Question

The following question is based on $Sc\;(Z = \;21)$ For any $1s$ electron, ${{\text{Z}}^{\text{*}}}$ (effective nuclear charge) is :
A.$20.65$
B.$16.85$
C.$9.75$
D.$3.00$

Answer 1

To answer this question, you should recall the concept of screening effect and Slater’s Rule. This decrease in the force of attraction exerted by the nucleus on the valence electrons due to the presence of electrons in the inner shells is called screening effect or shielding effect
The formula used:
${{\text{Z}}_{{\text{eff}}}} = {\text{Z}} - {\text{S}}$ where ${\text{Z}}$ = atomic number and ${\text{S}}$= screening constant

Complete step by step answer:
In a multielectron atom, the electrons of the valence shell are attracted to the nucleus and also these electrons are repelled by the electrons present in the inner shells. According to Slater's Rule the actual charge felt by an electron is a little less due to a certain amount of charge and repulsion from other electrons. Slater's rules allow you to estimate the effective nuclear charge ${{\text{Z}}_{{\text{eff}}}}$ from the real number of protons in the nucleus and the effective shielding of electrons in each orbital shell.
Effective nuclear charge ${{\text{Z}}_{{\text{eff}}}} = {\text{Z}} - {\text{S}}$ where ${\text{Z}}$ = atomic number and ${\text{S}}$= screening constant
The value of ${\text{S}}$ for different orbits-
= $0.35$per electron for an electron in ${n^{th}}$orbit.
= $0.85$per electron for electrons in ${\left( {n{\text{ }} - {\text{ }}1} \right)^{th}}\;$orbit
= $1.00$per electron for electrons in ${\left( {n{\text{ }} - {\text{ }}2} \right)^{th}},{\text{ }}{\left( {n{\text{ }} - {\text{ }}3} \right)^{th}},{\text{ }}{\left( {n{\text{ }} - {\text{ }}4} \right)^{th}}$orbit
= $0.30$per electron in 1s-orbital (when alone)
So, for $1s$ electron
${{\text{Z}}_{{\text{eff}}}} = 21 - 0.35 = 20.65$.

Hence, the correct option is A.

Note:
The electronic configuration of elements is based on majorly 3 rules:
According to the Pauli exclusion principle in an atom, no two electrons will have an identical set or the same quantum numbers. There salient rules of Pauli Exclusion Principle are that only two electrons can occupy the same orbital and the two electrons that are present in the same orbital should be having opposite spins.
According to Hund’s Rule of Maximum Multiplicity rule for a given electronic configuration of an atom, the electron with maximum multiplicity falls lowest in energy.
According to the Aufbau principle, the electrons will start occupying the orbitals with lower energies before occupying higher energy orbitals.