🚀 go-pugleaf

In article <9204080901.aa00587@Paris.ics.uci.edu> kibler@turing.ICS.UCI.EDU (Dennis Kibler) writes:
>How is radioactive dating done?
>
> I understand that by knowing the current % (say Z) of X in Y,
>and the half-life of X, that we can project backwards
>and figure out the % (say Z') of X in Y at any previous time.

Yep.  The formula is 
                       t = tau_p ln{(P+D)/P} 
                                              where tau_p is the mean 
lifetime (not the half-life) of the parent nucleus.  This assumes no 
daughters present at time zero, but it also works if the daughter 
population can be estimated independently.

>So to figure out the age of Y  we need to know the original
>percentage of X in Y.  But how is that known?

In the case of metallic ores, the problem is one of geology: is this 
metal expected to be found with its daughters.  In the case of alpha 
decay, it can be assumed that the helium gas was not trapped in the 
rock when it was formed.  In the case of C-14, the problem is one of 
biology and cosmic-ray backgrounds.  Every case has different problems; 
I think you may find them discussed in a nuclear chemistry text. 

> Let me put it in a more concrete form. Suppose we use carbon
>dating to measure the age of a fossilized plant. I don't
>understand why we aren't measuring the age of the carbon,
>created I presume at the some time before the age of the earth,
>rather than the age of the plant.

C-14 has tau ~ 8000 years so it does not originate from the big bang or 
supernovae but rather from cosmic-ray reactions in the atmosphere.  One 
starts by assuming this production rate is constant, but much work has 
led to calibration curves that effectively tell you about the time 
variation of those reactions.  More on that later.  The key point is 
that living organisms exchange carbon with their environment and thus 
maintain a fixed ratio of C-14 to C-14 that is reflected in a particular 
specific radioactivity (that is, radioactive decays per gram of carbon 
per second).  This interchange ceases at death, and from that point on 
the drop in specific radioactivity tells you the age. 

Calibration has been done by correlations with tree ring records that now 
go back a long ways (about 7 or 8000 years I think) and Egyptian mummys 
that are 4 to 5000 years old.  The deviation is not much from linear 
until you get back to > 5000 years.  More information on the variations 
and other terrestial measures of the time-dependence of cosmic ray fluxes 
requires someone with more expertise than I. 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)