The provided answer, option 3 - fusion, is the correct explanation for the constancy of the sun`s surface temperature at 6000°C. Fusion is the process in which light atomic nuclei combine to form heavier nuclei, releasing a tremendous amount of energy in the form of radiation.

Option 1 - fission, is the process of splitting heavy atomic nuclei, which is not applicable to the sun`s temperature constancy.

Option 2 - radioactivity, refers to the spontaneous emission of radiation from unstable atomic nuclei. While radioactivity occurs in the sun, it does not explain the constancy of its temperature.

Option 4 - black hole evaporation, is not applicable to the sun, as black holes are extremely dense objects with powerful gravitational forces.

Therefore, option 3 - fusion, is the only logical explanation for the constancy of the sun`s surface temperature. During fusion, the sun converts hydrogen atoms into helium through a series of nuclear reactions, releasing a steady amount of energy that maintains its temperature.