# nuclear physics

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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 -

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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