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2 April, 05:13

You are using a Geiger counter to measure the activity of a radioactive substance over the course of several minutes. If the reading of 400. counts has diminished to 100. counts after 66.7 minutes, what is the half-life of this substance? Express your answer with the appropriate units.

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  1. 2 April, 06:50
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    Answer: 33.35 minutes

    Explanation:

    A (t) = A (o) * (.5) ^[t / (t1/2) ] ... equ1

    Where

    A (t) = geiger count after time t = 100

    A (o) = initial geiger count = 400

    (t1/2) = the half life of decay

    t = time between geiger count = 66.7 minutes

    Sub into equ 1

    100=400 (.5) ^[66.7 / (t1/2)

    Equ becomes

    .25 = (.5) ^[66.7 / (t1/2) ]

    Take log of both sides

    Log 0.25 = [66.7 / (t1/2) ] * log 0.5

    66.7 / (t1/2) = 2

    (t1/2) = (66.7/2) = 33.35 minutes
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