Final answer:
The question concerns two magnitude scales: the Richter scale for quantifying earthquake energy and the astronomical apparent magnitude scale for stellar brightness, with specific factors of brightness differences corresponding to different magnitude intervals.
Step-by-step explanation:
The student is asking about two different systems of magnitude measurement. One is the Richter scale, which measures the energy produced by an earthquake. Richter scale numbers like 2.3, 4.0, 6.1, and 7.0 represent the magnitude of an earthquake's energy output. The second system is the astronomical apparent magnitude scale, which measures the brightness of stars and other celestial objects. For example, a difference of 5 magnitudes on this scale corresponds to a brightness factor of 100, while a difference of 0.75 magnitudes corresponds to a brightness factor of approximately 2.
In summary, both the Richter scale and the astronomical magnitude scale are measures of intensity, one for seismic activity and the other for stellar brightness. These systems are utilized to categorize and communicate data about earthquakes and stars, respectively, in a quantifiable manner.