Final Answer:
The first, second, and third half-lives of a radioactive element within a rock sample containing 16 grams would result in 8 grams after the first half-life, 4 grams after the second half-life, and 2 grams after the third half-life.
Step-by-step explanation:
Radioactive decay follows an exponential decay model, where the amount of a radioactive substance decreases by half during each half-life period. Initially, with 16 grams of the radioactive element, after the first half-life (_t_1/2), the amount reduces by half to 8 grams. After the second half-life, another halving occurs, leaving 4 grams of the element. Following the third half-life, another halving reduces the remaining 4 grams to 2 grams. This consistent halving of the original amount characterizes the successive half-life periods, showcasing a pattern of exponential decay.
Understanding the concept of half-life is crucial in radiometric dating and determining the age of rocks or artifacts. The process provides a way to estimate the age of a sample based on the remaining amount of a radioactive element. The decay rate remains constant for a particular substance, allowing scientists to calculate the elapsed time by measuring the proportion of the original substance remaining. This foundational principle finds applications in various scientific fields, including geology, archaeology, and nuclear physics.
The exponential decay pattern seen in successive half-lives demonstrates a consistent reduction in the amount of the radioactive element, providing a reliable framework for understanding the decay process in radioactive materials.