Explanation:

In the given compounds, [Co(SO4)(NH3)5]Br and [Co(SO4)(NH3)5]Cl, the central cobalt ion (Co) is surrounded by five ammonia (NH3) ligands and one sulfate (SO4) ligand. The difference between the two compounds is the presence of different halide ions (Br and Cl) in the outer sphere of coordination complex.

No Isomerism:

The correct answer is option 'D' - No isomerism. This is because there is no variation in the coordination number, the type of ligands, or the connectivity between the ligands and the central metal ion in the two compounds. Isomerism occurs when there is a difference in the arrangement of atoms or ligands within a molecule or coordination complex, leading to different chemical properties.

Types of Isomerism:

1. Linkage Isomerism: Linkage isomerism occurs when the ligand is attached to the central metal ion through a different atom. For example, in the compound [Co(NH2CH2CH2NH2)5]Cl2, the ligand ethylenediamine (en) can coordinate through either of the two nitrogen atoms, resulting in two different isomers.

2. Ionisation Isomerism: Ionisation isomerism occurs when the counter ions in the coordination complex are exchanged. In the given compounds, the counter ions are different (Br and Cl), which could lead to ionisation isomerism if the ligand exchange occurs.

3. Coordination Isomerism: Coordination isomerism occurs when the ligands and counter ions exchange places in the coordination complex. This can result in different isomers with the same chemical formula but different connectivity. In the given compounds, the ligands and counter ions are not exchanging places, so coordination isomerism is not applicable.

Conclusion:

Based on the analysis of the given compounds, it can be concluded that there is no isomerism present. The compounds [Co(SO4)(NH3)5]Br and [Co(SO4)(NH3)5]Cl have the same connectivity, ligands, and coordination number, with only a difference in the counter ions (Br and Cl). Therefore, the correct answer is option 'D' - No isomerism.