Posted: May 12, 2016 2:21 pm
by skipbond
Calilasseia wrote:I can think of one reason why we can find isotopes with shorter half-lives than 100 million years. They're the decay products of some of those longer-lived isotopes. That's why we find radium in coal dust - it's a decay product of uranium. Any reasonably ancient piece of rock containing uranium will also contain radium in small but measurable quantities. Since uranium percolates through geological water flows into coal seams and becomes resident in the coal in measurable quantities, radium appears in the coal as well. It's one of the reasons that ash from coal burning is a quantifiable radiological hazard. Find out more about this from this scientific paper among others. :)

Then, some of those longer-lived isotopes induce other elements alongside them to become radioactive. Neutron activation is a well-known phenomenon arising from nuclear reactors. My old favourite resource, Kaye & Laby, has a nice long article on neutron activation cross sections. Basically, what happens is this. Long-lived alpha-decay emitters such as uranium and thorium emit alpha particles (helium nuclei). In the case of 232Th, these have an energy of around 35.4 MeV, whilst those for 238U have an energy of 47.3 MeV. These can interact with other nuclei via collisions, producing an effect known as spallation, where the collision results in the liberation of a neutron or other fragment from the target nucleus. That neutron, in turn, can be absorbed by a stable nucleus, and transformed into a radioactive nucleus. For example, a stable 58Ni nucleus can absorb a spallation neutron, becoming 59Ni, which is radioactive, decaying via electron capture to the stable 59Co, with a half-life of 75,400 years.

Of course, which of the surrounding stable nuclei absorb the spallation neutron is dependent upon several factors, but this mechanism produces elements such as technetium in tiny quantities in appropriate geological strata. No isotope of technetium has a half life greater than 4.2 million years (this is an element with no stable isotopes), so its detection in a natural rock sample indicates that it was produced by neutron activation of molybdenum followed by beta decay (typically neutron activation of 98Mo to become 99Mo, which beta-decays with a half-life of 65 hours to produce 99Tc, which has a half-life of 211,000 years. Other technetium isotopes are produced by spontaneous fission of uranium, such as that occurring in the Oklo natural nuclear reactor.

Incidentally, a tiny fraction of 238U nuclei can undergo spontaneous fission, not only producing elements such as technetium directly, but producing other elements via neutron activation (three neutrons are released by the fissioning nucleus). However, a comparison of the interaction cross sections shows that this is a very infrequently occurring process - the cross section for 238U fission is around 4 × 10-6 barns (which means it doesn't happen very often). Compare this with the fission cross section for 235U, which is 583 barns, or 239Pu, which is 748 barns (both are fissile materials capable of being utilised in a nuclear reactor or a nuclear weapon as a result).

Radioactive dating is claimed to prove that the earth is billions of years old, but the methods are based on a number of unprovable assumptions. For example, it is assumed that radioactive decay rates have not changed in the past. Specifically, geochronologists assume that radioactive decay rates are unaffected by physical conditions like temperature and pressure. They also assume they are independent of the chemical environment.

The atomic nucleus is extremely tiny compared with the overall size of the atom—about 100,000 times smaller in diameter. Since the nucleus is located at the centre of the atom, it is well shielded by the surrounding electrons from external physical and chemical conditions. Radioactive decay, being a nuclear process, is thus considered to be independent of external conditions. The constancy of decay rate is a foundational assumption of the whole radioactive dating methodology. Faure states:

‘ … there is no reason to doubt that the decay constants of the naturally occurring long-lived radioactive isotopes used for dating are invariant and independent of the physical and chemical conditions to which they have been subjected …’1

One of the modes of radioactive decay, electron capture, occurs when a proton in the nucleus of an atom spontaneously captures an electron from one of the shells2 and becomes a neutron.3 The mass of the atom remains the same but the atomic number decreases by one. Electron capture is the only radioactive decay mode that is recognised as possibly being affected by physical conditions such as pressure, but the effect is considered insignificant and is ignored.1

However, a recent paper about the decay of beryllium-7 (7Be) has found that, contrary to previous thinking, the chemical environment noticeably affects the half-life of radioactive decay by electron capture.4 Beryllium is a rare, hard, light metallic element in the second column of the periodic table—an alkaline earth element. Its nucleus contains four protons, and the usual stable form also contains five neutrons, and thus has a mass number of nine. There is a lighter isotope of beryllium with a mass number of seven, with only three neutrons in its nucleus. The lighter isotope is unstable and decays to Lithium-7 (7Li) by electron capture (Figure 1). The energy released in this process is mostly emitted as a gamma ray. The half life of 7Be is about 53 days.

In the recent paper, geochemist Chih-An Huh reported that the decay rate of 7Be depends on its chemical form.4 The measurements were done at the unprecedented high precision of ±0.01%, some ten times better than any reported previously. An extremely sensitive and stable spectrometer was used to monitor gamma rays from the decay of 7Be. Three different chemical forms of 7Be were measured, the hydrated Be2+ ion in solution surrounded by four water molecules ([Be(H2O)4]2+), the hydroxide (Be(OH)2), and the oxide (BeO). The measured half lives were 53.69 days, 53.42 days and 54.23 days respectively—a 1.5% variation from the shortest to the longest. The variation is much greater than previously considered.

Creationists, for many years, have disputed the billions of years from radioactive dating calculations because they conflict with the 6000-year Bible time-scale. One assumption they have challenged is the constancy of decay rates. Curiously, Richard Kerr has picked up this scepticism in his report of Huh’s findings, and makes a particular point of addressing creationists:

‘Creationists hoping to trim geologic history to biblical proportions will be disappointed—the variations seen so far are much too small, just a percent or so, to affect the Earth’s overall time scale.’5

Despite these comments, the 1.5% variation in the half-life of 7Be due to chemical environment was a surprise, and shows that the previous assumption that rates are constant is not correct. One of the most widely used geological dating methods, the radioactive decay of 40K to 40Ar, nearly always occurs by electron capture.6 The effect of chemical environment on the decay rate for 40K should be less than for 7Be because potassium has extra electrons in outer shells. These electrons would shield those inner electrons that are more vulnerable to electron capture from the external chemical environment. The important question, though, is what factors may have controlled the distribution of radioactive isotopes within the rocks of the earth.
1)Faure, G., Principles of Isotope Geology, 2nd ed., John Wiley & Sons, New York, p. 41, 1986.
2)Only from the s orbitals, because all others have nodes at the nucleus, i.e. regions of zero probability of finding an electron.
3)An electron-neutrino is also released.
4)Huh, C.-A., Dependence of the decay rate of 7Be on chemical forms, Earth and Planetary Science Letters 171:325–328, 1999.
5)Kerr, R.A., Tweaking the clock of radioactive decay, Science 286(5441):882–883.
6)Faure, Ref. 1, p. 30. .