A solution of sodium iodide containing iodine- 131 was given...

A solution of sodium iodide containing iodine- 131 was given to a patient to test for malfunctioning of the thyroid gland. What fraction of the iodine- 131 nuclei would remain undecayed after $5.0 \mathrm{~d}$ ? If a sample contains $2.5 \mu \mathrm{g}$ of $^{131}$ I, how many micrograms remain after 5.0 d? The halflife of $\mathrm{I}-131$ is $8.07 \mathrm{~d}$.

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Key Concepts

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a single nucleus will decay. It is directly related to the half-life by the relation ? = ln(2)/T1/2. The decay constant provides an alternative way to describe the kinetics of radioactive decay and is crucial for deriving time-dependent behavior using the exponential decay formula.

Exponential Decay Law

The exponential decay law states that the number of undecayed nuclei decreases exponentially over time. Mathematically, it is expressed as N(t) = N0 * (1/2)^(t/T1/2), where N0 is the initial quantity, t is the elapsed time, and T1/2 is the half-life. This law underpins calculations of remaining radioactive material over a given period.

Half-Life

Half-life is the time it takes for half of the nuclei in a sample of a radioactive isotope to decay. It is a characteristic property of each radioactive nuclide and provides a measure of the rate at which the substance decays, independent of the initial amount.

Radioactive Decay

This concept describes the process by which an unstable atomic nucleus loses energy by emitting radiation. The transformation occurs spontaneously, and it is inherently probabilistic, meaning that while the behavior of a large number of atoms can be predicted statistically, the decay of a single atom is random.

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