Question

An igneous rock that you are analyzing contains the mineral zircon. The zircon was processed to acquire a precise measurement of the Parent and Daughter atoms locked within that mineral. You discover that there is a ratio of 15 Lead 207 atoms (207Pb) to 0.0667 Uranium 235 atoms (235U). How many half-lifes passed since that mineral formed? What is the age of the rock based on its half-life?

A. 4 Half-lives / 2.8 billion years old
B. 3 Half-lives / 2816 trillion years old
C. 3 Half-lives / 2816 billion years old
D. 2 Half-lives / 2.8 billion years old
E. 4 Half-lives / 2.8 million years old
F. 2 Half-lives / 2.8 million years old

Answer 1

The rock's ratio of Pb-207 to U-235 suggests that it has undergone four half-lives. With the half-life of U-235 being 704 million years, the rock is approximately 2.8 billion years old, corresponding to answer choice A.

Step-by-step explanation:

The student is asking about the age of a rock based on the isotopic ratio of uranium (U-235) and its decay product lead (Pb-207). To answer this, we use the concept of half-lives in radiometric dating. The half-life of U-235 is approximately 704 million years. We're provided with a ratio of 15 atoms of Pb-207 to every 0.0667 atoms of U-235 in the zircon mineral.

Starting with a 1:1 ratio of parent to daughter isotopes, after one half-life, there would be 1 part parent (U-235) to 1 part daughter (Pb-207), resulting in a 1:1 ratio. After two half-lives, the ratio would be 1 parent to 3 daughters (1:3), and after three half-lives, it would be 1 parent to 7 daughters (1:7). Considering our ratio of 15:0.0667 simplifies (by multiplying the denominator by approximately 15) to about 1:15, which is close to the expected 1:15 ratio after four half-lives. Therefore, the rock has undergone four half-lives.

Since one half-life of U-235 is 704 million years, four half-lives would be 4 x 704 million years, equaling 2.816 billion years. Therefore, the correct answer is A: 4 Half-lives / 2.8 billion years old.