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    half-life

    3) Californium-252 has a half-life of 2.645 years. If the equation describing the decay of the readioactive nuclei is given by y=y_0e^{kt}, find:
    a) the value of k
    b) how long it will take for 95% of the radioactive nuclei to disintegrate.

    Please offer a step-by-step solution; I don't know how to do half-lifes really, but need to for my exam.
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    Quote Originally Posted by jangalinn View Post
    3) Californium-252 has a half-life of 2.645 years. If the equation describing the decay of the readioactive nuclei is given by y=y_0e^{kt}, find:
    a) the value of k
    b) how long it will take for 95% of the radioactive nuclei to disintegrate.

    Please offer a step-by-step solution; I don't know how to do half-lifes really, but need to for my exam.
    This is the second problem in which you say you have an exam coming up but have no idea how to do a problem. That's a very bad situation!

    Half life MEANS "time until only half is left"- if you start with y_0, after one "half life" you will have y_0/2 left.

    Put that into your given equation: y_0/2= y_0e^{kt} when t is the half life- which you are told is 2.045 years: y_0/2= y_0e^{2.045k}. The " y_0"s cancel leaving 1/2= 0.5= e^{2.045k}. Solve for k by taking the logarithm of both sides.

    Once you know k, use 0.95y_0 instead of y_0/2 and the value of k you just found: 0.95y_0= y_0e^{kt} and solve for t.
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    Quote Originally Posted by HallsofIvy View Post
    This is the second problem in which you say you have an exam coming up but have no idea how to do a problem. That's a very bad situation!

    Half life MEANS "time until only half is left"- if you start with y_0, after one "half life" you will have y_0/2 left.


    Once you know k, use 0.95y_0 instead of y_0/2 and the value of k you just found: 0.95y_0= y_0e^{kt} and solve for t.
    The general solution for finding half-life for a radioactive decay is t_{1/2} = \frac{ln2}{2}. It is derived from finding k in terms of t
    Last edited by mr fantastic; June 15th 2009 at 04:28 AM. Reason: Fixed a bit of latex
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