The Arecibo radio telescope in Puerto Rico can detect a radio wave with an intensity as low as 1 x 10-23 W/m2. Consider a "best-case" scenario for communication with extraterrestrials: suppose an advanced civilization a distance x away from Earth is able to transform the entire power output of a Sun-like star completely into a radio-wave signal which is transmitted uniformly in all directions.
(a) In order for Arecibo to detect this radio signal, what is the maximum value for x in light-years (1 ly ( 1016m)?
(b) How does this maximum value compare with the 100,000-ly size of our Milky Way galaxy? The intensity of sunlight at Earth's orbital distance from the Sun is 1350 W/m2.