Physics

Problem

A zircon crystal contains

3.0\times10^{17}

atoms of

^{238}\text{U}

and

4.5\times10^{17}

atoms of

^{206}\text{Pb}

. Laboratory analysis shows that

0.5\times10^{17}

of the lead atoms were present when the crystal formed. Assuming all additional

^{206}\text{Pb}

arose from the decay of

^{238}\text{U}

(half-life

4.5\times10^{9}\,\text{years}

), the best estimate of the crystal’s age is a)

2.6\times10^{9}\,\text{years}

6.6\times10^{9}\,\text{years}

5.5\times10^{9}\,\text{years}

4.5\times10^{9}\,\text{years}

Intuitive explanation

Radioactive dating works by tracking how much of a parent isotope has decayed into a daughter product over time. Here, uranium-238 decays into lead-206, so the extra lead beyond what was originally present tells you how many uranium atoms have decayed. Use the decay constant and the ratio of remaining uranium to decayed uranium to find the elapsed time—this is the core of the radioactive dating method.

Intuitive explanation

Browse the problem library