Question

Use the data shown below to determine the following: a. the isotopes that would be best for dating ancient rocks b. the isotopes that could be used as tracers State reasons for your answers. $$ \begin{array}{ll}{\text { Element }} & {\text { Half-Life }} \\ {\text { potassium- } 40} & {1.28 \times 10^{9} \mathrm{y}} \\ {\text { potassium-42 }} & {12.36 \mathrm{h}} \\ {\text { uranium-238 }} & {4.468 \times 10^{9} \mathrm{y}} \\ {\text { uranium-239 }} & {23.47 \mathrm{min}}\end{array} $$

Short answer

Potassium-40 and uranium-238 are best for dating ancient rocks. Potassium-42 and uranium-239 can be used as tracers.

Step-by-step solution

Understand Half-Life

Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is crucial for determining the usefulness of isotopes for different applications like dating or tracing.

Identify Isotopes for Dating

For dating ancient rocks, we need isotopes with long half-lives since they need to remain measurable over geological time scales. Compare the half-lives of the given isotopes.

Select Isotopes for Dating

Potassium-40 and uranium-238 have the longest half-lives (\(1.28 \times 10^9 \text{ years}\) and \(4.468 \times 10^9 \text{ years}\) respectively). These long half-lives make them suitable for dating ancient rocks.

Identify Isotopes for Tracers

Tracers usually need short half-lives to minimize radiation exposure and because the processes they trace occur over shorter timescales. Compare the short half-lives of the given isotopes.

Select Isotopes for Tracers

Potassium-42 and uranium-239 have the shortest half-lives (\(12.36 \text{ hours}\) and \(23.47 \text{ minutes}\) respectively). These short half-lives make them suitable as tracers.

Key concepts

half-life

Half-life is a fundamental concept in radioactivity. It refers to the time it takes for half of the radioactive atoms in a sample to decay. Think of it as the measure of how quickly or slowly a substance undergoes radioactive decay.
This can range from a few milliseconds to billions of years. Because of this wide range, different isotopes are suited to different applications.
A longer half-life means the isotope remains radioactive for a longer period, which is useful for long-term processes like dating ancient rocks. A shorter half-life is more practical for applications that require only brief periods of radioactivity, such as in medical tracers.
Understanding the half-life of an isotope helps scientists determine its best use, whether for geological dating, medical imaging, or other applications.

isotope dating

Isotope dating utilizes the natural decay of radioactive isotopes to estimate the age of various materials. This method is often applied to date ancient rocks and fossils.
The process works by comparing the ratio of parent isotopes to their decay products in a sample. For this to be effective, the isotope used must have a sufficiently long half-life.
For instance, potassium-40 and uranium-238, with half-lives of 1.28 billion years and 4.468 billion years respectively, are ideal for dating ancient geological samples. These long half-lives ensure there is still enough of the original isotope present to measure accurately, even over millions or billions of years.

radioactive tracers

Radioactive tracers are isotopes with short half-lives that are used to trace processes within living organisms or other dynamic systems.
These tracers are incorporated into a system, and their movement or uptake is tracked over a short time period. Because they decay quickly, they pose minimal risk of long-term radiation exposure.
Potassium-42 and uranium-239, with half-lives of 12.36 hours and 23.47 minutes respectively, are perfect for such purposes. Their quick decay allows for effective tracing and minimizes the duration of radiation exposure.
This makes short-lived isotopes invaluable in medical diagnostics, studying metabolic pathways, or even tracking environmental processes.

potassium-40

Potassium-40 is a noteworthy isotope commonly used in geological dating due to its long half-life of 1.28 billion years.
This extended decay period makes it suitable for dating rocks and minerals that are millions or even billions of years old.
The decay product of potassium-40 is argon-40, a gas that becomes trapped within rock structures over geological time. By measuring the ratio of potassium-40 to argon-40, scientists can calculate the age of the rock.
This method, known as potassium-argon dating, has been instrumental in advancing our understanding of geological and evolutionary timelines.

uranium-238

Uranium-238 is another vital isotope used in dating ancient geological formations. Its half-life of 4.468 billion years makes it ideal for dating Earth's oldest rocks.
When uranium-238 decays, it goes through a series of stages before finally becoming a stable isotope of lead (lead-206). By examining the ratios of uranium-238 to lead-206, scientists can accurately determine the age of a sample.
This method, known as uranium-lead dating, is one of the oldest and most reliable dating methods. It has played a crucial role in understanding not only the age of the Earth but also the evolution of its geological features.
These techniques have been fundamental in piecing together the history of our planet and the life it supports.