Question

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

Explanation:

Step1: Use the half - life formula

The formula for the decay constant \(k\) in terms of half - life \(T\) is \(k=\frac{\ln 2}{T}\).

Step2: Substitute the value of \(T\)

Given \(T = 10.6\) days. So \(k=\frac{\ln 2}{10.6}\).
Since \(\ln 2\approx0.693147\), then \(k=\frac{0.693147}{10.6}\).

Step3: Calculate the value

\(k=\frac{0.693147}{10.6}\approx0.065391\)

Answer:

\(0.065391\)