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4 August, 19:22

The half life of a certain radioactive element is 800 years. How old is an object if only 12.5% of the radioactive atoms in it remains?

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  1. 4 August, 22:45
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    Given, half life of a certain radioactive element = 800 years.

    Amount of substance remaining at time t = 12.5%

    Lets consider the initial amount of the radioactive substance = 100%

    Using the half life equation:

    A = A₀ (1/2) ^t/t₁/₂

    where A₀ is the amount of radioactive substance at time zero and A is the amount of radioactive substance at time t, and t₁/₂ is the half-life of the radioactive substance.

    Plugging the given data into the half life equation we have,

    12.5 = 100. (1/2) ^t/800

    12.5/100 = (1/2) ^t/800

    0.125 = (0.5) ^t/800

    (0.5) ^3 = (0.5) ^t/800

    3 = t/800

    t = 2400 years

    Thus the object is 2400 years old.
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