Question #44690

Consider two homoleptic octahedral complexes, $P$ and $Q$, of $3d$ transition metals $M_1$ and $M_2$ respectively. Complex $P = \ce{[M_1(CN)6]^{4-}}$ is diamagnetic. Complex $Q = \ce{[M_2F6]^{3-}}$ is paramagnetic with a spin-only magnetic moment of $\approx 4.90 \text{ BM}$. The isolated metal ions $M_1^{2+}$ and $M_2^{3+}$ are isoelectronic. Let $r_1$ and $r_2$ be the effective ionic radii of the metal ions in the specific spin states present in complexes $P$ and $Q$, respectively. Let $\lambda_P$ and $\lambda_Q$ be the wavelengths of the lowest energy $d-d$ transition in $P$ and $Q$. Which of the following correctly relates their ionic radii and absorption wavelengths?