Final answer:
The accuracy of measuring a rock's age using a radioactive element is determined by the half-life of the element and the presence and abundance of the radioactive isotope and its daughter product in the rock.
Step-by-step explanation:
The accuracy of measuring a rock's age using a radioactive element is determined by the half-life of the element. The half-life is the time it takes for half of the parent atoms to decay into daughter atoms. Shorter half-lives are used for younger rocks, while longer half-lives are used for older rocks. For example, carbon-14 is useful for dating organic materials up to about 50,000 years old, while potassium-argon dating can be used for rocks that are millions or billions of years old.
Another factor is the presence and abundance of the radioactive isotope and its daughter product in the rock. The more parent atoms that have decayed and converted into daughter atoms, the more accurate the measurement of the rock's age will be.
It is important to note that different radioactive elements have different half-lives and are suitable for dating rocks of different ages. For example, uranium-238 has a half-life of 4.5 billion years and is used to date very old rocks, while carbon-14 has a half-life of only 5,730 years and is used for more recent materials.