Half-Life Compound Decay

  1. A 100 mg sample of magnesium-27 decays by 7% of its previous mass every minute. Determine its half-life and start the half-life decay equation.

    The textbook that I got this from (Nelson Physics 11) tells me the answer, but uses a long and annoying process to find it: creating a table at different points in time and then graphing. I am just wondering if there is an equation or some sort of trick to this type of question? It would save me a lot of time and trouble, thank you in advance.
  2. jcsd
  3. ChrisVer

    ChrisVer 2,403
    Gold Member

    It's a series.. it tells you that at each minute it loses 7% of what it had before... So it's better to use a table and see it...
  4. Yes, it is very possible to derive a general expression for the amount left after a given time. If the sample loses 7% of its mass every minute, what is the ratio of mass left to original mass after 1 minute? What is the ratio after two minutes? Three minutes? Do you see a pattern? In that case, what should be the mass left after a time T?
  5. arivero

    arivero 3,074
    Gold Member

    To honour the "Compound" in the title of the post... Can someone point to the general formula for a decay chain, with elements having different half-lifes?
  6. mfb

    Staff: Mentor

    The right formula depends on what you want to know, but it is possible to get everything with the right integral for the considered problem.
  7. Meir Achuz

    Meir Achuz 2,076
    Science Advisor
    Homework Helper
    Gold Member

    The question seems too simple.
    ##\exp(-t/\tau)=0.93##, so ##\tau=-1/\ln(.93)## in minutes.
    Last edited: Aug 29, 2014
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