Question

2. Chernobyl is back in the news, with wildfires in the “uninhabited” forest that has grown up around the damaged reactor. Two of the radioactive fission products released in the Chernobyl reactor accident were 131I (t1/2 = 8.0 d) and 137Cs (t1/2 = 30 yr). (a) The Chernobyl accident occured in Spring 1986 (34 years ago), releasing 100 kg of 137Cs: how much of the released 137Cs remains after 34 years (“now”)? (b) What was the radioactivity (decays/second) from 137Cs when the accident occurred? What is it now? (c) About five atoms of 137Cs atoms are produced by fission for each atom of 131I produced (it’s not that a single fission produces 5 atoms of 137Cs, it’s just that it’s more likely to be produced, on average); how long after the initial accident did it take for these two sources of radioactivity to be equal in decay rate?

Answer 1

If is the half life of a material then the fraction of it that reamined after decaying in time t is given by

=

So ammount of Cs137 remained is 100*0.456=45.6 kg.

b. Mass of Cs is 137u(about).

In 100 kg Cs the number of atoms is

Dissociation constant

We have used the fact that one solar day = 86400 sec.

Decay rate when accident occured =

Decay rate now

This is because N is decayed to 0.456 of initial ammount.

c. Decay rate =

Decay rate will be same when

Where N is the current number of atoms and N0 are the initial ammount now initially N0 for Cs is 5 times the N0 of I. Also the half lives are denoted by . So my equation gives after some simplification and converting both the half lives in days(137*365 for Cs and 8 for I),

= 82.316 days.

After 82.316 days the decay rates will be same for both elements.