Question

A tree killed by being buried under volcanic ash was found to have a ratio of carbon-14 atoms to carbon-12 atoms of 5.2 × 10^-14. The rate constant of the C-14 → C-12 decay is k = 1.21 × 10^-4 yr^-1 and the ratio of carbon-14 to carbon-12 is 1.2 × 10^-12 in a contemporary sample. How long ago did the eruption occur in years? 

          A tree killed by being buried under volcanic ash was found to have a ratio of carbon-14 atoms to carbon-12 atoms of 5.2 × 10^-14. The rate constant of the C-14 → C-12 decay is k = 1.21 × 10^-4 yr^-1 and the ratio of carbon-14 to carbon-12 is 1.2 × 10^-12 in a contemporary sample. How long ago did the eruption occur in years?
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Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
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A tree killed by being buried under volcanic ash was found to have a ratio of carbon-14 atoms to carbon-12 atoms of 5.2 × 10^-14. The rate constant of the C-14 → C-12 decay is k = 1.21 × 10^-4 yr^-1 and the ratio of carbon-14 to carbon-12 is 1.2 × 10^-12 in a contemporary sample. How long ago did the eruption occur in years?
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Transcript

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00:01 So here in this question, we're going to use the formula n is equal to n -0, e -to -the -minus k -t for our decay process here.
00:16 N is going to be the amount of carbon atoms that would be at the end.
00:26 So this would be 5 .2 times 10, then 0, is the amount of carbon atoms that would be at the end.
00:34 Initial amount which is 1 .2 times 10 to the minus 12, e to the minus k.
00:42 I'll solve in a minute here, divide by 1 .2 times 10 to the minus 12.
00:52 And this would give me, we have 5 .2 14 minus divided by 1 .2 exponent 12 minus and this is 0 .0433...
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