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12 April, 20:16

A whalebone that originally contained 212 grams of C-14, half-life of 5700 years, now contains only 53 grams of C-14. How old is the whale bone?

A) 2850 years

B) 5700 years

C) 11400 years

D) 17100 years

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Answers (1)
  1. 12 April, 20:18
    0
    The answer is C) 11400 years

    Let's first calculate the remaining amount in percent:

    212g is original amount or 100%.

    53 g is x percents.

    212 g : 100% = 53 g : x

    x = 100% * 53 g : 212 g

    x = 25% = 0.25

    Now, using the formula to calculate the number of half-lives:

    (1/2) ⁿ = x,

    where

    x is the remaining amount: x = 0.25

    n is the number of half-lives

    1/2 stands for half-life.

    (1/2) ⁿ = 0.25

    ⇒ n*log (1/2) = log (0.25)

    n = log (0.25) / log (1/2) = log (0.25) / log (0.5) = - 0.602/-0.301 = 2

    The number of half-lives is 2.

    Now, the number of half-lives (n) is a quotient of total time elapsed (T) and length of half-life (L):

    n = T/L

    We know:

    n = 2

    L = 5700 years

    T = ?

    Thus

    T = L * n

    L = 5700 years * 2

    L = 11400 years
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