# Nitrogen vs. Carbon re: Production of 14c

Dr. Paul Giem, carbon-14 researcher and former assistant professor of ermergency medicne at Loma Linda University, had originally published this statement: "nitrogen-14 captures neutrons 110,000 times more easily than does carbon-13..." (Giem, P. 2001. Carbon-14 content of fossil carbon. Origins 51:6–30). He has now corrected it to: "nitrogen creates carbon-14 from neutrons 110,000 times more easily than does carbon..."

Here is an explanation from Dr. Giem via his private communication to Real Science Radio, June 11, 2013:

Supposing that one has a given material that is mostly carbon but has a small amount of nitrogen in it, and it is irradiated with neutrons. The question is, what percentage of nitrogen would cause the production of carbon-14 from nitrogen to equal that from carbon? This will be weight percent rather than molar percent. Or a related question is, if we start with equal weights of carbon and nitrogen, which produces more carbon-14 from neutrons, and how much? The second question will give us the number 110,000. and this is how.

The production of carbon-14 from a given isotope is given by

phi * sigma * n,

where phi is the neutron flux, sigma is the cross-section of the nuclide in barns, and n is the number of atoms being irradiated. Notice that by hypothesis, phi is the same for both carbon and nitrogen, which is true for small or mixed samples. So (using ( ) for subscripts).

14C(N)     phi   sigma(14N) * n(14N)         sigma(14N) * n(14N)
______ =  ___  ___________________ =  ___________________
14C(C)     phi   sigma(13C) * n(13C)         sigma(13C) * n(13C)

Nitrogen is 99.636% 14N, which has a cross section for the production of carbon-14 of around 1.8 barns (the smallest number I have seen is 1.74 barns, and we will use it). Carbon is 1.07% 13C, which has a cross-section for the production of carbon-14 of 1.22 millibarns or 0.00122 barns.

For 12.011 grams of either carbon or nitrogen (chosen to equal 1 mole of carbon), the number of carbon atoms is 6.02 x 10^23, and the number of nitrogen atoms is [12.011/14.0 (the molecular weight of nitrogen which is mostly 14N)] * 6.02 x 10^23. Since Avogadro's number is on both sides of the fraction, we can cancel it out, and obtain

1.74 barnes   *  (12.011 / 14.0) moles * 0.99636
=  __________________________________________  =  114,000
0.00122 barns            *  1 mole             * 0.0107

Since we probably are not justified in more than two significant figures here, I rounded it out (down) to 110,000.

One may argue about the precise percentage, but I have it within 10 percent, and the estimate is low. The point remains. A specimen with 1/100,000 nitrogen content by weight (or 0.001%) should have just over double the amount of carbon-14 than a pure carbon specimen, if they are both irradiated by the same neutron source. A specimen with 1% nitrogen (not unheard of for coal) should have 1,100 times as much carbon-14 as a pure carbon specimen, with equivalent neutron irradiation. Thus my point about, in theory, the carbon-14 content of coal varying wildly with the nitrogen content, is a valid one. If it does not happen in practice, it strongly suggests that the neutron theory is defective.

During our RSR interview (rsr.org/giem) Dr. Giem criticized his own quote on this topic. As originally published, it stated that,"nitrogen-14 captures neutrons 110,000 times more easily than does carbon-13..." which he indicated is slightly inaccurate. As stated on air, and again here via private communication, Dr. Giem wrote: