In 1992, Swiss police arrested two men who were attempting to smuggle osmium out

Question

In 1992, Swiss police arrested two men who were attempting to smuggle osmium out Eastern Europe for a clandestine sale. However, by error, the smugglers had picked up 137Cs. Reportedly, each smuggler was carrying a 1.0g sample of 137Cs in pocket. In bequerels, what was the activity of each sample? The isotope 137Cs has a half-life of 30.2 years. (The activities of radio-isotopes commonly used in hospitals range up to a few millicuries.) In 1992, Swiss police arrested two men who were attempting to smuggle osmium out Eastern Europe for a clandestine sale. However, by error, the smugglers had picked up 137Cs. Reportedly, each smuggler was carrying a 1.0g sample of 137Cs in pocket. In bequerels, what was the activity of each sample? The isotope 137Cs has a half-life of 30.2 years. (The activities of radio-isotopes commonly used in hospitals range up to a few millicuries.)

Explanation / Answer

activity in becqurel=number of undecayed nuclei*decay constant

decay constant=ln(2)/half life

=ln(2)/(30.2*365*24*3600 seconds)=7.278*10^(-10) s^(-1)

number of nuclei=number of moles*6.022*10^23

=(mass/molar mass)*6.022*10^23

=(1/137)*6.022*10^23=4.39562*10^21

so activity=4.39562*10^21*7.278*10^(-10)=3.2*10^12 Bq

[note : as 1 Curie=3.7*10^10 Bq

activity=86.463 Curie]

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