Note: This post acknowledges replies from Richard Wein, Joel Duff,
and David Bowman.
On Thu, 23 Mar 2000 22:05:34 -0000 Richard Wein wrote:
>As I said, I'm no expert, but I'm pretty d___ sure that, after 10
>half-lives, you still have 1 in 1024 (2^10) of the original atoms.
>Doesn't that follow from the definition of half-life? So how can
>you be down to the last few atoms, unless you had only an
>insignificant number of atoms in the first place?
Richard,
Another sharp question. For many of these radioactive isotopes, we are
talking about minuscule amounts relative to the abundance of stable isotopes
of the same element. For example, my ancient CRC Handbook of Chemistry and
Physics lists the natural abundances of potassium (K) isotopes as:
K-39 -- 93.1%
K-40 --- 0.00118%
K-41 --- 6.88%
This suggests that for a K-bearing mineral solidifying today, an average of
12 K atoms out of every million K atoms will be K-40. Of course, the ratio
would have been higher in the past. Yet, potassium (all isotopes combined)
is also the 8th most abundant element in the Earth's crust.
Therefore, your cogent mathematical observation caused me review my sources.
First, I could not find my source for that 10 half-life rule of thumb. I
believe it was in some notes relating to a classroom laboratory experiment
demonstrating the nature of radioactive decay. Thus it is very possible
that the 10 half-life rule was based on detection limits rather than the
"decay of the last few atoms" and that I mistakenly expanded that
observation to a more general rule. I also found some exceptions to the "10
half-life" rule. While scanning Dalrymple's "Radiometric Dating, Geologic
Time, and the Age of the Earth: A Reply to 'Scientific' Creationists" (USGS
Open-File Report 86-110), I see where he was optimistic that new analytical
techniques may extend the limits of C-14 dating back to 100,000 years. That
is almost 20 half-lifes or 1 in 10^6 (2^20) original atoms.
But, how do these revelations affect my original point? Actually, if
anything, they improve it. The question still stands. With the exceptions
noted in my first post (and David Bowman's correction of my sunlight/cosmic
ray blunder), why are there no naturally-occurring radioactive isotopes
having half-lifes of 70 million or less? This question is valid whether all
Sm-146 (70 M.Y. half life) has decayed or whether it has simply decayed to
the point that we can no longer detect it. Note that a 4.55 B.Y. old Earth
would be 65 half lifes for Sm-146 or 1 atom left for every 37*10^18 original
atoms.
Joel Duff pointed out a possible YEC response:
>I think the YEC response might be that there might have been
>different decay rates in the past such that accross the board
>radioactive decay occurred at higher rates in the past. If this
>were so then the fact that the isotope ratios we see today seemt
>to suggest a 770 Ma to 7 BY age would not be a coincidence.
Yes that would be a typical response. To explore that, let's assume that
all Sm-146 decayed in only 10,000 years. If it took the same 65 half-lifes
to accomplish this, then the *average* half-life for Sm-146 would be 154
years instead of 70 million years. This would be a 45,000,000% change.
Yet under the most severe laboratory conditions, the only observed change in
decay rates has been a couple of percent.
Also note that the YEC response would require that ALL radioactive decay
rates have changed in exactly the same proportions. This would be necessary
to explain the listed data in my original post and the concurrence of
several results found when analyzing a single rock multiple times and by
multiple radiometric techniques.
This YEC response is simply speculation without any corroborating evidence.
It reminds me of a comic that I saw many years ago. Two scientists in lab
coats were standing before a chalkboard covered with a complex mathematical
equation. One scientist was pointing to a spot in the middle of the
equation where appeared the words ...Then a miracle occurred... and saying
(as I remember it) "I think you need a little more work on this point."
Steve
P.S. BTW, although humbling, I consider it an honor to be able to correct
my errors. Almost everyone who has written peer-reviewed papers understands
and ultimately appreciates correction -- especially before publication.
Perhaps someday, in another post, I will relate the story of person whom
I've worked with here -- one of my heros of scientific integrity who
personally and very publicly refuted his own published paper after redoing
his experiment.
[As always, the opinions express herein are my own
and are not to be attributed to my employer.]
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Steven M. Smith, Geologist Office: (303)236-1192
U.S. Geological Survey Fax: (303)236-3200
Box 25046, M.S. 973, DFC smsmith@usgs.gov
Denver, CO 80225
--The USGS National Geochemical Database NURE HSSR Data Web Site--
http://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0492/
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