Answer :
Final Answer:
An isotope of cesium (cesium-139) has a half-life of 31.5 years. If 1500 g of cesium-139 disintegrates over a period of 189 years then after 189 years, approximately 375 grams of cesium-139 would remain.
Explanation:
To calculate the remaining grams of cesium-139 after 189 years, we can use the concept of radioactive decay and the half-life of cesium-139, which is 31.5 years.
First, we need to determine how many half-lives have passed during the 189-year period. We can do this by dividing the time elapsed (189 years) by the half-life (31.5 years):
Number of half-lives = 189 years / 31.5 years = 6
This means that during the 189 years, cesium-139 has undergone 6 half-lives. In each half-life, half of the radioactive material decays. So, we can calculate the remaining amount as follows:
Remaining amount = Initial amount * [tex](1/2)^{number of half-lives[/tex]
Remaining amount = 1500 g * (1/2)⁶
Remaining amount ≈ 1500 g * 0.015625
Remaining amount ≈ 23.44 g
Therefore, after 189 years, approximately 23.44 grams of cesium-139 would remain.
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