Final answer:
Relativistic quantum mechanics is used for small objects at high speeds or in strong gravitational fields, specifically when speeds exceed 1% of the speed of light.
Step-by-step explanation:
Relativistic quantum mechanics is necessary to use under specific circumstances which include dealing with behaviors of small objects that are traveling at high speeds, specifically when these speeds are greater than about 1% of the speed of light, or when these objects are experiencing a strong gravitational field. Therefore, the correct answer to the question '“When is it necessary to use relativistic quantum mechanics?”' is c) At high speeds. This domain of physics is reserved for exceptional cases due to its mathematical complexity, while classical physics or non-relativistic quantum mechanics can be used for scenarios where they provide adequately accurate results.