Final answer:
To calculate the numerical age of a rock, geologists measure the ratio of parent to daughter isotopes and apply the standard radiometric age equation using the half-life of the isotope, which allows them to accurately determine the rock's age.
Step-by-step explanation:
To calculate the numerical age of a rock using isotopic composition, geologists examine the material's chemistry to determine the ratio of parent to daughter isotopes. This ratio reveals how many half-lives or what fraction of a half-life has passed since the rock was formed. By using the standard radiometric age equation: t=ln(1+(D/P))/(λ), where t is the time (the age of the rock), ln is the natural log, P is the parent isotope ratio, D is the daughter isotope ratio, and λ is the decay constant (related to the half-life of the isotope), one can calculate the rock's age.
For example, using the rubidium-strontium dating method, if a rock has a measured parent-daughter ratio of 1:0.89 for potassium-40, the age can be found using the known half-life of the isotope. When a geologist measures these ratios using techniques like mass spectrometry and applies the half-life of the isotope, the age of the rock can be calculated accurately.