To determine when it would be safe to work with a radioactive sample that initially emits radiation at 64 times the permissible safe level, we need to use the concept of half-life. The half-life of this sample is 2 hours, which means that every 2 hours, the amount of radiation emitted will reduce to half of its previous value.
Understanding Half-Life and Radiation Reduction
Half-life is a crucial concept in radioactivity, representing the time required for half of the radioactive atoms in a sample to decay. In this case, we start with a radiation level that is 64 times higher than what is considered safe. Our goal is to find out how many half-lives it will take for the radiation level to drop to a safe level.
Calculating the Number of Half-Lives
To find out how many half-lives are needed to reduce the radiation from 64 times the safe level to a safe level, we can use the following formula:
- After 1 half-life: 64 / 2 = 32 times the safe level
- After 2 half-lives: 32 / 2 = 16 times the safe level
- After 3 half-lives: 16 / 2 = 8 times the safe level
- After 4 half-lives: 8 / 2 = 4 times the safe level
- After 5 half-lives: 4 / 2 = 2 times the safe level
- After 6 half-lives: 2 / 2 = 1 time the safe level
From this breakdown, we see that it takes 6 half-lives to reach a safe level of radiation. Since each half-life is 2 hours, we can calculate the total time required:
Calculating Total Time
Total time = Number of half-lives × Duration of each half-life
Total time = 6 × 2 hours = 12 hours
Final Answer
Therefore, the minimum time after which it would be possible to work safely with the radioactive source is 12 hours. This means that option 2, which is 12 hours, is the correct choice.
