The question asks for the purest form of carbon. Let`s analyze each option to determine which one fits the description.

Option 1: Charcoal. Charcoal is a form of carbon that is created by heating organic matter, such as wood, in the absence of oxygen. While it consists mostly of carbon, it also contains ash and other impurities. Therefore, charcoal is not the purest form of carbon.

Option 2: Coke. Coke is a fuel made by heating coal in the absence of air. It is primarily composed of carbon, but it may still contain impurities depending on the production process. Thus, coke is not the purest form of carbon.

Option 3: Fullerene. Fullerene is a pure form of carbon composed entirely of carbon atoms arranged in spheres, tubes, or cages. It is known for its unique structure and is considered one of the purest forms of carbon. Therefore, option 3, Fullerene, is the correct answer.

Option 4: Carbon black. Carbon black is a fine powder made from incomplete combustion or thermal decomposition of hydrocarbons. While it is predominantly carbon, it may contain impurities and other substances, making it not the purest form of carbon.

In conclusion, out of the given options