Answer :
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.
