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## Homework Statement

The acitvities from the fission products

^{131}I and

^{133}I were measured in the air of Gothenburg April 28 1986 at 17:00. The result was 0.12 Bq/m

^{3}and 0.39 Bq/m

^{3}for

^{131}I and

^{133}I respectively. These isotopes came from the Chernobyl nuclear reactor disaster. Use this information to calculate when the reactor container exploded. The relative amount of

^{131}I and

^{133}produced in the fission of

^{236}U is 2.892 and 6.686 percent respectively.

## Homework Equations

t

_{½}(

^{131}I) = 8 days = 24 x 60 x 60 x 8 seconds = 691200 sec

t

_{½}(

^{133}I) = 21 hours = 21 x 60 x 60 seconds = 75600 sec

The activity for short-lived nuclides: [tex]A(t)=\lambda N_{0}e^{-\lambda t}[/tex], where [tex]A[/tex] is the acitivity, [tex]N[/tex] the number of radioactive nuclei and [tex]N_{0}=N(t=0)[/tex]

## The Attempt at a Solution

The decay law, numerical values inserted for [tex]^{131}I[/tex] and [tex]^{133}I[/tex] respectively, divided by each other to get rid of [tex]N_{0}[/tex] which is unknown:

[tex]\frac{2.892 \times 0.12}{6.686 \times 0.39}=\frac{e^{-\lambda_{131}t}}{e^{-\lambda_{133}t}}[/tex]

Some algebra gives [tex]t=137707[/tex] seconds. Subtracting this from the given date gives April 27 02:44:53 as the date of the Chernobyl disaster. Wikipedia (for instance) states that the accident happened "26 April 1986 01:23:45 a.m. (UTC+3)" which is the same as April 26, 03:23:45 a.m Gothenburg time. Since my solution is so far off from the actual date I figured I must have done something wrong. Can anybody help me out here, please?

Thanks in advance!