Final answer:
In the case of gold-198's half-life, after 5.4 days, which is two half-lives, one quarter of the original amount of gold-198 would remain. The amount remaining at any given time is calculated by dividing the time by the half-life and applying the fraction of half-lives to the original amount.
Step-by-step explanation:
The half-life of a radioactive isotope like gold-198 is the time it takes for half of the isotope's atoms in a sample to decay. Given that the half-life of gold-198 is 2.7 days, finding out how much of the substance remains after a certain period involves calculating the number of half-lives that have passed and applying that to the original amount.
Let's say you start with 1 gram of gold-198. After one half-life (2.7 days), you would have 0.5 grams remaining. After two half-lives (5.4 days), you would be left with 0.25 grams, which is a quarter of the original amount.
To determine the amount of gold-198 left after a specific time period
, you would divide that time period by the half-life of gold-198 and use the resulting number of half-lives to calculate the remaining quantity as a fraction of the initial amount.