Problema Solution
The radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 35-g mass of americium-241.
How much will be left after 383 years? Compute the answer to three significant digits.
Answer provided by our tutors
The formula for determining the amount of substance left is A=ce^(kt) where C is the initial amount, k is the decay constant, and t is time. Solve the above equation for k
Given the half-life of 432 years.
A/2=A ce^(432k).
½=e^(432k).
Taking log both sides.
Ln(1/2 )=ln(e^(432k).
-0.693=432k.
K=-0.693/432.
=-0.0016
Amount after 383 years.
A=35*e^(-0.0016*383).
=18.964 grams.