Question

complete the table shown to the right for the half-life of a certain radioactive substance.
half-life
4691 years
decay rate, k
k =
(round to six decimal places as needed.)

Explanation:

Step1: Recall the formula for decay rate

The formula that relates the half - life ($t_{1/2}$) and the decay rate ($k$) for radioactive decay is $k=\frac{\ln(2)}{t_{1/2}}$.

Step2: Substitute the given half - life value

We are given that $t_{1/2} = 4691$ years. Substitute this value into the formula: $k=\frac{\ln(2)}{4691}$.
We know that $\ln(2)\approx0.693147$. So, $k=\frac{0.693147}{4691}$.

Step3: Calculate the value of k

Perform the division: $k\approx0.693147\div4691\approx0.00014776$.

Answer:

$k\approx0.000148$ (rounded to six decimal places)