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Finding the half-life of an unknown substance

  1. Jul 22, 2003 #1

    Sam

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    1000 particles of an unknown radioisotope decays to 472.37 particles in 50 days.

    (a) What is the half-life of this substance?


    Any problems that I had done previously, the half-life was given.

    Any help will be greatly appreciated.

    Well, I know a few things, but don't know if they apply to this problem:

    The decay constant = .693/T base 1/2
    t 1/2 = half-life

    Time to decay to a single particle = LN(Nbase0)/decay constant

    N = number of particles remaining at some elapsed time
    Nbase0 = number of particles we started with
    e = a symbol that represents the irrational number 2.718281828...
    lambda = decay constant
    x = elapsed time

    The formula to determing how much of the substance will be remaining at any particular time is: N = Nbase0 e^-lambda x
     
  2. jcsd
  3. Jul 22, 2003 #2
    Hi Sam,
    you give the correct formulae
    N = N0e-[lamb]x
    and
    [lamb]=.693/T1/2.
    You could combine these, solve for T1/2, and plug in N0, N, and x.

    Or, more instructive, you could use the equation
    N = N0 * (1/2)x/T1/2.

    In both cases, the important step is applying the ln() to both sides of the equation.
     
    Last edited: Jul 22, 2003
  4. Jul 22, 2003 #3

    Sam

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    Thank you.

    I'll give it a try.
     
  5. Jul 22, 2003 #4

    Sam

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    Is this correct?

    I used, based on the above:

    N(t) = N base0^(-lambda x /T),
    where T is the half-life
    t = 50 days
    N base0 = 1000

    I rounded to the nearest whole number for days and came up with 46.

    Is that correct?
     
  6. Jul 22, 2003 #5
    Re: Is this correct?

    I think it should read
    N(x) = N0eln(1/2)x/T, but that's probably just a typo, since
    is correct (except x=50 days), and your answer is also correct, although they probably expect you to come up with some more decimals...:wink:
     
    Last edited: Jul 22, 2003
  7. Jul 31, 2003 #6

    Sam

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    More Help, Please...

    I have two more parts to this problem:

    (a) How much will be left after 75 days?
    (b) How long will it take the 1000 particles to decay to a single particle?

    For (a), I came up with: 324.656 particles
    For (b), I came up with: 460.521 days

    Will you please verify my answers?

    Thank you!
     
  8. Jul 31, 2003 #7
    Both of your answers are correct.
     
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