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1 May, 17:19

Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.137 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood

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  1. 1 May, 20:32
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    Answer: 4282.928 = 4283 years

    Explanation:

    Data given;

    Carbon 14 half life = 5740

    No (initial radiation) = 0.230 Bq/g

    Nf (final radiation) = 0.137 Bq/g

    First we find the decimal fraction of the remaining half life of the carbon 14

    k = No / Nf

    k = (0.137 / 0.230) = 0.595652

    So to find how many half-life has elapsed, we say

    (1/2) ^n = k

    (1/2) ^n = 0.595652

    Therefore

    n log 0.5 = log 0.595652

    n = (log 0.595652) / (log 0.5)

    n = 0.747457

    To get the elapsed time or how old the sample is;

    We say

    Carbon 14 half-life * n

    5730 yrs * 0.747457

    = 4282.928

    = 4283 years.

    So the sample of the wood is 4283 years old.
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