This Year in Uranium Decay

Pumice from the Bishop Tuff (~767 ka).  Zircons in this pumice are rich (relatively) in uranium, with up to 0.5% U.[1,2]  Image credit: Bill Mitchell (CC-BY).
Pumice from the Bishop Tuff (~767 ka). Zircons in this pumice are rich (relatively) in uranium, with up to 0.5% U.[1,2] Image credit: Bill Mitchell (CC-BY).

With 2016 now upon us, I felt it would be appropriate to think about what a new year means for uranium geochronology. What can we expect from the year ahead? Without getting into any of the active research going on, I felt it would be useful to address simply what is physically happening.

On Earth, there is roughly 1×1017 kg of uranium.[3] The ratio of 238U:235U is about 137.8:1, and 238U has a mass of roughly 238 g/mol (=0.238 kg/mol). Looking only at 238U, that gives us
1x1017[kg]x(137.8/138.8)/0.238[kg/mol] = 4.17x1017 mol [238U]

Radioactive decay is exponential, with the surviving proportion given by e-λt where λ is the decay constant (in units of 1/time) and t is time, or alternatively, e-ln(2)/T1/2*t, where T1/2 is the half-life and t is time.

To find the proportion that decays, we subtract the surviving proportion from 1: (1-e-λt)

Multiplying this proportion by the number of moles of 238U will give us the moles of decay, and multiplying by the molar mass will give the mass lost to decay:

(1-e-λt)*molU

Plugging in numbers, with λ238 = 1.54*10-10 y-1, t = 1 y and the moles of 238U from above, we get:

(1-e-1.54*10-10)*4.17*1017 mol [238U] = 6.4*107 mol

That yields (with proper use of metric prefixes) roughly 64 Mmol U decay, or 15 Gg of U on Earth that will decay over the next year.

Although those numbers sound very large, they are much smaller than even the increase in US CO2 emissions from 2013 to 2014 (50 Tg, or 50,000 Gg); total US CO2 emissions in 2014 were estimated at 5.4 Pg (=5.4 million Gg).[US EIA]

As for what’s in store for geochronology as a field, I think there will be a lot of discussion and consideration regarding yet another analysis of the Bishop Tuff.[4] Dating samples which are <1 Ma (refresher on geologic time and conventions) using U/Pb can be tricky, and Ickert et al. get into some of the issues when trying to get extremely high-precision dates from zircons. The paper is not open access, but the authors can be contacted for a copy (@cwmagee and @srmulcahy are active on Twitter, too!).

***
[1] J. L. Crowley, B. Schoene, S. A. Bowring. “U-Pb dating of zircon in the Bishop Tuff at the millennial scale” Geology 2007, 35, p. 1123-1126. DOI: 10.1130/G24017A.1
[2] K. J. Chamberlain, C. J. N. Wilson, J. L. Wooden, B. L. A. Charlier, T. R. Ireland. “New Perspectives on the Bishop Tuff from Zircon Textures, Ages, and Trace Elements” Journal of Petrology 2014, 55, p. 395-426. DOI: 10.1093/petrology/egt072
[3] G. Fiorentini, M. Lissia, F. Mantovani, R. Vannucci. “Geo-Neutrinos: a short review” Arxiv 2004. arXiv:hep-ph/0409152 and final DOI: 10.1016/j.nuclphysbps.2005.01.087
[4] R. B. Ickert, R. Mundil, C. W. Magee, Jr., S. R. Mulcahy. “The U-Th-Pb systematics of zircon from the Bishop Tuff: A case study in challenges to high-precision Pb/U geochronology at the millennial scale” Geochimica et Cosmochimica Acta 2015, 168, p. 88-110. DOI: 10.1016/j.gca.2015.07.018

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