Carbon-14 Dating: Where to Begin?

[Kmcquiggan]

Homework Statement

Carbon-14 testing on the body of Iceman showed that the level of carbon-14 was at 52%. In approximate what year did he die?

Relevant Equations

There is no equations that were given, the only information that was supplied was he was found in 1991.

I had tried to come up with a formula that would help me figure it out, but I honestly am not sure where to begin. In my book it states that the carbon-14 half life is 6000 years. ( I have read somewhere else that it is 5730 but I am using 6000 as that is what was supplied)
so the only thing i could come up with is nothing that made any sense. If some one could help me where to look or start that would be great

 

[kuruman]

What is the meaning of half-life? What happens to the original sample after one half life has elapsed?

 

[Kmcquiggan]

It means that you can use this method of radiocarbon dating to approx time an organism died. So every 6000 years half of the carbon is gone.

 

[Charles Link]

See https://en.wikipedia.org/wiki/Radiocarbon_dating They give $N_o$ at the starting point to have a fraction of $f≈1.25 \cdot 10^{-12}$. The problem is simple though= Since they tell you that $\frac{N}{N_o}=.52$, you don't even need to compute $N_o$.

 

[kuruman]

It means that you can use this method of radiocarbon dating to approx time an organism died. So every 6000 years half of the carbon is gone.

You meant to say that half of the carbon 14 is gone, of course. So how much of the carbon 14 in the Iceman's body is gone in this case?

 

[Kmcquiggan]

48%

 

[kuruman]

48%

Which as a fraction translates to what, approximately?

 

[Kmcquiggan]

48/6000 ? he was alive 2880 years before 1991?

 

[kuruman]

Nope. 48% means 48 out of 100, not 48 out of 6000. Try again, to one significant figure what is 48%?

 

[Kmcquiggan]

.5

 

[kuruman]

Good. Now go back and read your post #3. Can you put it together with post #10?

 

[Kmcquiggan]

So he died approx 3000 years before 1991? Thats it? I was thinking i needed more a technical answer

 

[kuruman]

So he died approx 3000 years before 1991? Thats it? I was thinking i needed more a technical answer

This is technical enough. The problem is asking for an approximate answer that this line of reasoning can provide. However, the Iceman did not die approximately 3000 years before 1991. Think of it this way, if approximately 50% of C-14 is left, how many half-lives have elapsed since he died? To what number of years does that number translate if one half life is 6000 years?

 

[Kmcquiggan]

what about if I did it this way. If you lose 50% every 6000 years that means you would lose 1% every 120 years. So if he lost 48% as there is 52% remaining does that mean I can take 48 %* 120 years which then means he died 5760 years ago in 1991 when he was found?

 

[kuruman]

what about if I did it this way. If you lose 50% every 6000 years that means you would lose 1% every 120 years.

That is incorrect thinking, you are applying a linear interpolation over a period of a half-life which is unnecessary and incorrect. According to your reasoning, in the next 6000 years after 1991 there will be no carbon-14 left if it is gone at the rate of 1% per 120 years. Actually, 6000 years after 1991 there will be left approximately half of what there was in 1991 or 25%.

 

[Kmcquiggan]

So the iceman has gone through approx 1 full stage of half life carbon cycle. So he was alive approx 6000 years before 1991? and then using that thinking if he had only 25 % percent carbon 14 than he would have lived 2 half life cycles which would mean he was alive 12000 years? am i getting it now?

 

[kuruman]

So the iceman has gone through approx 1 full stage of half life carbon cycle. So he was alive approx 6000 years before 1991? and then using that thinking if he had only 25 % percent carbon 14 than he would have lived 2 half life cycles which would mean he was alive 12000 years? am i getting it now?

You got it now. In radioactive decay problems it is handy to think in terms of the half-life because it is the "natural" time unit for the decaying system as opposed to the year (time required for the Earth to go around the Sun) that has no relation to the decaying system. Once you solve the problem in terms of half lives, you can always convert them back to years, minutes, seconds, etc.

 

[Kmcquiggan]

Thank you so much for helping me. I understand now!