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Government limits for sea water are based on an iodine 131 value of 40 Bq/L and a cesium 137 value of 90 Bq/L. On April 17, 2011, sea water contamination levels based on samples 20 km from the site had iodine 131 and cesium 137 concentrations of 161 Bq/L and 186 Bq/L, respectively. How much time must pass before the sea water sample reaches the government's limits?

Answer :

we know the equation of radiactive decreasing is:

[tex]m_f=m_ie^{-\lambda t}[/tex]

where mf is the final concentration (40 and 90 bq/L) mi is the initial concentration (161 and 186 bq/L), lamda is the decreacion constant of each element and t is the time, so we replace the information and solve the equation for t:

[tex]\begin{gathered} \ln (\frac{m_f}{m_i})=-\lambda t \\ \lambda(\ln (m_i)-\ln (m_f))=t \end{gathered}[/tex]

So if lamda is equal to 20 we replace:

[tex]\begin{gathered} 20\ln (\frac{161}{40})=t \\ 20\cdot1.4=t \\ 28=t \end{gathered}[/tex]

Si they have to wait 28 years

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