The half-life of the radioactive carbon isotope 14C is 5730 yr. A wooden artefact contains only 12.5% of the original content of this isotope. How old is the artefact? 17,190 yr 22,920 yr 57,300 yr 28,650 yr 45,840 yr
Question
The half-life of the radioactive carbon isotope 14C is 5730 yr. A wooden artefact contains only 12.5% of the original content of this isotope. How old is the artefact? 17,190 yr 22,920 yr 57,300 yr 28,650 yr 45,840 yr
Solution
The half-life of a substance is the time it takes for half of the substance to decay. In this case, the half-life of 14C is 5730 years.
If an artifact contains only 12.5% of the original content of 14C, it means that it has gone through three half-lives. Here's why:
- After one half-life (5730 years), 50% of the original 14C would remain.
- After two half-lives (2*5730 = 11460 years), 25% of the original 14C would remain (half of the 50%).
- After three half-lives (3*5730 = 17190 years), 12.5% of the original 14C would remain (half of the 25%).
Therefore, the artifact is 17,190 years old.
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