What are the shortest and longest times (in years) that can be estimated by carbon-14 dating?

Radioactive decay is a fundamental process by which an unstable atomic nucleus loses energy by emitting radiation, including particles such as alpha particles, beta particles, or gamma rays. This spontaneous transformation leads to the nucleus becoming a different element or a different isotope of the same element. Imagine a large, bustling city where buildings (atoms) might suddenly and unpredictably crumble and change into something else - that's akin to radioactive decay at the atomic level.

The rate at which these atomic 'buildings' decay is what we use to measure time in the realm of atoms. It's a constant process, meaning that for a given quantity of a radioactive substance, approximately the same number of atoms will decay each second. The result of this natural clock allows us to date materials by determining the ratio of remaining radioactive material to the products of its decay, which have been accumulating over time.

The half-life of a radioactive substance is the time required for half of the atoms in a sample to undergo decay. This is a critical metric in geochronology and radiometric dating techniques, including carbon-14 dating. To explain it simply, if you had a 100-page book and every year, half the pages disappear, the half-life of the pages would be one year. After one year, you’d have 50 pages left, then 25 after two years, and so on.

In the case of carbon-14, its half-life is about 5730 years. This means if initially, we have a lump of carbon-14 the size of a baseball, in 5730 years we'd expect to have a lump the size of a baseball cut in half. This decay continues until it becomes too minute to measure reliably, which underpins the limitations of carbon-14 dating in estimating ages of artifacts or geological samples.

Geochronology is the science of determining the age of rocks, fossils, and sediments using signatures inherent in the rocks themselves. The primary tool is the decay of radioactive isotopes, such as carbon-14, potassium-40, or uranium-238, among others. It’s akin to a clock that starts ticking the moment a rock is formed or a plant dies.

This dating method informs much of what we know about the timeline of earth's history, the age of fossils, and human artifacts. Geochronology enables scientists to construct a detailed chronology of Earth's environmental changes, biological evolution, and even climate change. By understanding the past, it provides invaluable insights into the future. For instance, carbon-14 dating has been instrumental in archaeology and paleontology, giving scientists a time window to work with when investigating ancient objects and remains.