Thread: radio-carbon dating problem

1. radio-carbon dating problem

In an ancient cave, charcoal fragments have a decay rate of 1.69 disintegrations per minute per gram of carbon 14. In comparison the decay rate for living tissue is 13.5 disintegrations per minute per gram. Find the age of the carbon fragments..

let T be the time the charcoal was formed and t=0 be the present day.

Can someone explain why N'(T)/N(0) = N(T)/N(0)

additional info: half life is 5568 years and assuming exponential decay so N'=-kN and N(T)=n0*exp(-kT)

2. Originally Posted by Obstacle1
In an ancient cave, charcoal fragments have a decay rate of 1.69 disintegrations per minute per gram of carbon 14. In comparison the decay rate for living tissue is 13.5 disintegrations per minute per gram. Find the age of the carbon fragments..

let T be the time the charcoal was formed and t=0 be the present day.

Can someone explain why N'(T)/N(0) = N(T)/N(0)

additional info: half life is 5568 years and assuming exponential decay so N'=-kN and N(T)=n0*exp(-kT)
Isn't it the case that the number of disintegrations per unit time per unit mass goes down with passing time? If so how can an old specimen have a decay rate of 1.69 disintegrations per minute per gram compared to a decay rate of 13.5 disintegrations per minute per gram for a zero age specimen?

RonL

3. Originally Posted by CaptainBlack
Isn't it the case that the number of disintegrations per unit time per unit mass goes down with passing time? If so how can an old specimen have a decay rate of 1.69 disintegrations per minute per gram compared to a decay rate of 13.5 disintegrations per minute per gram for a zero age specimen?

RonL

Sorry I got this the wrong way round. The 1.69 represents current samples of the charcoal from the cave so its N'(0) and the 13.5 is decay rate for living tissue so its N'(T)...

4. Originally Posted by Obstacle1
In an ancient cave, charcoal fragments have a decay rate of 1.69 disintegrations per minute per gram of carbon 14. In comparison the decay rate for living tissue is 13.5 disintegrations per minute per gram. Find the age of the carbon fragments..

let T be the time the charcoal was formed and t=0 be the present day.

Can someone explain why N'(T)/N(0) = N(T)/N(0)

additional info: half life is 5568 years and assuming exponential decay so N'=-kN and N(T)=n0*exp(-kT)
Originally Posted by Obstacle1
Sorry I got this the wrong way round. The 1.69 represents current samples of the charcoal from the cave so its N'(0) and the 13.5 is decay rate for living tissue so its N'(T)...
First $N'(0)=k N(0)=k n_0 \exp(-k0)=k n_0$

$N'(T)=k n_0 \exp(-kT)=N'(0) \exp(-kT) \ \ \ \ \dots(1)$.

Also:

$N(T)=n_0 \exp(-kT)=N(0) \exp(-kT)$, so:

$\exp(-kT) = N(T)/N(0)$.

Now substitute this into $(1)$ to get:

$
N'(T)/N'(0) = N(T)/N(0)
$

RonL

5. Thanks