Final answer:
To estimate the age of rocks based on the mole ratio of U-238 to Pb-206, we can use the concept of radioactive decay and set up a proportion. By solving the proportion, we can find the age of the rocks.
Step-by-step explanation:
To estimate the age of rocks based on the mole ratio of U-238 to Pb-206, we need to use the concept of radioactive decay. The half-life of U-238 is 4.5 × 10⁹ years. In one half-life, a sample of uranium will have decayed to 0.50 grams of U-238. By comparing the amount of U-238 to the amount of Pb-206 in a rock sample, we can estimate its age. In this case, the mole ratio of U-238 to Pb-206 is 0.75. To find the age, we can use the fact that after one half-life, the mole ratio would be 0.50. We can set up a proportion:
(0.50/0.75) = (1 half-life/t)
From this, we can solve for t, which represents the age of the rock. Solving the proportion, we find that t = 4.5 × 10⁹ × (0.50/0.75).
The estimated age of rocks in which the mole ratio of U-238 to Pb-206 is 0.75 is approximately 3.0 × 10⁹ years.