Question

recall that cesium-137 has a half-life of about 30 years. if you begin with 200 mg of cesium-137, how long will it take until only 1 milligram remains?

Answer 1

The half-life of cesium-137 is about 30 years. Starting with 200 mg, it will take approximately 240 years for only 1 milligram of cesium-137 to remain.

Step-by-step explanation:

The half-life of cesium-137 is about 30 years. Starting with 200 mg of cesium-137, we can calculate how long it will take for only 1 milligram to remain. Each time the half-life is reached, the amount of cesium-137 is halved. So, after the first half-life, we will have 100 mg remaining, after the second half-life, 50 mg remaining, and so on.

To find out how many half-lives it will take to reach 1 milligram, we can set up an equation: 200 mg * (1/2)^(n) = 1 mg, where n represents the number of half-lives. Solving for n gives us:

1. 200 * (1/2)^(n) = 1
2. (1/2)^(n) = 1/200
3. n = log((1/200), (1/2))

Using a calculator, we find that n ≈ 7.64. Since it is not possible to have a fraction of a half-life, we round the value up to 8. Therefore, it will take approximately 8 half-lives for only 1 milligram of cesium-137 to remain. Multiplying the half-life by 8 gives us: 30 years * 8 = 240 years.