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5 February, 12:39

The half-life of C-14 is 5470 years. If a particular archaeological sample has one-quarter of its original radioactivity remaining, what is the best estimate for its age?

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  1. 5 February, 14:08
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    When there remains one-quarter of the sample, the age of the sample is 10940 years

    Explanation:

    Step 1: Data given

    The half-life of C-14 is 5470 years.

    The half - life time is the time required for a quantity to reduce to half of its initial value.

    This means after 5470 years there remains half of the C-14 sample.

    To remain a quarter of the sample, another cycle of 5470 years is required.

    This means 2 half-lives should have passed to remain a quarter of the sample.

    Step 2: Calculate it's age

    t / (t/1/2) = 2

    ⇒ with t = the age (or time) of the sample

    ⇒ with t (1/2) = the half-life time of the sample = 5470 years

    ⇒ with 2 = the number of halvf - lives passed

    t/5470 = 2

    t = 2*5470 = 10940 years

    When there remains one-quarter of the sample, the age of the sample is 10940 years
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