Final answer:
To find out how much titanium-44 remains after 240 years, calculate the remaining amount after each 60-year half-life. After four half-lives, 0.0375 grams of the original 0.600 grams will remain.
Step-by-step explanation:
To determine how much titanium-44 remains after 240 years, we need to use the concept of half-life, which is the time required for half of a radioactive substance to decay. In this case, the half-life of titanium-44 is 60 years. After one half-life (60 years), half of the substance will remain, after two half-lives (120 years), one quarter will remain, and so on.
After 240 years, which equals four half-lives (240 years ÷ 60 years/half-life = 4 half-lives), the calculation is as follows:
- Initial amount = 0.600 g
- After 1 half-life (60 years), 0.300 g remain (0.600 g / 2).
- After 2 half-lives (120 years), 0.150 g remain (0.300 g / 2).
- After 3 half-lives (180 years), 0.075 g remain (0.150 g / 2).
- After 4 half-lives (240 years), 0.0375 g remain (0.075 g / 2).
Therefore, after 240 years, 0.0375 grams of titanium-44 will remain from the original 0.600 grams.