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Math Help - Half-life

  1. #1
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    Question Half-life

    Radium-221 has a half-life of 30 seconds. How long will it take for 85% of a sample to decay?


    Ok so I really don't know what to do here. I know I can find r because its r=ln(2)/30 but what about the 85%? Any help is appreciated.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by n8thatsme View Post
    Radium-221 has a half-life of 30 seconds. How long will it take for 85% of a sample to decay?


    Ok so I really don't know what to do here. I know I can find r because its r=ln(2)/30 but what about the 85%? Any help is appreciated.
    Let N_0 be the initial amount of Radium-221, and let N be the current amount of Radium.

    Since 85% decayed, that means that the current amount is 15% of the original amount.

    Thus, this implies that N=.15N_0\implies \frac{N}{N_0}=.15

    Since the decay is modeled by N=N_0e^{-kt}, we see now that .15 = e^{-kt}

    Now, k can be found using the half-life formula: \lambda=\frac{\ln2}{k}\implies k=\frac{\ln 2}{\lambda}, where \lambda is the half-life.

    So our equation now has the form 0.15=e^{-\frac{\ln2}{\lambda}t}

    Can you take it from here?

    --Chris
    Last edited by Chris L T521; October 3rd 2008 at 11:20 PM.
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