half life question

[Momma]

My daughter is taking a college science course, and we are having terrible time with this problem. Any guidance you could give would be greatly appreciated!

The half life of C is about 5730 years, during which it (beta) decays into "N". In nature, about one atom in a million carbon atoms will be Carbon 14. A living organism constantly ingests carbon from its surrounding environment (and egests it back), so while alive the ratio C/C in the organisms remains at about the same as the surrounding environment 1/1,000,000. Once the organism dies, however, no new carbon in any form will be taken in.

Suppose that a sample of some dead organic matter is examined and is determined to have a C/C ratio of 1/4,000,000. About how long ago did this organism die?

 

[Dr.Peterson]

The half life of C is about 5730 years, during which it (beta) decays into "N". In nature, about one atom in a million carbon atoms will be Carbon 14. A living organism constantly ingests carbon from its surrounding environment (and egests it back), so while alive the ratio C/C in the organisms remains at about the same as the surrounding environment 1/1,000,000. Once the organism dies, however, no new carbon in any form will be taken in.

Suppose that a sample of some dead organic matter is examined and is determined to have a C/C ratio of 1/4,000,000. About how long ago did this organism die?

First, I suspect you have not copied the problem exactly, as it should be talking not about "the half-life of C", but about "the half-life of ¹⁴C", and not the "C/C ratio" but the ¹⁴C/¹²C ratio, or something similar. Details matter.

On the other hand, some details given here (such as the one-in-a-million claim) are not quite right, so this is a simplified version. And the calculation you need to do is far simpler than what you need in general, so I'm not going to refer you to a source on the topic, as I intended to.

Here's the question you need to ask yourselves: What fraction of the original Carbon-14 remains? How many times has it been halved?

EDIT: For the sake of clarity, the original ¹⁴C/¹²C ratio was 1/1,000,000 (one in a million), and now it is 1/4,000,000. This is not as clear as it could be in the problem, especially if they really said "C/C", so I want to point it out to you.

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