Uncertainty in Radioactive Decay Dating Calculation

AI Thread Summary
The discussion centers on calculating the uncertainty in dating charred wood remains using radioactive decay dating with 14C. The measured activity of the remains is 10.8 disintegrations per second per gram, while the atmospheric standard is 13.5 disintegrations per second per gram. The half-life of 14C is given as 5730 ± 30 years, leading to a calculated dating of 1844 years. The main challenge is applying the propagation of errors formula to derive the uncertainty, which is determined to be 10 years. Participants are seeking assistance in formulating the correct expression for this calculation.
Granger
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Homework Statement


Charred wood remains were found in Conimbriga, probably with Roman origin. When measured at 14C activity in these remnants, it afforded 10.8 disintegrations per second per gram. The half-processing 14C is 5730 ± 30 years and the activity of this isotope in the atmosphere and in living matter is 13.5 disintegrations per second per gram.

Calculate the uncertainty in dating, because of the imprecision of 30 years in the half-transformation of 14C.

Homework Equations


N = No x e^(-kt)
R = Ro x e^(-kt)

R is the activity
k is the decay constant

The Attempt at a Solution



So there were previous question, one was calculating k (k = 1.21 x 10^-4) and the other was for calculate the dating (1844 years).
But now I have to calculate the uncertainty of the dating I previously calculated.
So, I know I need to derivate and use the propagation of errors formula... But I'm having trouble to get to the right expression...
The right answer of the problem is 10 years.

THANKS!
 
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Granger said:
But now I have to calculate the uncertainty of the dating I previously calculated.
So, I know I need to derivate and use the propagation of errors formula... But I'm having trouble to get to the right expression...
Can you show your attempt?
 

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