how much cesium-137 would remain after 120.0 years if you started with 34.0 grams
To answer this question, we need to understand the concept of half-life and use the given information to calculate the amount of cesium-137 remaining after 120.0 years.
Cesium-137 has a half-life of approximately 30.2 years, which means that every 30.2 years, half of the initial amount of cesium-137 will decay.
To determine the remaining amount after 120.0 years, we can calculate the number of half-lives that have passed during this time period.
Since each half-life is 30.2 years, we divide 120.0 years by 30.2 years:
120.0 years / 30.2 years = 3.97 half-lives
Since we cannot have a fraction of a half-life, we can assume that after 3.97 half-lives, the remaining cesium-137 will be at approximately 3.97 half-lives.
To calculate the remaining amount, we use the formula:
Remaining amount = Initial amount × (1/2)^(number of half-lives)
Substituting the values:
Remaining amount = 34.0 grams × (1/2)^(3.97)
Calculating this using a calculator, we find:
Remaining amount ≈ 34.0 grams × 0.063
Remaining amount ≈ 2.14 grams
Therefore, approximately 2.14 grams of cesium-137 would remain after 120.0 years if you started with 34.0 grams.