Question

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

Explanation:

Step1: Recall the formula for half - life

The formula for the half - life \(T\) of a radioactive substance is \(T=\frac{\ln2}{k}\), where \(k\) is the decay rate.

Step2: Solve for \(k\)

We can rewrite the formula as \(k = \frac{\ln2}{T}\). Given \(T = 19.1\) days.
Substitute \(T\) into the formula: \(k=\frac{\ln2}{19.1}\).
We know that \(\ln2\approx0.693147\).
So \(k=\frac{0.693147}{19.1}\).

Step3: Calculate the value of \(k\)

\(k=\frac{0.693147}{19.1}\approx0.036290\)

Answer:

\(k\approx0.036290\)