The correct answer is: B. Spectroscopy
Spectroscopy is a method of analysis that uses the interaction of matter and electromagnetic radiation to identify and quantify substances. It can be used to determine the presence of cobalt in vitamin B12 by measuring the absorption of light by the cobalt atom.
Hydrolysis is a chemical reaction in which a molecule is broken down into smaller molecules by the addition of water. It is not a reliable method for determining the presence of cobalt in vitamin B12 because it can also break down other components of the vitamin.
The Borax-Bead test is a qualitative test for cobalt. It is based on the formation of a blue-green precipitate when cobalt ions react with borax. However, this test is not specific for cobalt and can also be positive for other metals, such as nickel and copper.
The Sodium Nitroprusside test is a qualitative test for cyanide. It is based on the formation of a red-purple precipitate when cyanide ions react with sodium nitroprusside. However, this test is not specific for cyanide and can also be positive for other compounds, such as thiocyanate and azide.
Therefore, the only method that can be used to reliably determine the presence of cobalt in vitamin B12 is spectroscopy.