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Topic: Calculating Half-Life from Measuring Counts with GM-Detector  (Read 3961 times)

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Offline Compaq

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Calculating Half-Life from Measuring Counts with GM-Detector
« on: August 20, 2013, 11:18:18 AM »
Hi:

I am struggling with a laboratory exercise. Our book has not arrived at the shop yet, and the Professor is away.

We measured a radio isotope with a GM-counter for 12 minutes (automatic instrument) at 15 seconds intervals. There half-life is supposedly relatively short, and I can see the number of counts dropping with time.

What I have to do, is to find the half life. We have some example graphs with time t on the x-axis and number of nuclides N on the y-axis. However, I am not quite sure how to manage my data set to get these values.

The solution of the first order diff. equation -dN/dt = λN is the following:

N = N0e-λt, where λ is the disintegration rate, N0 is the number of nuclides at t0.

So how do I get from counts or counts-per-minute to N? That is what I do not understand. The lab instructions do not explain how to do it very well. I do not ask you to do my work for me, I am merely asking for suggestions or new ways of thinking.

I hope someone can help me out! In addition of drowning in reports, I decided to write them all in LaTeX and this takes three times as long (because I am still new to LaTeX).

I have imported my data to R-Commander, and subtracted the background to each measurement. That is as far as I have come. Again, I would appreciate any *delete me*

Sincerely,
Anders

Offline Corribus

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Re: Calculating Half-Life from Measuring Counts with GM-Detector
« Reply #1 on: August 20, 2013, 01:57:20 PM »
Unless I'm reading your problem wrong, each count by the counter is equivalent to the loss of one nucleotide.

Therefore the counts per time is equivalent to N(t).

What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

Offline Enthalpy

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Re: Calculating Half-Life from Measuring Counts with GM-Detector
« Reply #2 on: August 22, 2013, 11:49:57 AM »
The counter does not intercept nor absorb each disintegration, but it doesn't have to.

The number of counts per second is proportional to the number of disintegrations per second which is proportional to the remaining unstable nuclides. With the ratio of activities and the interval between the two measures, you have the half-life.

Don't forget the convention is half-life, not the exponential factor. Main source of error.

In real life, you have mixes of many nuclides, especially the children within the radioactive chain, each with a  different half-life. Measures are then a mess, much worse to interpret. For instance one communication error at Fukushima early in the accident was a huge announced amount of a short-lived nuclide, because the measure was made many half-lives later - but wrongly extrapolated to the initial concentration because this nuclide resulted from the disintegration of a longer-lived parent that replenished it permanently.

Offline Compaq

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Re: Calculating Half-Life from Measuring Counts with GM-Detector
« Reply #3 on: August 25, 2013, 01:53:39 PM »
Thanks for the *delete me*

I found the half-life of 137Ba to be apprx. 2.7 minutes. We were told the half-life were "a couple of minutes", so I suspect I am right.

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