24.127 CP - Chemistry: Molecular Nature Of Matter And Change

Question

Carbon from the remains of an extinct Australian marsupial, called Diprotodon, has a specific activity of  0.61 pCi/g. Modern carbon has a specific activity of 6.89 pCi/g. How long ago did the Diprotodon apparently become extinct?

Step-by-Step Solution

Answer

The Diprotodon apparently become extinct t=20041.3796yr

Step 1: Definition of Diprotodon

Diprotodon is a Pleistocene period genus of giant marsupials that lived in Australia. It is one of Australia's most important "megafauna" species, ranging across the continent during the Pleistocene.

Step 2: How long ago did the Diprotodon apparently become extinct?

We must use the half-life formula to find the constant (k) in this situation.

$$\begin{gathered} t_{\frac{1}{2}}=\frac{\ln 2}{k}\to k=\frac{\ln 2}{t_{\frac{1}{2}}} \\ k=\frac{\ln 2}{t_{\frac{1}{2}}}=\frac{\ln 2}{5730yr} \\ =\frac{1.2096809x{10}^{-4}}{yr} \end{gathered}$$
 

We can solve for the value of t by using the expression for calculating the number of nuclei left.

$$\begin{gathered} \ln \frac{N_0}{N_t}=kt \\ \ln \frac{6.89pCi}{0.61pCi}=\frac{1.2096809x{10}^{-4}}{yr}\left(t\right) \\ t=20041.3796yr \end{gathered}$$

Thus, the Diprotodon apparently become extinct t=20041.3796yr