^90 Kr(t1 / 2=32 s) is used to study respiration. How soon...

$^{90} \mathrm{Kr}\left(t_{1 / 2}=32 \mathrm{s}\right)$ is used to study respiration. How soon after being made must a sample be administered to the patient if the activity must be at least 90$\%$ of the original activity?

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Key Concepts

Exponential Decay Law

This law describes how the quantity of a radioactive substance decreases over time in an exponential manner. It states that the remaining amount is given by the initial amount multiplied by an exponential function of time, incorporating the decay constant. This principle is fundamental in determining how radiation activity diminishes with time after production.

Half-life

The half-life of a radioactive isotope is the time required for half of the material to decay. It is an intrinsic property of the isotope and is used to characterize the rate of radioactive decay. Understanding half-life is essential for timing applications where maintaining sufficient activity is crucial, as seen in medical imaging techniques.

Decay Constant

The decay constant is a parameter that defines the probability per unit time that a radioactive atom will decay. It is directly related to the half-life through the equation ? = ln(2) divided by the half-life. This constant is key in applying the exponential decay law to calculate the activity remaining after a given time interval.

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