compare the values of the radii of fe+2 and fe+3 ions. write their electronic structures. explain the observations

The radii of Fe\(^{2+}\) and Fe\(^{3+}\) ions differ due to the changes in their electronic configurations and the effective nuclear charge experienced by the electrons. ### Electronic Structures: - **Fe (Iron) atomic number = 26**: The ground state electron configuration of neutral iron (Fe) is \( [\text{Ar}] 3d^6 4s^2 \). - **Fe\(^{2+}\)**: When iron loses two electrons to become Fe\(^{2+}\), it loses the two 4s electrons. Thus, the electronic configuration of Fe\(^{2+}\) is: \[ \text{Fe}^{2+} : [\text{Ar}] 3d^6 \] - **Fe\(^{3+}\)**: When iron loses three electrons to become Fe\(^{3+}\), it loses both the 4s electrons and one 3d electron. Thus, the electronic configuration of Fe\(^{3+}\) is: \[ \text{Fe}^{3+} : [\text{Ar}] 3d^5 \] ### Comparison of Radii: 1. **Ionic Radii**: The radius of an ion is influenced by both the number of electrons and the effective nuclear charge. As electrons are removed from the neutral atom, the remaining electrons are held more tightly by the nucleus because there are fewer electrons repelling each other. 2. **Fe\(^{2+}\) Ionic Radius**: The ionic radius of Fe\(^{2+}\) is typically larger than that of Fe\(^{3+}\) because Fe\(^{2+}\) has more electrons (6 electrons in the 3d subshell) and slightly less effective nuclear charge acting per electron. 3. **Fe\(^{3+}\) Ionic Radius**: The ionic radius of Fe\(^{3+}\) is smaller than that of Fe\(^{2+}\) since Fe\(^{3+}\) has one less electron compared to Fe\(^{2+}\), leading to a greater effective nuclear charge experienced by the remaining 5 d electrons. This results in a stronger attraction of electrons to the nucleus, causing the ion to have a smaller radius. ### Summary of Observations: - **Fe\(^{2+}\) has a larger ionic radius than Fe\(^{3+}\)** due to having more electrons and a lower effective nuclear charge acting on those electrons. - The stronger attraction in Fe\(^{3+}\) results from the higher positive charge of the ion, which effectively pulls the electrons closer to the nucleus, thus reducing the ionic radius compared to Fe\(^{2+}\). In terms of specific values, typical ionic radii at coordination number 6 for Fe\(^{2+}\) is about 0.78 Å and for Fe\(^{3+}\) is around 0.67 Å, illustrating the difference in size clearly.