# Homework Help: Gamma Emission of Cs Sample

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1. Feb 19, 2015

### Hertz

So I have a problem where I'm given the decay rate of a sample which contains Cs137, 10 mCi, and I'm basically given the percentage of radiation detected by the detector. But the wording of the question is:

"What count rate would be observed in a perfectly efficient gamma detector"

Sounds to me like they only care about the intensity of gamma rays and not other particles which are released. I found this diagram but it's what's causing my confusion:
http://en.wikipedia.org/wiki/Caesium-137#mediaviewer/File:Cs-137-decay.svg

So 95% of the nuclei decay into an excited Ba nucleus which then decays into a stable barium nucleus and a gamma ray. This seems to be the only way gamma rays are produced from the Cs137. Makes sense. So what is the 85%?? Only 85% of the excited barium nuclei release a gamma ray? Or 85% of the Cs137 release a gamma ray? What happens to the remaining excited barium nuclei, do they decay in a different way which doesn't release a gamma ray?

If we let P be the percentage of Cs radiation detected and R the overall decay rate of the sample and we suppose 85% of Cs decays result in a gamma ray, then is the detection rate of gamma rays $r=0.85RP$?

2. Feb 20, 2015

### TSny

I believe it's the latter; i.e., 85% of the Cs decays end up leading to a gamma emission by a Ba nucleus..

About 10% of the excited Ba nuclei decay by a process known as internal conversion.

See http://en.wikipedia.org/wiki/Internal_conversion

The remaining 90% of the excited Ba decay by gamma emission. Note 90% of 95% yields approximately 85%.

I think that's right, but I can't say for sure that I'm interpreting the wording of the problem correctly.

3. Feb 20, 2015

### Hertz

No problem! Thank you for the help!

If you are curious here is the exact wording:
1. A lump of radioactive rock contains 10 milliCuries (mCi) of 137Cs55. See the chart on commonly used radioactive sources at pdg.lbl.gov for half lives and photon emission characteristics. (a) How many 137Cs55 nuclei are present in the rock? (b) What count rate would be observed in a perfectly efficient gamma detector, with a surface area of 4 cm2 , at a distance of 50 cm from the rock? (c) What count rate would be observed by the same detector, 20 years later?

I'm on part B and I'm pretty sure I can do C if I understand B. To find P I took the area of the detector divided by the surface area of a sphere of radius 50cm

4. Feb 20, 2015

### TSny

When internal conversion occurs, an x-ray photon is usually produced from the atomic electrons. This occurs in about 90% of the internal conversions for the excited Ba 137 according to this link: http://www.phywe.com/index.php/fuseaction/download/lrn_file/versuchsanleitungen/P2524515/e/P2524515.pdf [Broken]. Apparently, the gamma detector would count these x-rays along with the gamma rays emitted from the nucleus. Browsing the web, I found data that indicate that for every 100 Cs 137 nuclei, you would get about 85 gammas and about 6 x-rays from internal conversion.

[Some internal conversions don't produce x-rays, they produce "Auger electrons" instead. See http://en.wikipedia.org/wiki/Auger_effect ]

Last edited by a moderator: May 7, 2017