Question

complete the table shown to the right for the half - life of a certain radioactive substance.
half - life: 18.5 days
decay rate, k
k =
(round to six decimal places as needed.)

Explanation:

Step1: Recall the decay formula

For radioactive decay, the relationship between half - life ($t_{1/2}$) and decay rate ($k$) is given by the formula $k=\frac{\ln(2)}{t_{1/2}}$.

Step2: Substitute the given half - life

We know that $t_{1/2} = 18.5$ days. So we substitute this value into the formula: $k=\frac{\ln(2)}{18.5}$.

Step3: Calculate the value

We know that $\ln(2)\approx0.693147$. Then $k=\frac{0.693147}{18.5}\approx0.037467$.

Answer:

$k\approx0.037467$