A radioactive sample has equal numbers of ^15 O and ^19 O nuclei. Use the half-lives found in

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A radioactive sample has equal numbers of ^15 O and ^19 O...

A radioactive sample has equal numbers of ${ }^{15} \mathrm{O}$ and ${ }^{19} \mathrm{O}$ nuclei. Use the half-lives found in Appendix $\mathrm{B}$ to determine how long it will take before there are twice as many ${ }^{15} \mathrm{O}$ nuclei as ${ }^{19} \mathrm{O}$. What percent of the ${ }^{19} \mathrm{O}$ nuclei have decayed during this time?

Key Concepts

Decay Constant

The decay constant (?) is a parameter that defines the probability per unit time that a nucleus will decay. It is an essential component of the exponential decay formula and determines how quickly a radioactive isotope decays, highlighting differences between isotopes with different half-lives.

Solving Ratio Problems in Radioactivity

This involves setting up equations based on the exponential decay laws of two different isotopes to find the point in time when their amounts reach a specified ratio. It requires combining the decay equations using the respective decay constants or half-lives of the isotopes, allowing for the determination of time intervals and percentage decays.

Half-Life

The half-life of a radioactive isotope is the time required for one-half of the original nuclei to decay. It is directly related to the decay constant by the relation t½ = ln(2)/?, and understanding this concept is crucial when comparing the decay rates of different isotopes and predicting their relative quantities over time.

Radioactive Decay Law

This concept describes the process by which an unstable nucleus loses energy by emitting radiation, and it is mathematically expressed by the exponential decay equation, where the number of undecayed nuclei at any time is proportional to the initial number multiplied by an exponential factor. This law underpins the analysis of how individual isotopes diminish over time.

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