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26 November, 08:51

How old is a bone if it now. 3125 of C-14 when it originally had 80.0g of C-14

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  1. 26 November, 09:44
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    42960 years

    Explanation:

    We are given;

    Remaining mass of C-14 in a bone is 0.3125 g Original mass of C-14 on the bone is 80.0 g Half life of C-14 is 5370 years

    We are required to determine the age of the bone;

    Using the formula; Remaining mass = Original mass * 0.5^n, where n is the number of half lives.

    Therefore;

    0.3125 g = 80.0 g * 0.5^n

    3.90625 * 10^-3 = 0.5^n

    Introducing logarithm on both sides;

    log 3.90625 * 10^-3 = n log 0.5

    Solving for n

    n = log 3.90625 * 10^-3 : log 0.5

    = 8

    Therefore, the number of half lives is 8 But, 1 half life is 5370 years Therefore;

    Age of the rock = 5370 years * 8

    = 42960 years

    Thus, the bone is 42960 years old
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