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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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 ​

 

[paranormal]

As a scientist, it is important to clarify and understand the given information before attempting to solve the problem. In this case, the disintegration value should be substituted into the rate equation R=kt, where R is the rate of decay, k is the decay constant, and t is time. This will allow you to solve for the time (t) that has passed since the plant died. You can also use the half-life equation, t(1/2) = 0.693/k, to solve for the time it takes for half of the carbon-14 to decay. Both equations use the decay constant (k) which can be calculated using k = 1/t, where t is the half-life of carbon-14. By plugging in the given values, you can determine the approximate time that has passed since the plant died. This type of calculation is important in fields such as archaeology and geology, where carbon-14 dating is used to determine the age of organic materials.