The half-life for radioactive decay of \(^{14}C\) is 5730 years. An archaeological artifact containing wood had only 80% of the \(^{14}C\) found in a living tree. Estimate the age of the sample.
The half-life for radioactive decay of \(^{14}C\) is 5730 years. An archaeological artifact containing wood had only 80% of the \(^{14}C\) found in a living tree. Estimate the age of the sample.
Solution and Explanation
\(k = \frac {0.693}{t_{\frac 12}}\)
\(k = \frac {0.693}{5730\ years}\)
\(It\ is\ known\ that,\)
\(t = \frac {2.303}{k} log \frac {[R]_0}{[R]}\)
\(t = \frac {2.303}{\frac {0.693}{5730} }log \frac {100}{80}\)
\(t = 1845\ years\ (approximately)\)
\(Hence,\ the\ age \ of \ the\ sample \ is \ 1845\ years.\)
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Concepts Used:
Rate of a Chemical Reaction
The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit time.
Consider the reaction A → B,
Rate of the reaction is given by,
Rate = −d[A]/ dt=+d[B]/ dt
Where, [A] → concentration of reactant A
[B] → concentration of product B
(-) A negative sign indicates a decrease in the concentration of A with time.
(+) A positive sign indicates an increase in the concentration of B with time.
Factors Determining the Rate of a Reaction:
There are certain factors that determine the rate of a reaction:
- Temperature
- Catalyst
- Reactant Concentration
- Chemical nature of Reactant
- Reactant Subdivision rate