Question

A Chemist has a 20-mg sample of polonium-218. He needed approximately 81.5% of it for an experiment. given that the half-life of polonium-218 is approximately 3.1 min, how many seconds will it take for the sample to decay to the desired mass

Answer 1

52 seconds

Answer 2

since it's a first-order process, you can use the integrated rate law equation:

\(ln[A]_t=-kt+ln[A]_o\)

where

\([A]_t\) is the amount of substance after t time has elapsed.
\([A]_o\) is initial amount
k is the decay constant
t is time

you can sub in: \(t_{1/2}=\dfrac{ln(2)}{k}\); where \(t_{1/2}\) is the half-life

you end up with:

\(ln[A]_t=-\dfrac{ln(2)*t}{t_{1/2}}+ln[A]_o\)

plug and chug.


The answer is 49.64 seconds

Answer 3

i knew that