4. The K-concentration in the silicate portion of the Earth (mantle+crust) is ab

ID: 1028279 • Letter: 4

Question

4. The K-concentration in the silicate portion of the Earth (mantle+crust) is about 260 ppm. The mass of silicate Earth is 4X10 gram. The total mass of Ar in the atmosphere s 1.68X1018 moles with a 4°Ar/Ar ratio of 295.5 (today). The initial 40Ar/6 Ar ratio for the Earth was 0.0001, thus the only source of 40Ar in the atmosphere is by degassing of 4°Ar produced from 4°K decay in the Earth. Using relevant data, equation and decay constants from the text book, lecture notes, and useful tables on the class website,

Explanation / Answer

Answer:

- 40Ar is created by radioactive decay of 40K. Ar has two other isotopes, 36Ar, and 38Ar; the 38Ar/26Ar ratio in the atmospheric is 0.188. The initial solar system 40Ar/36Ar is thought to be something like 10-3 to 10-4. Comparing this to the atmospheric ratio of 295.5 leads immediately to the conclusion that most of the Ar in the atmosphere is radiogenic. Furthermore, atmosphere Ar must owe its origin to degassing of the Earth’s interior (since there is no K in the atmosphere). Indeed, it is fairly easy to calculate that 40Ar must have been released from a substantial fraction of the solid Earth to account for its atmospheric abundance. The K content of the bulk silicate Earth is estimated at 250 ppm. Over the Earth’s history, this would produce about 140 x 1018 g 40Ar. The amount of 40Ar in the atmosphere is 66 x 1018 g. This amounts to 47% of all 40Ar produced in the Earth.

The 40Ar/36Ar ratio in MORB can be as high as 40,000 and ratios in OIB and related xenoliths can be as high as 10,000. In all these examples,

- 40Ar/36Ar is highly variable, due almost entirely to atmospheric contamination. In contrast to He, Ar is very abundant in the atmosphere (concentration of 0.93%), so that small amounts of atmospheric contamination have a large effect on the 40Ar/36Ar measured in basalts. The He concentration in the atmosphere is low enough that such small amounts of atmospheric concentration have little effect. In general, maximum 40Ar/36Ar ratios in MORB are higher than in OIB, even though MORB are systematically poor in K than OIB.

-While this could imply the time since degassing has been longer for MORB than for OIB, it is more often interpreted as implying the MORB source has been more thoroughly degassed than the OIB source(s). This more thorough degassing results in more complete loss of 36Ar, hence radioactive decay lead to higher 40Ar/36Ar ratios in such thoroughly degassed systems. This explanation is also consistent with the generally higher 3He/4He observed in OIB than MORB.

- Radiometric dating is based on the decay of long-lived radioactive isotopes that occur naturally in rocks and minerals. These parent isotopes decay to stable daughter isotopes at rates that can be measured experimentally and are effectively constant over time regardless of physical or chemical conditions. There are a number of long-lived radioactive isotopes used in radiometric dating. The main point is that the ages of rock formations are rarely based on a single, isolated age measurement. On the contrary, radiometric ages are verified whenever possible and practical, and are evaluated by considering other relevant data.

Parent isotope

End product

(daughter) isotope

Half-life

(years)

potassium-40 (40K)

argon-40 (40Ar)

1.25 × 109

rubidium-87 (87Rb)

strontium-87 (87Sr)

4.88 × 1010

carbon-14 (14C)

nitrogen-14 (14N)

5.73 × 103

uranium-235 (235O)

lead-207 (207Pb)

7.04 × 108

uranium-238 (238O)

lead-206 (206Pb)

4.47 × 109

thorium-232 (232Th)

lead-208 (208Pb)

1.40 × 1010

lutetium-176 (176Lu)

hafnium-176 (176Hf)

3.5 × 1010

rhenium-187 (187Re)

osmium-187 (187Os)

4.3 × 1010

samarium-147 (147Sm)

neodymium-143 (143Nd)

1.06 × 1011