Question

How many milligrams of a 16 mg sample of cesium-137 remain after 90 years?

a) 1 mg
b) 2 mg
c) 4 mg
d) 8 mg

Answer 1

After 90 years, which is equivalent to three half-lives of cesium-137, 2 mg of the original 16 mg sample would remain. This is because, with each half-life, the amount of the substance halves, resulting in 2 mg after three such intervals.

Step-by-step explanation:

The question asks about the remaining amount of a radioactive substance after a certain period, which involves knowing the half-life of the substance. Cesium-137 has a half-life of approximately 30 years. To calculate the remaining substance after 90 years, we use the concept of half-lives:

1. After 30 years (1 half-life), half of the original 16 mg remains, so 16 mg / 2 = 8 mg.
2. After 60 years (2 half-lives), half of the remaining amount is left, so 8 mg / 2 = 4 mg.
3. After 90 years (3 half-lives), half again, so 4 mg / 2 = 2 mg.

Therefore, 2 mg of the original cesium-137 sample would remain after 90 years, which corresponds to option b.