Statement I: Under the influence of a strong field ligand, d⁷-system will have only one unpaired electron either in coordination number six or four

Statement II: \(t_{2g}^6\) \(e_g^1\) is the electronic configuration for both cases

Statement I is correct but Statement II is false

The correct option is option 3. Statement I is correct, but Statement II is false.

Let us break down the statements and their correctness:

Statement I: Under the influence of a strong field ligand, a \(d^7\)-system will have only one unpaired electron either in coordination number six or four.

A \(d^7\) system refers to a transition metal ion that has 7 electrons in its d-orbitals. When this \(d^7\) ion is surrounded by strong field ligands (ligands that cause significant splitting of the d-orbitals), the energy difference between the orbitals becomes large. In an octahedral complex (coordination number six), where the metal ion is surrounded by six ligands, the d-orbitals split into lower energy \(t_{2g}\) \((d_{xy}, d_{yz}, d_{zx})\) and higher energy eg \((d_{x^2-y^2}, d_{z^2})\) sets.

Due to the strong field, the \(d^7\) configuration typically undergoes pairing of electrons (low-spin configuration), resulting in only one unpaired electron left. In a tetrahedral complex (coordination number four), the \(d^7\) configuration usually results in a high-spin configuration, where there is one unpaired electron because the ligand field splitting is less effective in pairing electrons.

Therefore, Statement I is correct because under the influence of strong field ligands, a \(d^7\) system in either coordination number six or four generally results in only one unpaired electron due to electron pairing caused by the strong ligand field.

Statement II: \(t_{2g}^6 e_g^1\) is the electronic configuration for both cases.

The notation \(t_{2g}^6\) \(e_g^1\) is not a standard notation for electronic configurations in coordination complexes. Typically, in an octahedral field, the \(d^7\) configuration after splitting would be described as \(t_{2g}^6 e_g^1\), indicating six electrons in the \(t_{2g}\) orbitals and one in the \(e_g\) orbital. In a tetrahedral field, the \(d^7\) configuration would be \(e_g^3 t_{2g}^4\), indicating three electrons in the \(e_g\) orbitals and four in the \(t_{2g}\) orbitals. Therefore, \(t_{2g}^6 e_g^1\) does not accurately represent the electronic configurations for these cases.

Thus, Statement II is false because the notation \(t_{2g}^6 e_g^1\) is not correct for describing the electronic configurations of \(d_7\) systems in octahedral or tetrahedral complexes.

In summary:

Statement I is correct because it accurately describes the behavior of a \(d^7\) system under the influence of strong field ligands.

Statement II is false because it uses incorrect notation to describe the electronic configurations of \(d^7\) systems in coordination complexes.

This analysis clarifies why Statement I is correct while Statement II is not.