Posted by **amy** on Thursday, February 3, 2011 at 12:03am.

A researcher wishes to extract

140

La from

140

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

140

La available?

b)What activity of

140

La does she collect, is she extracts the

140

La

completely from the

140

Ba, when the

140

La is at maximum

activity?

- nuclear physics -
**drwls**, Thursday, February 3, 2011 at 11:41am
The reactions involved are

140Ba -> 140La + e-,

half life 12.8 days

and

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

[140Ba^]*(1/2)^(t/12.8)

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.

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