Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
