Step 1: Understanding the Question:
We need to evaluate two statements related to coordination compounds. Statement I is about the number of unpaired electrons (and thus magnetic property) in a series of complexes. Statement II is about identifying diamagnetic species in given pairs of complexes.
Step 2: Detailed Explanation:
Analysis of Statement I:
We need to find the number of unpaired electrons in each complex.
\begin{itemize}
\item [Cu(NH₃)₄]²⁺: Copper is in the +2 oxidation state. Cu²⁺ has an electronic configuration of [Ar]3d⁹. A d⁹ system will always have 1 unpaired electron, regardless of the geometry (square planar or tetrahedral) or ligand field strength.
\item [Ni(en)₃]²⁺: Nickel is in the +2 oxidation state. Ni²⁺ has an electronic configuration of [Ar]3d⁸. `en` (ethylenediamine) is a strong field ligand, forming an octahedral complex. The d-orbital splitting will be large. The configuration is t₂g⁶eg². There are 2 unpaired electrons in the eg orbitals.
\item [Ni(NH₃)₆]²⁺: Nickel is in the +2 oxidation state, [Ar]3d⁸. NH₃ is a reasonably strong field ligand, but for Ni²⁺, it behaves similarly to a weak field ligand in terms of spin state. The complex is octahedral and high-spin, with a configuration of t₂g⁶eg². There are 2 unpaired electrons.
\item [Mn(H₂O)₆]²⁺: Manganese is in the +2 oxidation state. Mn²⁺ has an electronic configuration of [Ar]3d⁵. H₂O is a weak field ligand, so it forms a high-spin octahedral complex. The electrons will occupy all d-orbitals singly before pairing. The configuration is t₂g³eg². There are 5 unpaired electrons.
\end{itemize}
Comparison: The number of unpaired electrons are 1, 2, 2, and 5. The maximum is 5 for [Mn(H₂O)₆]²⁺.
Conclusion: Statement I is true.
Analysis of Statement II:
We need to determine the magnetic property (paramagnetic or diamagnetic) of each species and then check the given pairs.
\begin{itemize}
\item [NiCl₄]²⁻: Ni is in the +2 state (3d⁸). Cl⁻ is a weak field ligand. The geometry is tetrahedral. The configuration is e⁴t₂⁴, which has 2 unpaired electrons. It is paramagnetic.
\item [Ni(CO)₄]: Ni is in the 0 oxidation state (3d⁸4s²). CO is a very strong field ligand. It causes the 4s electrons to pair up in the 3d orbitals, leading to a 3d¹⁰ configuration. The geometry is tetrahedral. There are 0 unpaired electrons. It is diamagnetic.
\item [Ni(CN)₄]²⁻: Ni is in the +2 state (3d⁸). CN⁻ is a strong field ligand. It forms a square planar complex. The strong field causes pairing of electrons. The configuration has all 8 electrons paired. There are 0 unpaired electrons. It is diamagnetic.
\end{itemize}
Now let's check the pairs:
\begin{itemize}
\item Pair 1: {[NiCl₄]²⁻ (Paramagnetic), [Ni(CO)₄] (Diamagnetic)}. This pair does not contain *only* diamagnetic species.
\item Pair 2: {[NiCl₄]²⁻ (Paramagnetic), [Ni(CN)₄]²⁻ (Diamagnetic)}. This pair does not contain *only* diamagnetic species.
\item Pair 3: {[Ni(CO)₄] (Diamagnetic), [Ni(CN)₄]²⁻ (Diamagnetic)}. This pair contains *only* diamagnetic species.
\end{itemize}
The statement says the number of such pairs is two. Our analysis shows there is only one such pair.
Conclusion: Statement II is false.
Step 3: Final Answer:
Statement I is true, and Statement II is false. This corresponds to option (B).