Question

A rock sample contains zircon crystals thet have 1.82 atoms of 235U and 0.52 atoms of 207Pb. Calculate the age of the rock sample

Answer 1

The age of the rock sample is approximately 1.72 billion years.

How can we calculate the age of the rock sample?

We can use the principles of radiometric dating, specifically uranium-lead dating. This method relies on the radioactive decay of the uranium-235 isotope (²³⁵U) into the lead-207 isotope (²⁰⁷Pb) with a known half-life.

We calculate the initial ratio of ²³⁵U to ²⁰⁷Pb:

Divide the number of initial ²³⁵U atoms by the initial number of ²⁰⁷Pb atoms:

Initial ²³⁵U/²⁰⁷Pb ratio = 1.82 atoms ²³⁵U / 0.52 atoms ²⁰⁷Pb = 3.5 atoms ²³⁵U/atom ²⁰⁷Pb

Let t be the age of the rock sample in half-lives.

The current ratio of ²³⁵U to ²⁰⁷Pb will be:

Current ²³⁵U/²⁰⁷Pb ratio = 1 / (
`2^t`)

We can set up an equation to solve for t:

3.5 = 1 / (
`2^t`)

Solving for t gives approximately 2.45 half-lives.

Multiply the number of half-lives by the half-life of ²³⁵U (704 million years):

Rock sample age = 2.45 half-lives * 704 million years/half-life ≈ 1.72 billion years

Therefore, the age of the rock sample is approximately 1.72 billion years.