A radioactive sample contains 1.67 ×10^11 atoms of 47^108 Ag (half-life =2.42 min ) at some inst

step 1 First, we calculate our decay constant lambda. Lambda, we know, is defined as 0 .693 divided by

A radioactive sample contains 1.67 ×10^11 atoms of 47^108 Ag...

A radioactive sample contains $1.67 \times 10^{11}$ atoms of $_{47}^{108} \mathrm{Ag}$ (half-life $=2.42 \mathrm{min}$ ) at some instant. Calculate the decay constant and the activity of the sample in mCi. (Sce Sample Problem 25C.)

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This spontaneous process occurs at a characteristic rate for each isotope and forms the basis for understanding the kinetics of nuclear transformations in materials.

Half-life

The half-life of a radioactive substance is the time required for half of the unstable nuclei in a sample to undergo decay. It is a fundamental property of an isotope that provides insight into the rate of decay and helps determine how quickly the activity of a sample will decrease.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a nucleus will decay. It is mathematically related to the half-life through the equation ? = ln(2)/t?/?, where t?/? is the half-life, serving as an alternative measure of the radioactive decay rate.

Activity

Activity is a measure of the number of decays occurring in a sample per unit time. It is calculated as the product of the decay constant and the number of radioactive atoms present in the sample, offering a quantitative assessment of the radiation emitted.

Units Conversion

Units conversion in radioactivity involves translating between different measures of activity, such as converting from decays per second (becquerels or curies) to other units like milliCuries. This is critical in ensuring consistency in calculations and in communicating the strength of radioactive sources accurately.

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