
Step 1: Analyse \(Ni(CO)_4\).
Nickel is in oxidation state 0.
Electronic configuration:
\[ Ni: [Ar]3d^8 4s^2 \Rightarrow d^{10} \text{ after bonding} \]
CO is a strong field ligand, pairing all electrons.
Hybridisation:
\[ sp^3 \]
No unpaired electrons:
\[ \mu = 0 \]
So,
\[ A \rightarrow R \]
Step 2: Analyse \([Ni(CN)_4]^{2-}\)
Ni is in +2 oxidation state:
\[ Ni^{2+} = d^8 \]
CN- is a strong field ligand → pairing occurs.
Hybridisation:
\[ dsp^2 \ (\text{square planar}) \]
All electrons paired:
\[ \mu = 0 \]
So,
\[ B \rightarrow S \]
Step 3: Analyse \([NiCl_4]^{2-}\).
\([Ni]^{2+}\) = \(\ d^8\).
\([Cl]^{-}\)is a weak field ligand With no pairing.
Hybridisation:
\[ sp^3 \]
Two unpaired electrons:
\[ \mu \approx 2.84\ \text{BM} \]
So,
\[ C \rightarrow Q \]
Step 4: Analyse \([MnBr_4]^{2-}\).
\([Mn]^{2+}\) = \( \ d^5\).
Br- is weak field → high spin.
Hybridisation:
\[ sp^3 \]
Five unpaired electrons:
\[ \mu \approx 5.92\ \text{BM} \]
So,
\[ D \rightarrow P \]
Step 5: Compile matching.
\[ A = R,\quad B = S,\quad C = Q,\quad D = P \]
Step 6: Match with options.
This corresponds to option (A).
Step 7: Final conclusion.
\[ \boxed{A = R,\ B = S,\ C = Q,\ D = P} \]