Question

The correct sequence which shows the decreasing order of the ionic radii of the elements is:
A. $A{{l}^{3+}}>M{{g}^{2+}}>N{{a}^{+}}>{{F}^{-}}>{{O}^{2-}}$
B. $N{{a}^{+}}>M{{g}^{2+}}>A{{l}^{3+}}>{{O}^{2-}}>{{F}^{-}}$
C. $A{{l}^{3+}}>M{{g}^{2+}}>N{{a}^{+}}>{{F}^{-}}>{{O}^{2-}}$
D. ${{O}^{2-}}>{{F}^{-}}>N{{a}^{+}}>M{{g}^{2+}}>A{{l}^{3+}}$

Answer 1

Hint: Ionic radius is the radius of a monatomic ion in an ionic structure. The sum of ionic radii of the anion and cation gives the distance between the ions in a lattice. Ionic radii are typically given in units of either picometers (pm) or angstroms (Å), having the value of 1 Å equals to 100 pm.

Complete step by step solution:
Depending on electric charge, ions may be larger or smaller than the neutral atom. When an atom loses an electron to form a cation then other electrons are attracted more towards the nucleus as a result of which the radius of the ion gets smaller. Similarly when an electron is added to an atom forming an anion then it increases the size of the electron cloud by interelectronic repulsion. The ionic radius is not a fixed property of a given ion; it varies with many parameters like coordination number, spin state etc. As like other types of atomic radius, ionic radii increase on down the group. Ionic size for the same ion also increases with increasing coordination number and an ion in a high-spin state will be larger than the same ion in a low-spin state. In general ionic radius decreases with increasing positive charge and increases with increasing negative charge. The elements mentioned in the question are isoelectronic species. Isoelectronic are those ions which have the same number of electrons. In a group of isoelectronic species the ionic radii decrease with increasing positive charge because with increase in positive charge effective nuclear charge also increases and we know that radius is inversely proportional to effective nuclear charge.

Thus the decreasing order of ionic radii is
 ${{O}^{2-}}>{{F}^{-}}>N{{a}^{+}}>M{{g}^{2+}}>A{{l}^{3+}}$, option D is correct.

Note: In an ionic crystal the distance between two ions can be determined by X-ray crystallography which gives the lengths of the sides of the unit cell of a crystal. The effective nuclear charge is the net positive charge experienced by an electron. The term effective is used because the shielding effect of negatively charged electrons shields the higher orbital electrons from experiencing the full nuclear charge of the nucleus by the repelling effect of inner layer electrons.