Carbon-14 Dating Age Calculation

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The discussion focuses on calculating the age of a carbon sample using Carbon-14 dating. The formula provided is t = Ln(N) / Ln(No) * -lambda, which can be adapted to t = Ln(A) / Ln(r) * -lambda, where A is the activity of the sample and r is the current ratio of carbon-14 to total carbon. The user is seeking assistance in incorporating additional terms, specifically the mass of carbon and the decay constant, into the equation. The challenge lies in integrating these variables while maintaining the accuracy of the age calculation. Clarification on the relationship between these terms is needed for a complete solution.
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Homework Statement



Find the age t of a sample, if the total mass of carbon in the sample is m_c, the activity of the sample is A, the current ratio of carbon 14 to total carbon in the atmosphere is r , and the decay constant of carbon 14 is lamda . Assume that, at any time, carbon 14 is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to carbon 14 . Also assume that the ratio of carbon 14 to total carbon in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of carbon 14 atoms in the sample was set.
Express your answer in terms of the mass m_a of a carbon 14 atom, m_c ,A , r , and lamda.


Homework Equations



t = Ln(N) / Ln(No)* -lamda


The Attempt at a Solution




t = Ln(N) / Ln(No)* -lamda
t = Ln(R) / Ln(Ro)* -lamda
= Ln(A) / Ln (r)* -lamda

but then I don't know how to corporate with other terms..
please help me.. thanks..
 
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