Carbon-14 is a radioactive nucleus with a half-life of 5760 years. In livingmatter the amount of carbon-14 decays at a rate of 15.3 decay events perminute per gram of carbon. A fossil is analysed and found to have a carbon-14 decay rate of 7.70 decay events per minute per gram of carbon. How oldis the fossil?
Question
Carbon-14 is a radioactive nucleus with a half-life of 5760 years. In livingmatter the amount of carbon-14 decays at a rate of 15.3 decay events perminute per gram of carbon. A fossil is analysed and found to have a carbon-14 decay rate of 7.70 decay events per minute per gram of carbon. How oldis the fossil?
Solution
Step 1: Understand the problem
The problem is asking us to find the age of a fossil based on the decay rate of carbon-14. We know that the half-life of carbon-14 is 5760 years, which means that after 5760 years, half of the carbon-14 in a sample will have decayed.
Step 2: Calculate the number of half-lives
The decay rate of the fossil is 7.70 decay events per minute per gram of carbon, which is half of the decay rate of living matter (15.3 decay events per minute per gram of carbon). This means that one half-life has passed.
Step 3: Calculate the age of the fossil
Since one half-life of carbon-14 is 5760 years, the fossil is 5760 years old.
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