GR0177 Problem #14

dtheili1 · Post by **dtheili1** » Mon Oct 10, 2005 7:46 pm

I can't quite get problem #14 on the GR0177 ETS exam (I'm paraphrasing):

An 8cm diameter by 8cm long gamma ray detector dectects specific energy from a point source. When the source is placed just next to the detector at the center of the circular face, 50% of all emitted gamma rays at that energy are detected. If the detector is moved to 1m away, the fraction of detected gamma rays drops to...

A) 10^-4
B) 2x10^-4
C) 4x10^-4
D) 8pi x10^-4
E) 16pi x10^-4

The answer is C. Here's how I see it;

If the point source is up against a circular face of the cylinder it makes sense that 50% is detected as long as all radiation that hits (and/or enters) the cylinder gets detected. So, when the source is at 1m away, can't you compare the surface area of the circular face of the cylinder to the surface area of a 1m radius sphere and get the fraction of radiation that gets detected? Am I misinterpreting the setup of the detector? Is the detector hollow?

Thanks for any help.

Dale

thermalEquilibrium · Post by **thermalEquilibrium** » Tue Oct 11, 2005 10:29 am

yep, you pretty much have it - this problem is a different spin on the Inverse square law.

The fraction of gamma rays detected will be the ratio of surface area of the face of the detector (pi*r^2=pi*(0.04m)^2) to the surface area of a sphere at 1m (4*pi*r^2=4*pi). Ans. C

The NaI detector isnt taken to be hollow.

Since in a Scintillation Detector the gamma rays can only be detected by entering through the circular face of the cylinder (not the sides or the back), the fraction will only depend on the surface area of the face.

dtheili1 · Post by **dtheili1** » Tue Oct 11, 2005 4:55 pm

Yes, thank you. This was one of those cases I was so sure I had my math right, I didn't go back and start from scratch like I should have. Amazing how often it's just a simple mistake like that.

Thanks for the help.

Dale