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Radioactive decay ratio problem

  1. Nov 2, 2008 #1
    1. The problem statement, all variables and given/known data
    A source contains two radioactive isotopes of phosphorus. P-32 has a half life of 14.3 days and P-33 has a half-life of 25.3 days.

    If 10% of the radioactive decays from the source are from P-33 atoms, calculate the ratio of the number of P-33 to P-32 in the source. The answer says 5.1 : 1.

    2. Relevant equations

    [tex]T_{1/2} = \frac{ln2}{\lambda} [/tex]

    3. The attempt at a solution

    Well I have calculated decay constant, but I don't know what to do with any of it. I really have no idea where to start.

    decay constant P-32 = 5.61E-7 s^-1
    decay constant P-33 = 3.17E-7 s^-1

    I tried:
    [tex] 0.1 = \frac{P_{33}}{P_{33} + P_{32}} [/tex]

    and rearranged and got 9. Which isn't 5.1. Last time I checked, anyway.
    Last edited: Nov 2, 2008
  2. jcsd
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