Interstellar Medium, 21 cm line

[mebwtm]

Somewhere in our Galaxy resides a cloud of neutral hydrogen gas with a radius of 10 pc. The gas density is 10^7 atoms/m^3.
(a)How many 21-cm photons does the cloud emit every second?
(b)If the cloud is 100 pc from the Sun, what is the energy flux of this radiation (in W/m^2) at the Sun?

Relevant Equations:
possibly Em= integral(n^2)dl=(<n>^2)L
Aligned-to-opposed ratio of hydrogen line at 21 cm 3:1
frequency=1.4204 GHzThe attempt at a solution:
So far I've done the integral for the emission measure equation by changing n into
10 atoms/cm^3
L is the diameter so it's 20 pc
From this I found Em=2000pc/cm^6

I can't figure out how to get from here to photons/second for part a

For part b i know Flux is proportional to frequency^(-alpha), but I'm not sure proportionality will help me. I know the ratio is suppose to, but again I cannot connect the two.

 

[NateD]

Any help would be appreciated. a) The number of 21 cm photons emitted every second can be calculated using the equation:N = Em x ν x A,where N is the number of photons, Em is the emission measure, ν is the frequency of the 21 cm line (1.4204 GHz), and A is the aligned-to-opposed ratio of hydrogen line at 21 cm (3:1). Plugging in the values, we get:N = 2000 pc/cm^6 x 1.4204 GHz x 3 = 8482.8 GHz/sb) The energy flux of this radiation at the Sun is given by:Flux = N x hν / 4πd^2,where h is Planck's constant (6.62607004 x 10^−34 J s) and d is the distance from the cloud to the Sun (100 pc). Plugging in the values, we get:Flux = 8482.8 GHz/s x 6.62607004 x 10^−34 J s x 1.4204 GHz / (4π x (100 pc)^2)= 2.68 x 10^−14 W/m^2