Final answer:
A galaxy 500 Mly away is expected to be moving away from us at a speed of 10,000 km/s, as calculated by Hubble's Law using the Hubble constant. This corresponds to option (b).
Step-by-step explanation:
When a galaxy is 500 Mly away from us, we can estimate its speed using Hubble's Law, which describes the relationship between the distance of a galaxy and its recessional velocity resultant from the expansion of the universe. The Hubble constant (H0) is approximately 20 km/s per Mly, meaning that for every million light-years away a galaxy is, it is moving away from us at an additional 20 km/s due to the expansion of the universe.
By multiplying the Hubble constant with the distance, we find the speed (v) at which the galaxy is moving away:
v = H0 × distance
v = 20 km/s/Mly × 500 Mly
v = 10,000 km/s
Therefore, a galaxy 500 Mly away would be moving away from us at 10,000 km/s, which is option (b) 1×105km/s away from us. The direction is “away” because of the expanding universe, which makes distant galaxies recede from each other.