Let's analyze the question to determine the correct classification of the given complex compounds:
- The first compound is \([\text{Co(NH}_3)_5\text{SO}_4]\text{Br}\).
- The second compound is \([\text{Co(NH}_3)_5\text{Br}]\text{SO}_4\).
In coordination chemistry, isomers are compounds that have the same chemical formula but a different arrangement of atoms. Let's explore the options provided:
- Coordination isomers: These isomers involve the interchange of ligands between the cationic and anionic parts of a coordination complex. The given complexes do not fit this description as the ligand is being exchanged with the counter-ion, not between cation and anion parts.
- Geometrical isomers: These are compounds with the same formula but different spatial arrangements of atoms within a coordination sphere. The compounds given have different counter-ions, hence, they are not geometrical isomers.
- Optical isomers: These are isomers that are non-superimposable mirror images of each other. The difference in these compounds is not related to their optical activity but rather to the counter-ions.
- Ionisation isomers: These isomers occur when a ligand in a coordination compound exchanges places with an anion or cation outside the coordination sphere. In the given compounds, the \(\text{SO}_4^{2-}\) group and \(\text{Br}^-\;\) ion have exchanged positions between the coordination sphere and the counter-ion.
Given this explanation, the correct classification for the compounds \([\text{Co(NH}_3)_5\text{SO}_4]\text{Br}\) and \([\text{Co(NH}_3)_5\text{Br}]\text{SO}_4\) is ionisation isomers.
Therefore, the correct answer is: Ionisation isomers.