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Math Help - radio-carbon dating problem

  1. #1
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    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)
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  2. #2
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    Quote Originally Posted by Obstacle1 View Post
    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
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    Quote Originally Posted by CaptainBlack View Post
    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)...
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    Quote Originally Posted by Obstacle1 View Post
    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)
    Quote Originally Posted by Obstacle1 View Post
    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:

    <br />
N'(T)/N'(0) = N(T)/N(0) <br />

    RonL
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