In this assignment you will use the simple logic statements governing radiometric dating Parent - Daughter + radiation + heat and the rate of radioactive decay and build an understanding of radiometri - 教育

Answers:

To find the absolute age of the basaltic dike, we need to use the following formula: Age = (t 1/2) x log(Po/Pt) where t 1/2 is the half-life of the radioactive isotope (in this case, potassium-40), Po is the number of parent atoms originally present when the rock formed (7497 in this case), and Pt and Dt are the number of parent and daughter atoms today (1071 and 6426, respectively, since the total number of atoms today is equal to the number of parent atoms originally). Plugging in the values, we get: Age = (1.3 billion years) x log(7497/1071) = 54.2 million years

Therefore, the absolute age of the basaltic dike is 54.2 million years.

To find the absolute age of the granite, we use the same formula as above, but with the values of Po, Pt, and Dt for unit B: Po = 11480, Pt = 7653 (since the number of parent atoms today is the difference between the original number and the number of daughter atoms today, which is 3827), and Dt = 3827. Plugging in the values, we get: Age = (1.3 billion years) x log(11480/7653) = 100.4 million years

Therefore, the absolute age of the granite is 100.4 million years.

To find the absolute age of the folded metamorphic rock, we use the same formula as above, but with the values of Po, Pt, and Dt for unit C: Po = 2517, Pt = 1678 (since the number of parent atoms today is the difference between the original number and the number of daughter atoms today, which is 839), and Dt = 839. Plugging in the values, we get: Age = (1.3 billion years) x log(2517/1678) = 223.5 million years

Therefore, the absolute age of the folded metamorphic rock is 223.5 million years.

The measured ages make sense in the context of relative dating. The basaltic dike (unit A) is the youngest, followed by the granite (unit B), and then the folded metamorphic rock (unit C). This order is consistent with the principle of superposition, which states that in a sequence of undisturbed rocks, the oldest rocks are at the bottom and the youngest rocks are at the top. Additionally, the relative ages of the rocks are consistent with the principle of cross-cutting relationships, which states that a rock or feature that cuts across another rock or feature must be younger than the rock or feature it cuts across. In this case, the basaltic dike (unit A) cuts across both the granite (unit B) and the folded metamorphic rock (unit C), indicating that it must be younger than both of them