Question

Ionic radii are?
A. Inversely proportional to square of effective nuclear charge
B. Directly proportional to the effective nuclear charge
C. Directly proportional to square of effective nuclear charge
D. Inversely proportional to effective nuclear charge

Answer 1

Hint: Suppose If a quantity, X increases with respect to increase in other quantity Y and vice versa, then quantity X is called as directly proportional to Y, and when A quantity, X decreases with respect to increase in other quantity Y and vice versa, the X is called as, inversely proportional to Y. Now, think what could be the relation between the quantities given in the question.

Complete step by step answer:

Ionic radii - The ionic radius is half the distance between atomic ions in a crystal lattice. To find the value, ions are treated as if they were hard spheres.
You should know that the size of an element's ionic radius follows a predictable trend on the periodic table.

The effective nuclear charge - Nuclear charge is the charge exerted by the nucleons(i.e. protons and neutrons). For elements having less atomic number, there is no significant difference between effective nuclear charge and nuclear charge.
But when the atomic number increases (shells get bigger, and s, p,d, and f orbitals are involved) due to the penetration effect of the inner orbitals, the total charge of the nucleus is shielded. So something less than the actual nuclear charge is exerted which is called Effective Nuclear Charge.
${ r }_{ n }\quad =\quad \dfrac { { n }^{ 2 }{ a }_{ 0 } }{ Z }$ or ${ r }_{ n }\quad \propto \quad \dfrac { 1 }{ Z }$
This is the relation between ionic radius and effective nuclear charge.
Here n is the principal quantum number and Z is the effective nuclear charge.
So we can conclude that the radius of the ion depends on the effective nuclear charge, more the charge, more heavily the electrons are attracted towards the center and lesser in the size. Hence the ionic radii are inversely proportional to the effective nuclear charge.

Therefore, the correct answer is option D.

Note: We should also know that Ionic radius increases as the screening effect increases. Hence, Ionic radius is directly proportional to the screening effect.
Screening effect - Screening effect is also known as the shielding effect. This phenomenon occurs when the nucleus reduces its force of attraction on the valence electrons due to the presence of electrons in the inner-shell.
Penetration effect - Penetration effect is the penetration of nuclear charge through the orbitals which attracts the outermost shell electrons.
The penetration effect is opposite to the shielding effect. s orbital has the highest shielding power and d orbital has less shielding power due to double-lobed structure.