posted by amy on .
A researcher wishes to extract
Ba. She obtains a 1000 MBq virgin
Ba-140 sample and must wait until the maximum activity of La-140 is available.
a) Write down the decay relationship (include half-lives), and
include the final stable product. How long must the researcher
wait until there is maximum
b)What activity of
La does she collect, is she extracts the
completely from the
Ba, when the
La is at maximum
The reactions involved are
140Ba -> 140La + e-,
half life 12.8 days
140La -> 140Ce(stable) + e-,
half life 40.2 hours
Set up and solve the differential equation for [140La] and solve for the time is reaches its maximum value, which would be when d/dt[La] = 0
The population of 140Ba is
This will allow you to write an equation for the rate La is created. Set that equal to the rate La is destroyed by decay. You should be able to solve for [La] at that time. It is probably easier to do with decay coefficients rather than half lives.