Answer:
1.146 x 10⁴ year.
Explanation:
- The decay of carbon-14 is a first order reaction.
- The rate constant of the reaction (k) in a first order reaction = ln (2)/half-life = 0.693/(5730 year) = 1.21 x 10⁻⁴ year⁻¹.
- The integration law of a first order reaction is:
<em>kt = ln [A₀]/[A]</em>
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k is the rate constant = 1.21 x 10⁻⁴ year⁻¹.
t is the time = ??? years.
[A₀] is the initial percentage of carbon-14 = 100.0 %.
[A] is the remaining percentage of carbon-14 = 1/4[A₀] = 25.0 %.
∵ kt = ln [Ao]/[A]
∴ (1.21 x 10⁻⁴ year⁻¹)(t) = ln (100.0%)/[25.0 %]
(1.21 x 10⁻⁴ year⁻¹)(t) = 1.386.
∴ <em>t </em>= 1.386/
(1.21 x 10⁻⁴ year⁻¹) = <em>1.146 x 10⁴ year.</em>
