Question

complete the table shown to the right for the half - life of a certain radioactive substance. half - life: 18.4 days, decay rate, k. k = □ (round to six decimal places as needed.)

Explanation:

Step1: Recall decay - rate formula

The formula for the decay rate $k$ of a radioactive substance in terms of half - life $T$ is $k=\frac{\ln 2}{T}$.

Step2: Substitute the given half - life value

Given $T = 18.4$ days. Substitute $T$ into the formula: $k=\frac{\ln 2}{18.4}$.

Step3: Calculate the value of $k$

Using a calculator, $\ln 2\approx0.693147$, so $k=\frac{0.693147}{18.4}\approx0.037671$.

Answer:

$0.037671$