In general, low-spin complexes are formed by transition metals with higher oxidation states and/or ligands that create strong crystal field splitting (such as \( \text{CN}^- \)).
Based on this: - \( [\text{Fe(CN)}_5\text{NO}]^{2-} \) and \( [\text{Fe(CN)}_6]^{4-} \) are low-spin because \( \text{CN}^- \) is a strong field ligand.
- \( [\text{CoF}_6]^{3-} \) and \( [\text{Cr(H}_2\text{O})_6]^{2+} \) are high-spin due to weaker ligands or lower oxidation states.
Thus, the correct complexes that are low-spin are \( \text{Fe(CN)}_5\text{NO}^{2-} \) and \( \text{Fe(CN)}_6^{4-} \).
Based on Crystal Field theory, match the Complex ions listed in Column I with the electronic configuration in the d orbitals of the central metal ion listed in Column II.
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - ax - b = 0 \) with \( \text{Im}(\alpha) < \text{Im}(\beta) \). Let \( P_n = \alpha^n - \beta^n \). If \[ P_3 = -5\sqrt{7}, \quad P_4 = -3\sqrt{7}, \quad P_5 = 11\sqrt{7}, \quad P_6 = 45\sqrt{7}, \] then \( |\alpha^4 + \beta^4| \) is equal to: