How to Determine the Decay Constant of a Radioactive Substance?

[sweminka]

A piece of radioactive substance gives a received count rate of 6000 counts per minute in a detector whose efficiency is known to be 5%. If the sample contains 10^10 atoms, what is the decay constant ( λ ) of this radioactive substance ?

No idea how to solve this problem. Any help would be really appreciated.

Edit: I am a medical student studying abroad, and the physics teacher doesn't speak English properly. Please believe that I have tried to understand, but after 1 day of looking for information on the internet, I still have no idea how to solve this problem.

 

[fatra2]

Hi there,

To answer your question, there are many assumptions to be made:
1. I assume 6000 counts/minute in the first minute.
2. $$10^{10}$$ atoms is supposed to be be the initial excited/radioactive atoms in the sample
3. 6000 counts/minute assumes that all radiation emitted passes through the detector, with a 5% efficiency.

If all these assumptions are true, then you can simply apply the radioactive decay equation to your problem and the answer is solved in two lines.

 

[sweminka]

Here are my calculations :

N(t)=No*exp(-λt)

10^10 - 6000 = (10^10) * exp (-λ*60)

( 10^10 -6000) / (10^10) = exp (-λ*60)

ln ( ( 10^10 -6000) / (10^10) ) = -λ*60

λ= ( - ln ( ( 10^10 -6000) / (10^10) ) ) / 60

λ = 10*(-8) per second

 

[sweminka]

The answer is supposed to be 2*10^(-7) though :(

I guess it has something to do with the detector's efficiency ?

 

[fatra2]

Hi there,

You are forgetting the efficiency of the detector in your calculations. Don't forget that only 5% of the particles are detected.

 

[sweminka]

"only 5% of the particles are detected" This sentence suddenly made everything clear to me. I guess I couldn't understand the meaning of "efficiency". Anyway, I replaced 6000 by 120 000 (100%) in my calculations, and I find the correct answer.

Thank you very much :)