# Meanlife for an archaeologist

#### sgarrett

I am an archaeology graduate student trying to grasp the hard science behind radiometric (specifically radiocarbon) dating. I feel I have a general grasp of the concept of a half-life. What is confusing me is the meanlife. A quote from the paper I am reading will perhaps explain my confusion: "...there are several reasons why [radiocarbon dates] differ from a true age. First, radiocarbon dates are calculated using an obsolete measurement of 14C meanlife, 8033 years, even though it is now known more accurately as 8266 years." He moves on to explain other reasons (14C content has varied over the millenia-which I understand), without explaining what a meanlife is. So far, Google has not been very helpful.

Is the half-life derived from the meanlife? If so, why don't they just keep it simple and say that the known half-life is calculated using an obsolete measurement?

FYI I do understand the difference between a radiocarbon date [statistical measurement of 14C content] and a calendar date. That's not what I'm asking.

I would appreciate any help that you hard scientists can give me!

#### sgarrett

My hope is that this question will represent an interesting exercise in applied chemistry. I think the crucial thing is that I have seen this definition (from Britannica):

Meanlife: in radioactivity, average lifetime of all the nuclei of a particular unstable atomic species. This time interval may be thought of as the sum of the lifetimes of all the individual unstable nuclei in a sample, divided by the total number of unstable nuclei present. The mean life of a particular species of unstable nucleus is always 1.443 times longer than its half-life (time interval required for half the unstable nuclei to decay). Lead-209, for example, decays to bismuth-209 with a mean life of 4.69 hours and a half-life of 3.25 hours.

The problem is that I just plain don't understand it. My understanding of half-life goes- when a nucleus is unstable, it emits a Beta particle at a known interval. This causes the neutron to change into a proton [C14 becomes N14]. The average time for half of a group of C14 atoms to decay is its half-life. The % of C14 remaining in a tested sample indicates the # of half-lives the sample has expended [correct word choice here?].

Again, many thanks if you can help me fit meanlife into this basic understanding (also if you can amend any errors in my understanding of half-life)!!!

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#### sgarrett

I know, I'm posting in my own thread again...

I don't know what level chemists the average user on here might be. But, if there are any advanced chemists who are even vaguely interested in the topic, I believe it would be worthwhile to have one look over the way the concept is portrayed in the archaeological literature. There is probably some grant money to be won with an overall critique of the portrayal of advanced concepts.

Or, you could endeavor to write a concise article explaining the science in laymen terms, but sufficiently advanced that it can enhance our understanding of the concept.

Just an idea on the off chance that someone is looking for a project...