Answer :
Final answer:
Given a half-life of 3.80 days for Rhenium-186, we can calculate the amount remaining after a certain period using the formula for radioactive decay. After 19.0 days, which is approximately 5 half-lives, 290.3 grams of Rhenium - 186 would remain from an initial 9290 grams.
Explanation:
The question is asking about the application of radioactive decay and half-life. Rhenium-186 is a radioactive isotope with a half-life of 3.80 days. The half-life is the time it takes for half of the isotope to decay.
After 19.0 days, we calculate the number of half-lives that have passed by dividing the total time (19.0 days) by the half-life (3.80 days), which gives approximately 5 half-lives. Starting with 9290 grams of Rhenium-186, after one half-life, we would have half of this, or 4645 grams. After two half-lives, we would have half of 4645 grams, or 2322.5 grams, and so on for five half-lives.
After 5 half-lives (19.0 days), we have: 9290g * (0.5)^5 = 290.3 grams of Rhenium - 186 left.
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