Final answer:
c) Determining the rate of radioactive decay within the object.
The primary use of radioactive isotopes in determining the age of an object is by measuring the rate of radioactive decay and using the decay rate as a clock to estimate the object's age. This method, known as radiometric dating, is accurate because the half-life of radioactive isotopes is constant and unaffected by environmental factors.
Step-by-step explanation:
Significance of Radioactive Isotopes in Age Determination
The primary significance of radioactive isotopes in determining the age of an object is c) Determining the rate of radioactive decay within the object. Radioactive isotopes, such as uranium-235, have unique half-lives during which they decay into daughter isotopes at a known constant rate. Radiometric dating takes advantage of the predictable decay of radioactive isotopes to estimate the age of materials such as rocks, fossils, or archaeological artifacts.
This technique is possible because the half-life of a radioactive isotope is unaffected by environmental conditions, making it a reliable internal clock. By analyzing the chemistry of a geologic material and establishing the ratio of parent to daughter atoms, geologists can determine how many half-lives, or what fraction of a half-life, has passed since the material formed. Consequently, with knowledge of the half-life and the current ratio of isotopes, the age of the geologic material can be calculated with a reasonable degree of accuracy.
Therefore, the main use of radioactive isotopes in dating is not to establish the chemical composition, measure the density, or assess the physical dimensions of an object, but to utilize their constant decay rate to efficiently determine the object's age.