Question

complete the table shown to the right for the half-life of a certain radioactive substance.

\

$$\begin{tabular}{|l|l|} \\hline half-life & decay rate, k \\\\ \\hline 18.5 days & \\\\ \\hline \\end{tabular}$$

\\(k = \square\\)
(round to six decimal places as needed.)

Explanation:

Relate half-life to the decay rate \(k\)

$$ k = \frac{\ln(2)}{T_{1/2}} $$

Substitute the given half-life value

$$ k = \frac{\ln(2)}{18.5} $$

Calculate and round to six decimal places

$$ k \approx \frac{0.69314718}{18.5} \approx 0.037467415 \approx 0.037467 $$

Answer:

Complete the table shown to the right for the half-life of a certain radioactive substance.

\(k =\) <blank>0.037467</blank>
(Round to six decimal places as needed.)