A radioactive sample contains 2.45 g of an isotope with a half-life of 3.8 days. How much of the isotope in grams will remain after 11.4 days?
To solve this problem, we need to use the concept of radioactive decay and the half-life of the isotope.
The half-life is the time it takes for half of the radioactive sample to decay. In this case, we are given that the half-life of the isotope is 3.8 days. This means that after 3.8 days, half of the sample will have decayed, and after another 3.8 days, half of the remaining sample will have decayed, and so on.
First, let's determine how many half-lives have passed during the 11.4 days.
Number of half-lives = time elapsed / half-life
Number of half-lives = 11.4 days / 3.8 days
Number of half-lives = 3
So, during the 11.4 days, three half-lives have passed.
Now, we can calculate the amount of the isotope that remains after 11.4 days.
Amount remaining = initial amount * (1/2)^(number of half-lives)
Amount remaining = 2.45 g * (1/2)^3
Amount remaining = 2.45 g * (1/8)
Amount remaining = 0.30625 g
Therefore, after 11.4 days, approximately 0.30625 grams of the isotope will remain.