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There's a square detector of area A. When a point source is placed at the center of this detector, half of the emitted particles are detected. What fraction of the particles are detected when the point source is placed a distance x away?

I figured that at x=0, 50% of the particles are detected because the solid angle is [tex]2\pi[/tex], half of the full solid angle. I also know that the amount of gamma rays detectors falls with the radius as [tex]\frac{1}{r^2}[/tex]. Should I try to calculate the solid angle at a distance x?

There is an equation [tex]\Omega=\frac{A}{r^2}[/tex] that relates the solid angle, area, and r, but the area here is the area on the sphere, not of the detector, so I don't know how to proceed from here.

Any help is appreciated.

Thanks!

I figured that at x=0, 50% of the particles are detected because the solid angle is [tex]2\pi[/tex], half of the full solid angle. I also know that the amount of gamma rays detectors falls with the radius as [tex]\frac{1}{r^2}[/tex]. Should I try to calculate the solid angle at a distance x?

There is an equation [tex]\Omega=\frac{A}{r^2}[/tex] that relates the solid angle, area, and r, but the area here is the area on the sphere, not of the detector, so I don't know how to proceed from here.

Any help is appreciated.

Thanks!

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