Physics

Problem

A sample of volcanic rock contains

2.4\times10^{-4}\,\text{mol}

of potassium-40 and

1.8\times10^{-4}\,\text{mol}

of radiogenic argon-40 produced by its decay. Assume that no argon-40 was present when the lava solidified and that every decay of

^{40}

K in the mode considered produces one

^{40}

Ar atom. The half-life of

^{40}

K is

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

. (a) Write the mathematical expression you will use to relate the given quantities to the age of the rock. (b) Calculate the age of the volcanic rock to two significant figures.

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