Question

complete the table shown to the right for the half - life of a certain radioactive substance.
half - life: 4402 years
decay rate, k
k =
(round to six decimal places as needed.)

Explanation:

Step1: Recall decay formula

For radioactive decay, the formula relating half - life ($t_{1/2}$) and decay rate ($k$) is $t_{1/2}=\frac{\ln(2)}{k}$, so we can solve for $k$ as $k = \frac{\ln(2)}{t_{1/2}}$.

Step2: Substitute values

We know that $t_{1/2}=4402$ years and $\ln(2)\approx0.693147$. Substitute these values into the formula: $k=\frac{0.693147}{4402}$.

Step3: Calculate the result

Perform the division: $k=\frac{0.693147}{4402}\approx0.00015746$.

Answer:

$k\approx0.000157$ (rounded to six decimal places)