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?