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Homework Help: Half life of K

  1. Jun 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Hei!Half life of the reaction is about 1,25 billion years. Assuming that the age of earth is 5 billion years,the concentration of K on earth since its formation decreased:
    a)2times b)4times c)8 times d)16times


    3. The attempt at a solution
    So I just do like that T[itex]\underline{}1/2[/itex]=1,25 bilion years
    age=5 bilion years
    so in the begining we have X and then it is X/2 so we 1,25 bilion year
    then X/4 it is 2,5 bilion year and then X/8 so it is 5 bilion years
    so the answer i think is it decreased 8 times
    but my question is: is there easier way to do it?

    thanks in advance!
     
  2. jcsd
  3. Jun 24, 2012 #2

    Borek

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    Staff: Mentor

    After half life you are left with [itex]\frac 1 2[/itex] of the initial amount, after two half lives you are left with half of that or [itex]\frac 1 2 \times \frac 1 2 = (\frac 1 2)^2[/itex] of the initial amount, after three half lives you are left with half of that or [itex](\frac 1 2)^3[/itex] of the initial amount and so on.
     
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