Question

Recently, the skeleton of King Richard III was found under a parking lot in England. If tissue samples from the skeleton contain about 93.79% of the carbon-14 expected in living tissue, what year did King Richard III die? The half-life for carbon-14 is 5730 years.

Short answer

The half-life period of the carbon-14 in living tissues is 5730 years which has rate constant is 0.00012 year^-1 and the time-period taken to kill Richard-III die in 218.88 years or 219 years.

Step-by-step solution

Reaction Rate

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.

Numerical Explanation

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.