The images below show a sedimentary sequence in central Mexico which is known for its abundance of cultural artifacts in the uppermost sediments and paleosols. Archeologists would like to know the age of the sediments so they can date the onset (and decline) of several cultural periods in this region. As a geologist you know that you cannot date sediments and soils directly, but you might be able to date the lava flow between the two sedimentary units to obtain an age limit for the sediments above and below. You collect a few specimens and take them to the lab for radiometric dating.
Fig. 1: View of the Tlaxcala sedimentary sequence. White and greenish lacustrine sediments are shown in the lower left of the image, brown volcanic deposits containing paleosols make up the top of the hill. The two sedimentary units are separated from each other by a lava flow of (yet) unknown age (shown between the yellow lines). The mountain in the background is Iztaccihuatl, a volcano just east of Mexico City. Fig. 2: Hand specimen of olivine basalt collected from the lava flow shown in Figure 1.
Based on the mineralogy of the igneous rocks you decide to use Potassium Argon dating (see the textbook for more details). The half life of Potassium is approximately T1/2 = 1,300 million years, that means that during this time period approximately half of the radioactive potassium will have decayed into argon, a noble gas. To determine the age of the rock you measure the number of daughter isotopes (D) and remaining parent isotopes (P) and calculate the ratio D/N. The age of the specimen can then be calculated using the following equation:

where T1/2 is the half life of potassium, D is the number of daughter isotopes, and N is the number of remaining parent isotopes. Ln is the natural logarithm.

You measure the following D/N ratios for five samples from the lava flow:

Sample D/N
1 0.00139
2 0.00133
3 0.00149
4 0.00141
5 0.00136

Questions:

a)  Calculate the likely age of the lava flow, using the equation given above.

b)  What can you say about the age of the lacustrine sediments and the paleosol units ?

c)  Based on other evidence, soil scientists estimate that the lowermost paleosol, which is located just above the lava flow, is no older than 160,000 years. How does this agree with your results from part a)? How do you explain the diference?

 
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