Final answer:
The amount of cesium-137 that existed in the sample 90 years ago is 0.375 g.
Step-by-step explanation:
To determine how much cesium-137 existed in the sample 90 years ago, we can use the concept of half-life. The half-life of cesium-137 is 30 years, meaning that every 30 years, the amount of cesium-137 in a sample is halved.
In this case, 90 years have passed since the sample was taken. Since each half-life is 30 years, three half-lives have occurred. Therefore, we can calculate the amount of cesium-137 that existed 90 years ago by multiplying the current amount (3 g) by 2-3 (since each half-life halves the amount).
Using this calculation, the amount of cesium-137 that existed in the sample 90 years ago is 3 g * (1/2)3 = 3 g * 1/8 = 3/8 g = 0.375 g.