A radioactive material has a half life of 500 years.
A) Given 20 grams of this material, how much will remain after 1,000 years?
B) Given 100 grams of this material, how much will remain after 750 years?
Thank you to whom ever can help me :)
well, 1000 years is 2 half-lives, so ...
To answer these questions, we can use the formula for radioactive decay:
Amount = Initial amount × (1/2)^(time/half-life)
A) Given that the half-life is 500 years and the initial amount is 20 grams, we can substitute these values into the formula to find the remaining amount after 1,000 years:
Amount = 20 grams × (1/2)^(1000 years/500 years)
= 20 grams × (1/2)^2
= 20 grams × 1/4
= 5 grams
Therefore, after 1,000 years, 5 grams of the radioactive material will remain.
B) Similarly, we can use the formula to find the remaining amount after 750 years, given an initial amount of 100 grams:
Amount = 100 grams × (1/2)^(750 years/500 years)
= 100 grams × (1/2)^(3/2)
= 100 grams × √(1/2)
≈ 100 grams × 0.7071
≈ 70.71 grams
Therefore, after 750 years, approximately 70.71 grams of the radioactive material will remain.