Final answer:
The age of a rock can be determined using the potassium-argon dating method, which measures the ratio of potassium-40 to argon-40 in the rock. By comparing the amounts of these isotopes, the approximate age of the rock can be calculated to be 1.7 billion years.
Step-by-step explanation:
The age of a rock specimen can be determined using the potassium-argon dating method. This method measures the ratio of potassium-40 (K-40) to argon-40 (Ar-40) in the rock sample. The half-life of K-40 is 1.25 billion years. By comparing the amounts of K-40 and Ar-40 in the rock, we can calculate its age.
In this case, the rock specimen has 15 mmol of potassium and 45 mmol of argon. To calculate the age, we need to determine the ratio of Ar-40 to K-40. Since the atomic mass of potassium is 39.1 g/mol and the atomic mass of argon is 39.9 g/mol, we can calculate:
The molecular weight ratio of potassium to argon is 39.1/39.9 = 0.98.
The molar ratio of potassium to argon is 15/45 = 0.33.
Therefore, the age of the rock is approximately 1.7 billion years.