Question

${O^{2 - }}$ and $S{i^{4 + }}$ are isoelectronic ions. If the ionic radius of ${O^{2 - }}$ is $1{A^o}$, the ionic radius of $S{i^{4 + }}$ will be:
A.$1.4{\text{ }}{A^o}$
B.$0.41{\text{ }}{A^o}$
C.$2.8{\text{ }}{A^o}$
D.$1.5{\text{ }}{A^o}$

Answer 1

Isoelectronic ions are the ones which have a similar electronic configuration. To find the radius of isoelectronic species we first need to calculate the ratio of atomic number to number of electrons. The larger the ratio smaller is the size of the ion.

Complete step by step answer:
Let’s start with discussing the isoelectronic ions for better understanding of the question. Isoelectronic ions are the ones which have a similar electronic configuration.
In the question we are given $2$ species which are ${O^{2 - }}$ and $S{i^{4 + }}$ both are having the similar electronic configuration which is $1{s^2}2{s^2}2{p^6}$. We are given with the radius of ${O^{2 - }}$ ion which is $1{A^o}$, we need to find the radius of $S{i^{4 + }}$. To find the radius of isoelectronic species we first need to calculate the ratio of atomic number to number of electrons. The larger the ratio smaller is the size of the ion. So the ratio for ${O^{2 - }}$ is given below,
${O^{2 - }} \Rightarrow \dfrac{z}{e} = \dfrac{8}{{10}} = 0.8$, the atomic number $z$ of $O$ is $8$ and the number of electron is $8 + 2 = 10$.
Similarly for $S{i^{4 + }}$, the ratio will be
$S{i^{4 + }} \Rightarrow \dfrac{z}{e} = \dfrac{{14}}{{10}} = 1.4$, the atomic number $z$ of $Si$ is $14$ and the number of electron in $S{i^{4 + }}$ is$14-4 = 10$.
Since the ratio of $S{i^{4 + }}$ is greater than ${O^{2 - }}$, its size will be smaller than ${O^{2 - }}$, hence the size of $S{i^{4 + }}$ will be smaller than ${O^{2 - }}$. So, the size of $S{i^{4 + }}$ will be less than $1{A^o}$.
$\therefore$ The answer to this question is option B. $0.41{A^o}$.

Note:
The reason behind the reducing size as the ratio between atomic number to number of electron increases is that, the atomic number of any species remain the same as it’s the number of proton present in it but the number of electron can be changed, so if the atom accepts electron due to electron-electron repulsion in outermost orbit the size of electron increases whereas if the atoms are donated then the inward attractive force of the atom increases as there are more proton than electron results in smaller size.