Step 1: Determine Electronic Configuration
Nickel (Ni) has atomic number 28. Its electronic configuration is: \[ [Ar] 3d^8 4s^2 \]. Determine the oxidation state of Ni in the given complexes.
Step 2: Analyze Each Complex
(A) [Ni(Cl)$_4$]$^{2-}$
Chloride (Cl$^-$) is a weak field ligand.
The geometry is tetrahedral, involving sp$^3$ hybridization.
This complex is paramagnetic due to unpaired electrons. It is not the correct answer.
(B) [Co(C$_2$O$_4$)$_3$]$^{3-}$
Cobalt (Co$^{3+}$) is complexed with a strong field ligand (oxalate).
The structure is octahedral, not tetrahedral. This is an incorrect choice.
(C) [Ni(CN)$_4$]$^{2-}$
Cyanide (CN$^-$) is a strong field ligand.
This complex exhibits dsp$^2$ hybridization, resulting in a square planar geometry.
It is diamagnetic but not tetrahedral. This is an incorrect choice.
(D) [Ni(CO)$_4$]
Carbon monoxide (CO) is a strong field ligand.
It induces electron pairing and sp$^3$ hybridization, forming a tetrahedral structure.
The absence of unpaired electrons makes it diamagnetic. This is the correct answer.
Final Answer: The complex that is both diamagnetic and tetrahedral is [Ni(CO)$_4$].