Final answer:
To find how much time has passed for a cobalt-60 sample to decay from 12,400 cpm to 775 cpm, we use the half-life formula to solve for time, considering the half-life of cobalt-60 which is 5.27 years. The correct calculation would give the number of years that have elapsed, reflecting the sample's radioactive decay.
Step-by-step explanation:
The subject at hand involves calculating the time that has passed given the decay of a radioisotope, specifically cobalt-60, which is a concept covered in high school Chemistry. Cobalt-60 has a half-life of 5.27 years and decays following first-order kinetics, meaning the amount of material and the intensity of radiation it emits is cut in half every 5.27 years. To find how much time has passed when the activity drops from 12,400 counts per minute (cpm) to 775 cpm, we can use the concept of half-lives.
Understanding Half-Life Calculations
The half-life is the time required for half the atoms in a radioactive sample to decay. Given that cobalt-60 has a half-life of 5.27 years (half-life of cobalt-60), to calculate the number of half-lives that have elapsed, we use the formula:
Remaining activity = Initial activity × (1/2)^(Time/Half-life)
Let's rearrange this to solve for time:
Time = Half-life × log(Initial activity/Remaining activity) ÷ log(2)
Substituting in the given values,
Time = 5.27 × log(12400/775) ÷ log(2)
After performing the calculations, we can determine the number of years (Co-60 decay) that have elapsed since the sample's activity was 12,400 cpm. Each half-life reduces the activity to its half, and this decay process is important in applications such as cancer treatment where a cobalt-60 source (cobalt-60 source) is used for its gamma rays emission.