Dating method based on rate of decay of radioactive isotopes

Archaeologists have estimated that this occurred about 11,000 yr ago, but some argue that recent discoveries in several sites in North and South America suggest a much earlier arrival.Analysis of a sample of charcoal from a fire in one such site gave a The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value.The techniques that have been developed for this application are known as radioisotope dating techniques.The most common method for measuring the age of ancient objects is carbon-14 dating.

In fact, radioactive decay is a first-order process and can be described in terms of either the differential rate law () or the integrated rate law: $N = N_0e^$ $\ln \dfrac=-kt \label$ Because radioactive decay is a first-order process, the time required for half of the nuclei in any sample of a radioactive isotope to decay is a constant, called the half-life of the isotope.

In a first-order reaction, every half-life is the same length of time. Calculate the half-life for the hydrolysis reaction under these conditions.

If a freshly prepared solution of cis-platin has a concentration of 0.053 M, what will be the concentration of cis-platin after 5 half-lives? What is the percent completion of the reaction after 5 half-lives? Given: rate constant, initial concentration, and number of half-lives Asked for: half-life, final concentrations, and percent completion Strategy: at 650°C.

The half-lives of several isotopes are listed in In our earlier discussion, we used the half-life of a first-order reaction to calculate how long the reaction had been occurring.

Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.

In fact, radioactive decay is a first-order process and can be described in terms of either the differential rate law () or the integrated rate law: $N = N_0e^$ $\ln \dfrac=-kt \label$ Because radioactive decay is a first-order process, the time required for half of the nuclei in any sample of a radioactive isotope to decay is a constant, called the half-life of the isotope.In a first-order reaction, every half-life is the same length of time. Calculate the half-life for the hydrolysis reaction under these conditions.If a freshly prepared solution of cis-platin has a concentration of 0.053 M, what will be the concentration of cis-platin after 5 half-lives? What is the percent completion of the reaction after 5 half-lives? Given: rate constant, initial concentration, and number of half-lives Asked for: half-life, final concentrations, and percent completion Strategy: at 650°C.The half-lives of several isotopes are listed in In our earlier discussion, we used the half-life of a first-order reaction to calculate how long the reaction had been occurring.Because nuclear decay reactions follow first-order kinetics and have a rate constant that is independent of temperature and the chemical or physical environment, we can perform similar calculations using the half-lives of isotopes to estimate the ages of geological and archaeological artifacts.What is the half-life for the reaction under these conditions?