Some help with a X-Ray astronomy question please

[Maitreya]

I've got to solve this problem and I am having quite an hard time figuring out how... Sorry, but I think I need help:

"An astronomer takes a spectrum of a distant quasar using a 4m telescope. With an exposure
time of one hour, the optical spectrum contains about 10,000 photons. The source emits 1/10
as much power in the X-ray band as it emits in the optical band. The astronomer manages to
get a 30 kilosecond observation with an X-ray observatory that has an effective area of 1000
cm2.
Assuming that the effciency of the telescope and spectrograph combination is 30%, how
many photons will the resulting X-ray spectrum contain?"

As far as I understand, What I should do here is
1) to compare the two telescopes as if they had the same area and the same exposure time, so that I can infer how many optical photons the optical telescope would have gathered if it had the area and the exposure time of the X-Ray one.
2) Then, I would take 1/10th of this result (the source is emitting 1/10 of Xray photons as compared to the optical ones) which will tell me the theoretical number of X-Ray photons the X-Ray telescope would have gathered with perfect efficiency.
3) But knowing that the efficiency was only the 30%, I could have an estimate of the number of photons actually detected in the X-Ray spectrum.

Problem is, I have no idea how to calculate step 1)


Any suggestions?

Thanks a lot.

 

[mgb_phys]

Step 1 is just to calculate the number of photons/m^2/second on each telescope
(Be careful with the units)

 

[Maitreya]

You mean that if I calculate the photons per m^2 per second for the optical one whatever result I'll get the 1/10th of that number will be the photons per m^2 per second of the X-Ray one?

 

[ideasrule]

Yes.

 

[Maitreya]

Guys, thanks a lot. Really appreciate. I'm happy to have discovered this forum, and I'll hopefully be able to actually help someone one day :)