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The reaction involved the effective collision of two reactants to produce the desired products. Reactions can be natural, which occur in the surrounding environment, whereas it can be artificially done in the laboratory to form the desired product.

The reaction rate can be defined as the reaction speed to produce the products. The reaction rate can be slow, fast or moderate. The reaction can take less than a millisecond to produce products, or it can take years to produce the desired product.

The half-life period can be defined as the time period at which half the concentration of the reactants gets converted into a product.

The half-life period of the first-order decay of carbon-14 is:

\({\bf{Half - life period = }}\frac{{{\bf{ln }}\left( {\bf{2}} \right)}}{{\bf{k}}}\)

The half-life period of the carbon-14 = 5730 years

\(\begin{align}Half - life{\bf{ }}period{\bf{ }} &= {\bf{ }}\frac{{0.693}}{k}\\5730years{\bf{ }} &= {\bf{ }}\frac{{0.693}}{k}\\k{\bf{ }} &= {\bf{ }}\frac{{0.693}}{{5730years}}\\k &= 0.000121yea{r^{ - 1}}\end{align}\)

Rate constant of the reaction = 0.00012 year^-1 \(\)

The time period taken it to 93.79% of the initial dose is as follows:

\(\begin{align}k &= {\bf{ }}\frac{{2.303}}{t}Log{\bf{ }}\frac{{\left( A \right)}}{{{{\left( A \right)}_0}}}\\t &= {\bf{ }}\frac{{2.303}}{k}Log{\bf{ }}\frac{{0.9379{{\left( A \right)}_0}}}{{{{\left( A \right)}_0}}}\\t &= {\bf{ }}\frac{{2.303}}{{0.000121}}Log{\bf{ }}64\\t &= {\bf{ }}\frac{{2.303}}{{0.000121}} \times 0.0115\\t &= {\bf{ }}218.88years\end{align}\)

Therefore, the time period was taken to kill Richard-III died in 218.88 years or 219 years.