The argon-40 method of radioisotope dating was developed in the Geology Department at Stony Brook University to determine the age of rocks brought back from the moon.This method assumes that no ⁴⁰Ar gas was trapped when the molten rock solidified, and that no ⁴⁰Ar could escape from the solid rock.One sample that was analyzed had a ⁴⁰K to ⁴⁰Ar ratio of 0.100 N_K/N_Ar =0.100).⁴⁰K decays into ⁴⁰Ar by positron emission with a half-life of 1.28 = 109 years.How many years ago was this moon rock formed?

Question

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The correct answer is C.The age of the moon rock can be calculated using the following equation:t = (1/λ) * ln(1 + (N_Ar/N_K))where:t is the age of the rock in yearsλ is the decay constant for ⁴⁰K (1.28 * 10^-10 years^-1)N_Ar is the number of atoms of ⁴⁰Ar in the sampleN_K is the number of atoms of ⁴⁰K in the sampleSubstituting the given values into the equation, we get:t = (1/1.28 * 10^-10 years^-1) * ln(1 + (0.100))t = 4.4 * 10^9 yearsTherefore, the moon rock was formed 4.4 billion years ago.

The Argon-40 Method of Radioisotope Dating Was Developed in the Geology