The number of ²³⁸ U atoms in an ancient rock equals the number of ²⁰⁶ Pb atoms. The half-life of decay of ²³⁸ U is 4.5x10⁹ years. Estimate the age of the rock assuming that all the ²⁰⁶ Pb atoms are formed from the decay of ²³⁸U.

Explanation

Since the number of `.^(205)Pb` atoms equals the number of `.^(238)U` atoms, half of the original `.^(238)U` atoms have decayed. It takes one half-life to decay half of the active nuclei. Thus, the sample is `4.5xx10^(9)y` old.