Find the age of the rock.

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Chapter 44, Problem 46P

(a)

To determine

Find the age of the rock.

(b)

To determine

Find the ratio of 235U to 207Pb and of 232Th to 208Pb to yield the same age of rock.

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Two rocks are found that have different ratios R' of 238U to 206Pb: R' = 0.76 and 3.1. What are the ages of the two rocks? Did they likely have the same origin?

Potassium-Argon dating is a common method of determining the age of rocks based on the time they were last liquified, and thus we can determine the age of a surface by examining the ratio of the parent K40 to the decay product Ar40. This works because argon is a gas, which is free to bubble out of liquified rock whenever the rock is hot enough to no longer be in it's solid state (think of magma covering a surface). This means that just after the rock solidifies, there should be effectively no Ar40 remaining and that any Ar40 that we do find in the rock at the time of the collection of the sample must be due to radioactive decay. With all of this in mind, if we find that a rock sample has 31 Ar40 atoms for every 1 K40 atom, and the half-life of K40 is 1.3 billion years, how much time has passed in years since that rock was geologically active (aka it was last liquified)?

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