If 100.0 g of ^14C decays until only 6.25 g of carbon is left after 28650 y, what is the half-life of this isotope?
Answer (2)
The half-life of ^14C can be calculated as the time it takes for the sample to reduce from 100.0 g to 6.25 g. After completing the calculations, we find that the half-life of ^14C is approximately 7162.5 years. This conclusion is based on determining the number of half-lives that have occurred in a specific period, which is 28650 years in this case.
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To find the half-life of carbon-14 (^14C), we can use the concept of half-life decay in radioactive materials. The half-life is the time it takes for a quantity of a substance to reduce to half its initial amount.
Step-by-Step Solution:
Initial and Remaining Amounts:
Initial amount of ^14C = 100.0 g
Remaining amount of ^14C = 6.25 g
Determining the Number of Half-Lives: We need to find out how many times the substance has halved to go from 100.0 g to 6.25 g.
First half-life: 100.0 g to 50.0 g
Second half-life: 50.0 g to 25.0 g
Third half-life: 25.0 g to 12.5 g
Fourth half-life: 12.5 g to 6.25 g
Therefore, the substance has undergone 4 half-lives.
Total Time and Half-life Calculation: We know the total time taken for these 4 half-lives is 28,650 years. We can calculate the half-life by dividing the total time by the number of half-lives:
Half-life = Number of half-lives Total time = 4 28650 years = 7162.5 years
Therefore, the half-life of carbon-14 is approximately 7162.5 years.
