How Long Ago Did the Plant Die Using Carbon-14 Dating?

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Homework Help Overview

The discussion revolves around a problem involving carbon-14 dating to determine the time since a plant died. The context includes the half-life of carbon-14 and the disintegration rates of a sample.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the appropriate use of disintegration values in equations, questioning whether to use them as R or A. There are attempts to clarify the meaning of A and how to express the disintegration rate mathematically.

Discussion Status

Some participants have provided hints and guidance regarding the interpretation of the variables involved. There is ongoing exploration of the calculations, with one participant questioning the validity of a proposed solution based on the relationship between the values.

Contextual Notes

Participants are navigating the implications of the carbon-14 decay equations and the significance of the disintegration rates provided in the problem statement. There is a focus on ensuring correct application of the formulas without reaching a definitive conclusion.

yan__90
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Homework Statement


half life of carbon 14 is 5730 years. living matter produces 15.3 disintegrations per min per gram of carbon it contains. A 1g sample of a plant from an excavation shows 7 disintegrations per min from carbon-14. how long did the plant die?


Homework Equations


k = 1/ t
t(1/2) = 0.693/k
A=Aoexp(-kt)
R=kt


The Attempt at a Solution


may i know if the disintegration value is to be sub into R or A?
 
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hi yan__90! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
yan__90 said:
half life of carbon 14 is 5730 years. living matter produces 15.3 disintegrations per min per gram of carbon it contains. A 1g sample of a plant from an excavation shows 7 disintegrations per min from carbon-14. how long did the plant die?

may i know if the disintegration value is to be sub into R or A?

hint: what is the meaning of A?

how would you write "7 disintegrations per min" as an equation? :wink:
 


tiny-tim said:
hi yan__90! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)


hint: what is the meaning of A?

how would you write "7 disintegrations per min" as an equation? :wink:


A stands for concentration.
this is my solution:
k = 0.693 / t
= 0.693 / (5730x365x24x60)
= 2.301 x 10 ^ -10

[A] = [Ao]exp(-kt)
15.3 = 7 exp(-2.301 x 10 ^-10 t)
t = 6465.5 years

is it correct?
 
Last edited:
yan__90 said:
15.3 = 7 exp(-2.301 x 10 ^-10 t)

how can that be correct? …

the RHS is less than 7 :confused:
 

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