A gamma-ray burst 5000 Mpc away releases 10^45 joules of energy isotropically in the form of gamma rays, each of energy 250 keV. Some of the rays are detected by an instrument in Earth orbit with an effective collecting area of 0.75 m^2. How many gamma-ray photons strike the detector?
Okay...so far I think I've calculated the total amount of gamma rays (2.5 x 10^58) but how do I find the amount of photons hitting a 0.75 m^2 detector from 5000 Mpc away?! Is there some formula I'm missing? Any insights would be greatly appreciated! =)
Okay...so far I think I've calculated the total amount of gamma rays (2.5 x 10^58) but how do I find the amount of photons hitting a 0.75 m^2 detector from 5000 Mpc away?! Is there some formula I'm missing? Any insights would be greatly appreciated! =)
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Convert the Mpc to meters. Find the surface area of a sphere with a radius of 5000 Mpc (4 pi r^2). That's the area over which all these gamma rays are spread out. Then set up a ratio between the number of gamma rays hitting the detector (d) and the total number (g) and set that equal to the area of the detector (Ad) and the area of the sphere around the burst (As).
d/g = Ad/As
Solve for d.
d/g = Ad/As
Solve for d.
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you make the assumption that the photons spread/shoot out evenly in every direction so that when they reach Earth, the photons are spread evenly over the surface of a sphere 5000 Mpc in radius; calculate the surface area of this sphere and then divide the total number of photons by the surface area to get intensity (in photons per square meter) which you can then use to find the number of photons hitting the detector
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Is there some formula I'm missing?
Yes, you're forgetting how to calculate the area of a sphere. In this case, it will be a spherical wavefront with radius of 5000 Mpc. (Hint hint.) Remember to use the same length units, meters or parsecs -- it's entirely your choice.