In \([\text{Ni}(\text{CO})_4]\), nickel is in the zero oxidation state and has a \(3d^{10}\) electron configuration, leading to a fully paired electron configuration, making it diamagnetic.
In contrast, in \([\text{NiCl}_4]^{2-}\), nickel is in the \(+2\) oxidation state with a \(3d^8\) electron configuration. The chloride ligands are weak-field ligands and do not pair up the electrons, resulting in unpaired electrons and a paramagnetic nature.
Thus, the correct answer is:
\[ [\text{Ni}(\text{CO})_4] \text{ is diamagnetic and } [\text{NiCl}_4]^{2-} \text{ is paramagnetic.} \]Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32