Final answer:
As a black hole gets hotter, its Hawking radiation becomes brighter due to an increase in the energy of the emitted photons, corresponding to an increase in frequency and a decrease in wavelength of the most intense radiation.
Step-by-step explanation:
When a black hole gets hotter, Hawking radiation becomes brighter, which corresponds to option (a) 'It becomes brighter.' As the temperature increases, the wavelength of the most intense radiation – typically emitted by a blackbody – decreases, which means that the frequency increases. Since the energy of photons is directly proportional to their frequency, the energy increases as well. Thus, the black hole emits more energetic photons as its temperature rises, which results in brighter Hawking radiation.
Another way to understand this is through the concept of blackbody radiation, often depicted graphically. As the temperature of a blackbody increases, the curve showing radiation versus frequency becomes steeper but also shifts towards higher frequencies, indicating an increase in energy and intensity. This is analogous to what occurs with Hawking radiation: as the black hole's temperature increases, the energy of the emitted radiation also increases, which leads to a brighter output.