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

[yan__90]

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?

 

[tiny-tim]

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hi yan__90! welcome to pf!

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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? ​

 

[yan__90]

hi yan__90! welcome to pf!

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


hint: what is the meaning of A?

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

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?

 

[tiny-tim]

15.3 = 7 exp(-2.301 x 10 ^-10 t)

how can that be correct? …

the RHS is less than 7 ​