The Infinite vs. Finite Current Universe: Decay of the Uranium-238
Laboratory for Geochemistry, Cosmochemistry&Astrochemistry, University of Niš, P.O. Box 224, Niš, Serbia
The overall abundance of U in the Earth's crust is about 4 ppm, and it is concentrated in many minerals. On average the abundance of U in meteorites is about 0.008 ppm. We know that Earth’s and meteorite’s U was produced by several processes and that metal was inherited by the Solar system. This (natural) uranium (U) is primarily composed of two radioactive isotopes: 238U (99.3 %) and 235U (0.07 %). 238U has a half-time, t1/2, of about 4.5 Gy.
Let us assume that in our laboratory there is a 1 kg rock sample containing 3 % of 238U (or 0.14 gram-atom) = 0.14 × 6.023 × 1023 (Avogadro number) = 8.4 × 1022 of the 238U atoms. Let us also assume that this rock is about the age of Earth. The half-time of 238U atom t1/2 is related to its decay constant by λ = ln2/t1/2 (see bellow). ≈ 0.154 (Gy)-1. This also means for one year, the probability that a particular 238U will decay is 0.154 × 109 or 1 out of 6.5 × 109 Gy. As we noted above, our rock sample contains 8.4 × 1022 of the 238U atoms. This means that about 6.5 × 109 of these atoms sample will decay in one year or about 1.25 × 104 per minute.
The most
intriguing question in modern cosmology is probably whether the Universe is
infinite or finite in space. If
the current Universe is infinite there is a total infinite number of 238U atoms, NU, in it. The
modern cosmology claims that just before the Big
Bang event, space contained an unstable form of energy of unknown
nature. At the Big Bang moment, this energy was transformed into the energy
and matter present in the current Universe. If there is now an infinite number
of galaxies than the contents of energy and matter would be infinite in it.
According
to current thinking, the Universe similar to today's was formed about 12.8 Gy
or about one billion years after the Big Bang. Hence, the infinite Universe
would be formed at that time or before. But these two possibilities sound rather
peculiar. The possible
alternative is that the Universe has always been infinite and static. However,
consideration of this issue is out of the scope of this communication.
The radioactive decay rate of a source equals
the number N of identical radioactive atoms present in the
source, multiplied by their characteristic radioactive decay constant λ
Radioactive decay rate = λN
where the decay constant λ has dimensions of units of 1/time. The constant λ is one of the most important characteristics of each radioactive nuclide: λ is essentially independent of all physical and chemical conditions (although there are a few exemptions). The numerical value of λ is the statistical probability of decay of each radioactive atom (per unit o time) in a population of identical atoms. The half-life of a radioactive atom, t1/2, is related to its decay constant by
t1/2 = 0.692/λ.
The average or mean life of a set of nuclei is related
population is related to the decay constant
τ = 1/λ … (1)
or
τ = 1.44 t1/2 ...
(2).
It represents the average time between decays.
If the number of identical nuclei N is infinite then their decay constant λ = 0 and the average lifetime is non-defined.
As we
noted above, if the current Universe is infinite there would be an infinite
number of galaxies and hence the infinite number of planetary systems with the rocky
planets having a crust with more or less 238U compared with Earth’s crust. In this case,
there would be an infinite population of the 238U atoms, NU, in this Universe and all 238U atoms of our sample
would instantaneously disintegrate. However, experimentally, we know that the GM counter
detects about several hundred counts per minute of
our 238U sample. See also {1}. Therefore, the measured average life of the 238U atoms, τ (> 0), in
our laboratory sample would imply that the Universe is probably finite. This implies that the above-mentioned energy before Big
Bang was finite and that the contents of ordinary energy and matter (converted
into energy)[1] after
the Big Bang event were finite as well as current ordinary energy and matter
(converted into energy).
Reference
{1} R. B. McFee, EMS responds to uranium exposure, https://www.jems.com/operations/ems-responds-uranium-exposure/.
[1] Excluding dark energy and dark matter
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