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16 August, 01:15

Carbon-14 has a half-life of 5720 years and this is a first order reaction. If a piece of wood has converted 75% of the carbon-14, then how old is it?

A) 11440 years

B) 2375 years

C) 4750 years

D) 4290 years

E) 1430 years

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Answers (1)
  1. 16 August, 01:37
    0
    The amount of the substance (At) at any time t is calculated through the equation,

    At = (A0) (e^-kt)

    where A0 is the initial amount and k is constant.

    For the half-life,

    ln (At / A0) = ln 0.5 = - k (5270 years)

    The value of k is 1.3153x10^-4 / year.

    Substituting this value to the same equation, where At = 0.25A0

    ln 0.25 = - (1.3153 x 10^-4) (t)

    The value of t from this equation is 10540 years. The closest value to this is letter A.
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