The attraction of a complex to a magnetic field depends on the number of unpaired electrons in the complex. Let us analyze each given complex:
1.[Zn(H\(_2\)O)\(_6\)]\(^{2+}\): The electronic configuration of Zn\(^{2+}\) is \( 3d^{10} \). It has no unpaired electrons, so it is diamagnetic.
2. [Ni(H\(_2\)O)\(_6\)]\(^{2+}\): The electronic configuration of Ni\(^{2+}\) is \( 3d^8 \). In an octahedral field, this gives a \( t_{2g}^6 e_g^2 \) configuration, with 2 unpaired electrons.
3. [Co(en)\(_3\)]\(^{3+}\): The electronic configuration of Co\(^{3+}\) is \( 3d^6 \). Due to strong-field ligands (en), it undergoes pairing, resulting in a \( t_{2g}^6 e_g^0 \) configuration with no unpaired electrons. It is diamagnetic.
4. [Co(H\(_2\)O)\(_6\)]\(^{2+}\): The electronic configuration of Co\(^{2+}\) is \( 3d^7 \). In an octahedral field with weak-field ligands like water, it gives a \( t_{2g}^5 e_g^2 \) configuration with 3 unpaired electrons. Hence, [Co(H\(_2\)O)\(_6\)]\(^{2+}\) has the maximum number of unpaired electrons and will exhibit the maximum attraction to an applied magnetic field.
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: