Using the preceding values for the various parameters
gives the expected ratio of 14C atoms to 12C atoms as
= 7. 9 10− 44 ( 22)
which is about 6. 6 × 10–30 pMC as compared to the measured
From any of these perspectives, the claim that the 238U
content of coal would produce the observed levels of 14C
Effect from a uranium deposit adjacent to the coal
For the case of the 14C being generated by an adjacent
uranium ore body, a similar analysis can be done but with the
uranium uniformly distributed within some different material
than coal that is outside, but adjacent to, the coal seam.
Typically, uranium is found as uraninite (UO2) distributed
in some other rock. The richest uranium ore bodies are in the
Athabaskan Basin which is largely sandstone. Sandstone is
generally composed of feldspar, of which there are several
variants. Assuming orthoclase feldspar (NaAlSi3O8), the
macroscopic scattering cross-section is 0.19 cm– 1 vs 0.70
cm– 1 for coal, the transport mean free path is 2. 15 cm vs 5. 46
cm for coal, the diffusion length is 4 cm vs 14 cm for coal,
and the extrapolated path length is 3. 9 cm vs 1. 5 cm for coal.
Thus, as with coal, the neutron flux in the feldspar matrix
is determined by a relatively small volume and the neutrons
do not travel overly far from their source. This means that
only those from a relatively small portion of the uranium
deposit immediately adjacent to the coal would penetrate
the coal. Because the transport mean free path and diffusion
length in the coal is also quite small, only the nitrogen in
a relatively thin layer of the coal immediately adjacent to
the uranium deposit would be exposed to this uranium flux.
Furthermore, the neutron flux entering the coal would only
be a portion of that generated in the uranium ore, since at
least half the neutrons would be heading away from the coal.
Since the concentration of uranium required to sustain the
observed levels of 14C when the uranium is uniformly mixed
throughout the coal is already well above that of the richest
uranium ore, clearly this explanation also fails.
Empirical neutron density measurements
Additionally, this issue can be analyzed using the
empirically measured neutron density at depth. As reported
in the RATE paper, Kuhn et al. 25 measured thermal neutron
densities of 1. 1–33 neutrons per cm3 per year ( 3. 49 × 10–8
– 1.05 × 10–6 neutrons per cm3 per sec) in mines deeper
than 800 m. More recently, Šrámek et al. 26 have used a
more theoretical approach to calculate subterranean neutron
densities in the range of 10–3 to10–6 neutrons per kilogram
of rock per second. Using 2. 7 gm/cm3 as the density of the
continental crust results in a neutron density of 2. 7 × 10–9 to
2. 7 × 10–6 neutrons per cm3 per second. Using the geometric
mean of these values gives an ‘empirical’ neutron density
of approximately 1. 26 × 10–7 neutrons per cm3 per second
regardless of source.
Using this for S in equation 14 and setting this equal
to the rate of decay of 14C (assuming secular equilibrium),
rearranging and dividing both sides by NC12 gives
Substituting previously defined values gives
= 1. 48 10− 9 = 0.000000148 pMC .
Thus, using empirically determined subterranean neutron
densities, regardless of the source of these neutrons, generates
a level of 14C to 12C that is orders of magnitude less than the
Explanation within a biblical historical timeframe
Since the measured 14C in coal cannot be effectively
explained within an old-earth paradigm, it is reasonable to
ask how the results compare with the expectation based on
the history derived from a plain reading of the Bible. Rotta
discusses this from the perspective that the atmospheric
14C-to-12C ratio has not yet reached an equilibrium level
and that, therefore, the fundamental assumption used in
calculating radiocarbon ‘ages’ is incorrect. However, he does
not try to reconcile the calculated ages with the biblically
derived age. Therefore, what factors would affect the 14C-to-
12C ratio during the pre-Flood period, and how would these
reconcile these disparate ages?
Granting the usual explanation that coal formed from
buried vegetation, from a biblical perspective, this burial
would have happened during the global Flood. This means
that all the vegetation that was buried would have been
growing during some, or all, of the c. 1,650-year-long pre-Flood era. As such, the vegetation would all have about the
same 14C-to-12C ratio, regardless of the geological layer in
which it was buried. This precisely reflects the data.
Figure 4 shows the range of 14C-to-12C values for each
sample at ±2σ, with the geological layers ‘colour’ coded.
There is no distinction between any of the three samples,
which represent widely separated layers (in depth and,
supposedly, time). Qualitatively, the results match the
expectations of the biblical framework.