining shells: 1
(B) For ‘d’ or ‘f’ sub-shell:-
Electrons present in outermost shell: 0.35
Electrons present in remaining shells: 1
-Calculation of screening constant and effective nuclear charge of 4s and 3d electron of Zn (atomic number = 30):-
Electronic configuration of Zn = $1{{s}^{2}}/2{{s}^{2}}2{{p}^{6}}/3{{s}^{2}}3{{p}^{6}}3{{d}^{10}}/4{{s}^{2}}$

(A) For 4s sub-shell:-
Number of electrons present in outermost shell: 1 (since 1 electron is already experiencing the screening force)
Number of electrons present in ${{(n-1)}^{th}}$ shell: 18
Number of electrons present in remaining shells: 10
Since, screening effect is the summation of the contribution made by each electron.
Therefore, $\sigma$= 1(0.35) + 18(0.85) + 10(1) = 25.65
Effective nuclear charge (${{Z}_{eff}}=Z-\sigma$ )
= ${{Z}_{eff}}= 30-25.65$= 4.35

(B) For 3d sub-shell:-
Number of electrons present in outermost shell: 9 (since 1 electron is already experiencing the screening force)
Number of electrons present in remaining shells: 18
Since, screening effect is the summation of the contribution made by each electron.
Therefore, $\sigma$= 9(0.35) + 18(1) = 21.15
Effective nuclear charge (${{Z}_{eff}}=Z-\sigma$ )
= ${{Z}_{eff}}= 30-21.15$= 8.85

Note:
While solving screening effect questions, always arrange the electronic configuration according to the shell number.
-We generally get confused that shielding effect is the screening effect, but they are not the same. Every electron in the atom is constantly attracted by the nucleus however, the electrons act as a repulsive force in between which leads to net decrease in the force of attraction. So, shielding effect is the decrease in the effective nuclear charge due to inner electrons whereas screening effect is the decrease in nuclear pull which is felt by the electron as the size keeps increasing.