A radioactive isotope and its associated half-life are given. Assume that it dec
ID: 3018864 • Letter: A
Question
A radioactive isotope and its associated half-life are given. Assume that it decays according to the formula
A(t) = A0ekt
where A0 is the initial amount of the material and k is the decay constant.
Americium 241, used in smoke detectors, initial amount 0.28 micrograms, half-life of 432.7 years
Find the decay constant k. Round your answer to four decimal places.
k =
Find a function which gives the amount of isotope A which remains after time t. (Keep the units of A and t the same as the given data.)
A(t) =
Determine how long it takes for 60% of the material to decay. Round your answer to two decimal places. (HINT: If 60% of the material decays, how much is left?)
years
=
Explanation / Answer
A(t)=A0ekt
0.5A=A ek(432.7)
ln(0.5) = 432.7k
k=-0.0016
A(t)= 0.28 e-0.0016t
third part
60% decays means 40%left=0.4
0.4= e-0.0016t
ln 0.4=-0.0016t
t=572.68years
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.