The correct order for the size of Fe^{3+}, Fe, and Fe^{2+} ions is $(1)$ $Fe^{3+} < Fe^{2+} < Fe$.
When comparing the sizes of ions, we consider the concept of effective nuclear charge, which represents the net positive charge experienced by the outermost electrons of an atom. A higher effective nuclear charge leads to greater attraction between the nucleus and the electrons, resulting in a smaller atomic or ionic size.
In this case, \(Fe^{3+}\) has a higher effective nuclear charge than \(Fe^{2+}\) and Fe. \(Fe^{3+}\) has lost three electrons compared to the neutral Fe atom, resulting in a higher positive charge on the nucleus. The increased positive charge attracts the remaining electrons more strongly, causing the \(Fe^{3+}\) ion to have a smaller size than both \(Fe^{2+}\) and Fe.
\(Fe^{2+}\) has lost two electrons compared to the neutral Fe atom, resulting in a smaller effective nuclear charge than \(Fe^{3+}\) but still greater than Fe. Therefore, \(Fe^{2+}\) has a larger size than \(Fe^{3+}\) but a smaller size than Fe.
Lastly, the neutral Fe atom has the highest number of electrons and the lowest effective nuclear charge among the three species. Therefore, it has the largest size.
Putting it all together, the correct order for the size of Fe^{3+}, Fe, and Fe^{2+} ions is $(1)$ $Fe^{3+} < Fe^{2+} < Fe$. |
