In 1992, Swiss police arrested two men who were attempting...

In $1992,$ Swiss police arrested two men who were attempting to smuggle osmium out of Eastern Europe for a clandestine sale. However, by error, the smugglers had picked up ${ }^{137} \mathrm{Cs}$. Reportedly, each smuggler was carrying a $1.0 \mathrm{~g}$ sample of ${ }^{137} \mathrm{Cs}$ in a pocket! In (a) bequerels and (b) curies, what was the activity of each sample? The isotope ${ }^{137} \mathrm{Cs}$ has a half-life of $30.2 \mathrm{y}$. (The activities of radioisotopes commonly used in hospitals range up to a few millicuries.)

Key Concepts

Activity and Its Units

Activity quantifies the rate at which a radioactive sample undergoes decay and is expressed in units such as becquerels (decays per second) or curies. The conversion between these units is standard, with 1 curie equivalent to 3.7×10^10 becquerels.

Radioactive Decay

This concept explains the process by which an unstable atomic nucleus loses energy by emitting radiation. Decay is a random process at the level of single atoms, but it is characterized by a definite half?life for a large ensemble of identical nuclei, which enables the calculation of activity.

Half-Life

The half-life of a radioactive isotope is the time it takes for half of a sample of nuclei to undergo decay. It is a fundamental property of each radioactive isotope and is directly related to the decay constant through the equation t?/? = ln(2)/?.

Decay Constant

The decay constant is a proportionality factor that relates the number of undecayed nuclei in a sample to the probability of decay per unit time. It is obtained from the half-life using the relation ? = ln(2) / t?/? and is crucial for calculating the activity of a radioactive sample.

Mass-to-Atom Conversion

This concept involves converting the mass of a radioactive sample into the number of atoms it contains using the isotopic molar mass and Avogadro's number. This step is necessary to calculate the total number of radioactive nuclei present for activity calculations.

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