1) how many billions of years will it take 1000 grams of uranium-238 to decay to just 125 grams?
2) a researcher had 37.5 g left from a 600 g sample of sulfer-35. how many half-lives passed during that time?
3) look at problem 2. how many days passed during that time?
To answer these questions, we need to understand the concept of half-life and use the radioactive decay formula. The half-life of a radioactive substance is the time it takes for half of the radioactive atoms to decay.
1) To determine the number of billions of years it will take for 1000 grams of uranium-238 to decay to just 125 grams, we need to know the half-life of uranium-238. Let's assume the half-life of uranium-238 is 4.5 billion years.
Using the radioactive decay formula, we can calculate the number of half-lives required to reach 125 grams:
Number of half-lives = (log(initial mass / final mass)) / (log(1/2))
Number of half-lives = (log(1000 g / 125 g)) / (log(1/2))
Number of half-lives = (log(8)) / (log(1/2))
By using logarithmic calculations, we find that the number of half-lives is approximately 3.
Therefore, it would take 3 half-lives, or 3 * 4.5 = 13.5 billion years, for 1000 grams of uranium-238 to decay to 125 grams.
2) In the second question, the researcher had 37.5 grams left from a 600-gram sample of sulfur-35. We still need to determine the number of half-lives that have passed during that time. Let's assume the half-life of sulfur-35 is 87 days.
To find the number of half-lives, we can use the formula:
Number of half-lives = (log(initial mass / final mass)) / (log(1/2))
Number of half-lives = (log(600 g / 37.5 g)) / (log(1/2))
Number of half-lives = (log(16)) / (log(1/2))
By performing the logarithmic calculations, we find that the number of half-lives is approximately 4.
Therefore, during the time the researcher had 37.5 grams remaining from the 600-gram sample of sulfur-35, 4 half-lives had passed.
3) To calculate the number of days that passed during the time mentioned in problem 2, we need to know the half-life of sulfur-35, which we previously assumed to be 87 days.
The total time in days can be calculated by multiplying the number of half-lives (4) by the half-life of sulfur-35 (87 days):
Total time in days = Number of half-lives * Half-life of sulfur-35
Total time in days = 4 * 87 = 348 days.
Therefore, approximately 348 days passed during the time the researcher had 37.5 grams remaining from the 600-gram sample of sulfur-35.