Cobalt- 60 is used extensively in medicine as a source of γ-rays. Its halflife is 5.27 years. (a

step 1 Okay, so we're given a half -life here. So let's go ahead and use our half -life to find K. We k

Cobalt- 60 is used extensively in medicine as a source of...

Cobalt- 60 is used extensively in medicine as a source of $\gamma$ -rays. Its halflife is 5.27 years.
(a) How long will it take a Co-60 source to decrease to $18 \%$ of its original activity?
(b) What percent of its activity remains after 29 months?

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Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This natural process is stochastic in nature, meaning that the exact moment of decay for any individual nucleus cannot be predicted; however, statistically, a large number of nuclei will follow predictable decay behavior over time.

Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to undergo decay. It is a key parameter in describing the rate at which a radioactive substance loses its activity and forms the basis for many calculations involving exponential decay processes.

Exponential Decay Equation

The exponential decay equation mathematically models the decrease in the number of radioactive nuclei over time. It expresses the remaining quantity as a function of the initial amount, the decay constant, and time, allowing one to calculate the residual activity after any given duration.

Decay Constant

The decay constant is a fundamental parameter that represents the likelihood per unit time that a radioactive nucleus will decay. It provides a link between the half-life of a substance and the exponential decay equation through a logarithmic relationship, enabling the prediction of decay dynamics.

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