Kinetics of consecutive reactions are easily applicable to nuclear decay process

Question

Kinetics of consecutive reactions are easily applicable to nuclear decay process, in which a parent isotope produces a radioactive daughter isotope that also decays. Consider the first order consecutive reactions:

210Bi (t1/2,1 over arrow) 210Po (t1/2, 2 over arrow) 206Pb

The half-lives, t1/2, 1 and t1/2, 2 are 5.01 days and 138.4 days respectively. Calculate the kinetic constant for the two steps in the radioactive decay series. Using a plot of fraction (normalized concentration) vs. time, comment on the relative amounts of 210Bi, 210Po, and 206Pb over time.

Explanation / Answer

kinetic constant for 1 )

K1 = 0.693 / half life = 0.693 / 5.01

K 1= 0.138 day-1

kinetic constant for 2 )

k2 = 0.693 / half -life

K2 = 0.693 / 138.4

K2 = 5.0 x 10^-3 day-1

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