When a metal cation M^ 2+ is treated with dimethylglyoxime in an...

The formation of a bright red precipitate with dimethylglyoxime (DMG) in an ammoniacal medium is a characteristic test for the $Ni^{2+}$ cation. The complex formed is bis(dimethylglyoximato)nickel(II), $[Ni(dmg)_{2}]$.

In this complex, $Ni^{2+}$ has a $3d^{8}$ electronic configuration. DMG acts as a strong field bidentate ligand due to the formation of stable five-membered chelate rings stabilized by intramolecular hydrogen bonding. This strong ligand field forces the pairing of the $3d$ electrons, leaving one $3d$ orbital empty.

Therefore, the hybridization involves one $3d$, one $4s$, and two $4p$ orbitals, resulting in $dsp^{2}$ hybridization (square planar geometry). Since all electrons are paired, the complex is diamagnetic.

Answer: $dsp^{2}$ and diamagnetic