Difficult# Age of Ore and Radioactive Dating

CHEM-YXHEDN

Uranium decays to lead with a half-life of ${ 4.5\times 10 }^{ 9 }$ years.

$$_{ 92 }^{ 238 }{ U } \ \longrightarrow \ _{ 82 }^{ 206 }{ Pb } \ + \ 8_{ 2 }^{ 4 }{ He }+ \ 6_{ -1 }^{ 0 }{ \beta }$$

A small specimen of the ore was found to contain 7.34 mg of $ _{ 92 }^{ 238 }{ U } \ $ and 2.56 mg of $_{ 82 }^{ 206 }{ Pb }$.

What is the age of the ore?

Use the following formulas to answer the question:

$${ t }_{ 1/2 }=\cfrac { ln 2 }{ k } =\cfrac { 0.693 }{ k }$$

and

$$ln\cfrac { A_o }{ A } =kt$$