A geologist wants to determine the age of a volcanic ash layer believed to be approximately 500 million years old. Which isotope system is most appropriate?
DCarbon-12 / Carbon-13 (stable isotopes, no decay)
The half-life of the isotope system must be comparable to the age being measured. After ~10 half-lives, a parent isotope is effectively undetectable. Carbon-14's half-life of 5,730 years makes it useless for anything older than ~50,000 years. Uranium-238's half-life of ~4.47 billion years is appropriate for hundreds of millions of years. Carbon-12 and -13 are stable and cannot be used for dating at all.
Question 2 True / False
Radiometric dating relies on the assumption that radioactive decay rates were much faster in Earth's early history and that scientists apply a correction factor to account for this.
TTrue
FFalse
Answer: False
This is a common misconception. Radioactive decay rates are governed by nuclear physics (the weak and strong nuclear forces) and are independent of temperature, pressure, chemical environment, or electromagnetic fields. Rates are measured precisely in laboratories under controlled conditions. They have been verified to be constant across geological contexts — and multiple independent dating methods applied to the same rocks give consistent ages, which validates the assumption of constant rates.
Question 3 Short Answer
A sample of wood from an ancient campfire gives a carbon-14 activity that is one-quarter of what a living tree shows today. Approximately how old is the wood?
Think about your answer, then reveal below.
Model answer: Approximately 11,460 years (two half-lives of carbon-14).
Each half-life reduces the C-14 to half its previous amount. After one half-life (~5,730 years), the activity is 1/2 of modern. After two half-lives (~11,460 years), it is 1/4 of modern. The formula is: age = (half-life / ln 2) × ln(N₀/N), but the 'one-quarter remaining = two half-lives' reasoning is a direct application of the exponential decay law from prerequisite knowledge.