Step 1: Understanding the Concept of Coordination Number.
In coordination chemistry, the coordination number is the number of bonds formed between the metal and the ligands. Generally, the coordination number is equal to the number of ligands when each ligand binds through a single atom. However, in some cases, ligands like ethylenediamine (en), which is a bidentate ligand, bind through two atoms, so the coordination number will be different from the number of ligands.
Step 2: Analyzing the Options.
(A) [Pt(NH\(_3\))\(_6\)]\(^{4+}\): Correct. This compound has a coordination number of 6, which is equal to the number of ligands (6 NH\(_3\) molecules).
(B) [Co(en)\(_3\)]\(^{3+}\): Correct. This compound has a coordination number of 6 because each ethylenediamine (en) ligand binds through two atoms, so the coordination number is 2 × 3 = 6, but there are 3 ligands, which are different.
(C) [Cu(NH\(_3\))\(_4\)]\(^{2+}\): Correct. This compound has a coordination number of 4, which matches the number of ligands (4 NH\(_3\) molecules).
(D) [Co(NH\(_3\))\(_6\)]\(^{3+}\): Correct. This compound has a coordination number of 6, which is equal to the number of ligands (6 NH\(_3\) molecules).
Step 3: Conclusion.
The correct answer is (B) [Co(en)\(_3\)]\(^{3+}\), as it has a coordination number of 6, but only 3 ligands.