Final answer:
The peak wavelength of the corona around a black hole changes with its mass, as a larger mass results in a larger radius of the event horizon, affecting the accretion disk's temperature and emitted radiation. The mass and size of the black hole influence the energy output and peak wavelength of its emission.
Step-by-step explanation:
The peak wavelength of the corona around a black hole is influenced by the size of the black hole's event horizon, which is directly related to its mass. The larger the mass of the black hole, the greater the radius of the event horizon according to the Schwarzschild radius formula. When considering the accretion disk around a black hole, which emits radio radiation due to the heating of matter as it spirals inward, the peak wavelength of the emitted radiation is determined by the temperature of the accretion disk, which is influenced by the gravitational energy conversion as matter falls into the black hole.
Larger black holes have more massive accretion disks, which can emit radiation at different peak wavelengths. Observations of quasars, which are distant objects believed to be powered by accretion onto supermassive black holes, indicate that their luminosity and the peak wavelength of the emitted light change over time, with the most powerful quasars and their peak emissions occurring early in the universe's history.
Since the size or mass of the black hole influences the energy output and thus the characteristic wavelengths of the radiation from the accretion disk, the peak wavelength of the corona or surrounding emission region of a black hole ultimately depends on the black hole's mass and size.