Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
We are asked to determine the decay constant of a radioactive element. To do that we will use the following formula:
[tex]A=A_0e^{-kt}[/tex]Where:
[tex]\begin{gathered} A=\text{ quantity of the element} \\ A_0=\text{ initial quantity} \\ k=\text{ decay constant} \\ t=\text{ time} \end{gathered}[/tex]The half time is the time when the quantity of the element is half the initial quantity. Therefore, we have:
[tex]\frac{A_0}{2}=A_0e^{-kt}[/tex]Now, we cancel out the initial quantitu:
[tex]\frac{1}{2}=e^{-kt}[/tex]Now, we solve for "t". First, we take the natural logarithm to both sides:
[tex]\ln(\frac{1}{2})=-kt[/tex]Now, we divide both sides by -t:
[tex]-\frac{1}{t}\ln(\frac{1}{2})=k[/tex]Now, we plug in the value of the time:
[tex]-\frac{1}{0.44day}\ln(\frac{1}{2})=k[/tex]Solving the operations:
[tex]1.575\frac{1}{day}=k[/tex]Therefore, the decay constant is 1.575 1/day.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
