Crab nebula has a power law spectrum of the form?

Question

dN/dE = 9.7 E- 2.1 photons/(cm2-
s-keV) where E is the energy of the photon. How many photons will a X-ray
detector operating in the energy range of 2-10 keV and geometric area of 30 cm2
detect in 100 seconds? (assume detector has 100% efficiency in this energy
range).
A] 10240 B] 1300 C] 30240 D] 650

Answer 1

The number of photons in an an energy range is N = [integral]dE, integrated over the range in question. So in your case that is

N = 9.7 [integral from 2 to 10]E^-2.1 dE
N = 9.7/1.1 [1/2^1.1 - 1/10^1.1] = [0.4411 - 0.07943] = 3.19 photons per sqcm per sec.

Your detector is 30 sq cm and you integrate for 100 seconds, so your total photon count is 3.19 x 30 x 100 = 9567. Probably some rounding error somewhere so it looks like (A) is your answer.

Answer 2

Hi. The Crab nebula (M1) is pretty bright in X-rays I would guess that C may be correct, but just a guess. You might try the physics section.