For each of the following, indicate if the number of half-lives elapsed is: 1. one half-life 2. two half-lives 3. three half-lives c. a sample of Au-198 with a half-life of 2.7 days after 5.4 days

Verified step by step guidance

1. Identify the half-life of the substance, which is given as 2.7 days for Au-198.
2. Determine the total time elapsed, which is 5.4 days in this case.
3. Divide the total time elapsed by the half-life to find the number of half-lives that have passed: $\frac{5.4\text{ days}}{2.7\text{ days/half-life}}$.
4. Calculate the result of the division to determine the number of half-lives.
5. Match the calculated number of half-lives to the options provided: one half-life, two half-lives, or three half-lives.

Key Concepts

Half-Life

Half-life is the time required for half of a sample of a radioactive substance to decay. It is a constant property of the substance and is crucial for understanding the rate of decay. For example, if a substance has a half-life of 2.7 days, after this period, only half of the original amount remains.

Decay Process

The decay process refers to the transformation of unstable atomic nuclei into more stable forms, releasing energy in the form of radiation. This process occurs at a predictable rate defined by the half-life, allowing for calculations of remaining quantities over time. Understanding this process is essential for determining how many half-lives have elapsed.

Elapsed Time Calculation

Elapsed time calculation involves determining how many half-lives have passed based on the total time elapsed. By dividing the total time by the half-life duration, one can ascertain the number of half-lives that have occurred. In the case of Au-198 with a half-life of 2.7 days, after 5.4 days, two half-lives have elapsed.