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You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find that 0.1 gram of the radioactive material is still left. What is the half-life? (Round your answer to three significant digits.)

  • math -

    after the theft, there was 1 g left.
    If the half-life is n days, then the fraction left after t days is


    so, solve this for n:

    0.1 = (1/2)^(8/n)
    ln 0.1 = (8/n) ln 0.5
    ln .1/ln .5 = 8/n
    n = 8 * ln .5/ln .1
    n = 2.4 days

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