How many years will it take for cesium-137, with a half-life of 30 years, to go from 100 units of cesium-137 to less than 1 unit of cesium-137?

Question

22-01-2024
Chemistry

High School

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How many years will it take for cesium-137, with a half-life of 30 years, to go from 100 units of cesium-137 to less than 1 unit of cesium-137?

Answer :

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afreenmajid123 afreenmajid123 · Answer 1 · 2023-09-23T19:56:11-04:00

Final answer:

To calculate the time required for cesium-137 to decay from 100 units to less than 1 unit, we use the half-life concept. It takes 7 half-lives, or 210 years, for the cesium-137 to decay to less than 1 unit based on its 30-year half-life.

Explanation:

To determine how many years it will take for cesium-137, with a half-life of 30 years, to decay from 100 units to less than 1 unit, we can use the concept of radioactive decay.

Using the half-life formula, we calculate the number of half-lives needed to reach a specific fraction of the starting amount. Each half-life reduces the existing quantity by half. Here are the steps of decay for cesium-137 (each step represents a 30-year half-life):

100 (initial amount) → 50 (after 30 years)
50 → 25 (after 60 years)
25 → 12.5 (after 90 years)
12.5 → 6.25 (after 120 years)
6.25 → 3.125 (after 150 years)
3.125 → 1.5625 (after 180 years)
1.5625 → 0.78125 (after 210 years)

It takes 7 half-lives or 210 years for the cesium-137 amount to decay to less than 1. This illustrates how the half-life principle is used to estimate the decay of radioactive substances. Consequently, we can see that cesium-137 requires 210 years to reduce from 100 units to less than 1 unit.