Final answer:
The age of rocks can be estimated by comparing the amount of U-238 to the amount of Pb-206 found in a sample, using the half-life of U-238, which is 4.5 billion years. After one half-life, half of the original U-238 would have decayed into Pb-206, and this ratio is used to deduce the rock's age.
Step-by-step explanation:
The question concerns the age of rocks based on the percentage of lead found in them, which is determined through the process of radioactive dating, particularly using the decay of uranium-238 (U-238) into lead-206 (Pb-206). The half-life of U-238 is given as 4.5 billion years, and the calculation of the rock's age involves comparing the amount of remaining U-238 to the amount of Pb-206 that has formed from its decay. By analyzing the ratio of these two elements in a rock sample, scientists can estimate how many half-lives have passed since the rock solidified, and thus, determine its age.
Using the provided half-life of uranium-238, one can determine that after 4.5 billion years (one half-life), half of the original amount of uranium-238 would have decayed into lead-206. This information, along with the measurements of U-238 and Pb-206 in the rock, allows for the estimation of the rock's age. For instance, if a rock contains equal amounts of U-238 and Pb-206, it may be inferred that it is approximately 4.5 billion years old, having gone through one full half-life.
Understanding the concept of a half-life and the ability to measure the ratio of parent to daughter isotopes in a sample are key to applying this method and obtaining accurate age estimates for geological samples.