Question

Effective nuclear charge (${{\text{Z}}^{*}}$) can be calculated by using the formula:
A. ${{\text{Z}}^{*}}\text{=Z - S}$
B. ${{\text{Z}}^{*}}\text{=Z + S}$
C. ${{\text{Z}}^{*}}\text{=S - Z}$
D. $\text{Z=}{{\text{Z}}^{*}}\text{ -S}$

Answer 1

Hint:. We need to first see what is an effective nuclear charge. The effective nuclear charge is the net positive charge experienced by the valence electrons. Its value is less than nuclear charge.

Complete step by step answer:
The effective nuclear charge which is represented by (${{\text{Z}}^{*}}\text{or }{{\text{Z}}_{\text{eff}}}$) is the net positive charge experienced by an electron in a polyelectronic atomic structure. Term "effective" means that the shielding effect of electrons prevents electrons which are present in higher orbitals to experience complete nuclear charge of the nucleus due to repulsion of inner layer electrons. The effective nuclear charge is also known as core charge. The strength of the nuclear charge can be determined by the oxidation number of that atom. The physical and chemical properties of the elements can be expressed by its electronic configuration.
Let us see how the effective nuclear charge is determined. An atom with one electron experiences the full charge of the nucleus. But in an atom with many electrons, the outer electrons are attracted to positive nuclei and are simultaneously repelled by the electrons. The effective nuclear charge on that electron is:
${{\text{Z}}_{\text{eff}}}\text{=Z - S}$; where Z is the number of protons and S is the shielding constant. Shielding constant has different contribution for different orbitals can be determined by Slater’s rule-

Slater’s Rule	Electron is s or p orbitals	Electrons in d or f orbitals
Value of shielding experienced by electrons	${{\text{e}}^{-}}$ in n group	${{\text{e}}^{-}}$ in 1s orbital	${{\text{e}}^{-}}$ in n-1 group	${{\text{e}}^{-}}$ in n-2 or lower group	${{\text{e}}^{-}}$ in n group or same group	${{\text{e}}^{-}}$ in lower groups
	0.35	0.3	0.85	1.00	0.35	1.00

So, the correct answer is “Option A”.

Note: The trend in effective nuclear charge is
-Increases across a period because increase in nuclear charge is not supported by increase in shielding effect.
-Decreases down a group; nuclear charge increases down the group.