The activity of a sample containing radioactive ^108 Ag is 6.4 ×10^4 Bq. Exactly 12 min later, t

step 1 In this question, I look at the decay of silver. Silver 108. And we're given the initial activit

The activity of a sample containing radioactive ^108 Ag is...

The activity of a sample containing radioactive $^{108} \mathrm{Ag}$ is $6.4 \times 10^{4}$ Bq. Exactly 12 min later, the activity is $2.0 \times 10^{3} \mathrm{Bq} .$ Calculate the half-life of $^{108} \mathrm{Ag} .$

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable nuclei transform into more stable configurations by emitting radiation. This process is inherently probabilistic, meaning the decay of individual nuclei is random, but the decay of a large number of nuclei follows predictable statistical laws.

Exponential Decay Law

The exponential decay law explains how the quantity of a radioactive substance decreases over time, represented mathematically by A(t) = A0e^(–?t), where A0 is the initial activity, A(t) is the activity at time t, and ? is the decay constant. This model characterizes the predictable reduction in activity due to the decay process.

Half-Life

The half-life of a radioactive substance is the time required for half of the initial number of radioactive nuclei to decay, or equivalently, for the activity to reduce to half its initial value. It is a key measure in nuclear physics and is related to the decay constant by the formula T1/2 = ln(2)/?, providing insight into the rate and stability of the decay process.

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