Understanding Radioactive Decay
* Half-life: The time it takes for half of a radioactive substance to decay. Cs-137 has a half-life of 30.17 years.
* Exponential Decay: Radioactive decay follows an exponential pattern. This means that the amount of the substance remaining decreases by a factor of 1/2 for every half-life that passes.
Calculations
1. Determine the number of half-lives:
* Divide the total time (241.84 years) by the half-life (30.17 years): 241.84 years / 30.17 years/half-life ≈ 8 half-lives.
2. Calculate the fraction remaining:
* For each half-life, the amount remaining is halved. Since we have 8 half-lives, the fraction remaining is:
* (1/2) ^ 8 = 1/256
Answer: After 241.84 years, approximately 1/256 of the original Cs-137 would remain undecayed.
