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Math Help - Differential Equation - Radioactive Decay

  1. #1
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    Differential Equation - Radioactive Decay

    I have a pretty hard differential equation here:

    In the nuclear medicine department of a hospital, a radioactive isotope is being produced. The isotope is produced at the rate of 5 milligrams per minute, but has a half-life of only 20 minutes. Write differential equations to find the amount of the isotope present after an hour of production.


    Now this one's a bit wierd...

    I'm fine with an 'initial amount' problem but when there is a constant production, well it's a bit hard.

    What I think to put is

    dM/dt = 5-how much is lost (0.5M/20?????)

    But I can't really work with that... can someone please help me?
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  2. #2
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    Quote Originally Posted by jeta View Post
    I have a pretty hard differential equation here:

    In the nuclear medicine department of a hospital, a radioactive isotope is being produced. The isotope is produced at the rate of 5 milligrams per minute, but has a half-life of only 20 minutes. Write differential equations to find the amount of the isotope present after an hour of production.


    Now this one's a bit wierd...

    I'm fine with an 'initial amount' problem but when there is a constant production, well it's a bit hard.

    What I think to put is

    dM/dt = 5-how much is lost (0.5M/20?????)

    But I can't really work with that... can someone please help me?
    \frac{dm}{dt} = 5 - \lambda m subject to the boundary condition m = 0 when t = 0 and where 20 = \frac{\ln 2}{\lambda}.
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  3. #3
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    How do you know that k (you used lamda(sp??)) is equal to ln(2)/Half-life???
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  4. #4
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    Quote Originally Posted by jeta View Post
    How do you know that k (you used lamda(sp??)) is equal to ln(2)/Half-life???
    Read this: Exponential decay - Wikipedia, the free encyclopedia
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