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20 January, 23:06

Suppose the amount of a certain radioactive substance in a sample decays from to over a period of days. Calculate the half life of the substance. Round your answer to significant digit.

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  1. 20 January, 23:54
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    The given question is incomplete, the complete question is:

    Suppose the amount of a certain radioactive substance in a sample decays from 1.30 mg to 100. ug over a period of 29.5 days. Calculate the half life of the substance Round your answer to 2 significant digits.

    Answer:

    The correct answer is 7.974 days.

    Explanation:

    Based on the given question, the concentration of a radioactive substance present in a sample get decays to 100 micro grams from 1.30 milligrams in 29.5 days. There is a need to find the half-life of the substance.

    Radioactive decay is an illustration of first order reaction.

    K = (2.303 / t) log [a / (a-x) ]

    Here a is 1.30 mg and (a-x) is 100 micrograms = 100 * 10^-3 mg or 0.1 mg, and t is 29.5 days. Now putting the values we get,

    K = (2.303 / 29.5) log (1.30/0.1)

    = 2.303/29.5 log13

    = 2.303/29.5 * 1.1139

    K = 0.0869

    The half-life or t1/2 is calculated by using the formula, 0.693 / K

    = 0.693 / 0.0869

    = 7.974 days.
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