In a uranium ore the ratio of `U^(238)` nuclei to `Pb^(206)` nuclei is `eta= 2.8`. Evaluate the age of the ore, assuming all the lead `Pb^(206)` to be final decay product of the uranium series. The half-life of `U^(238)` nuclei is `4.5.10^(9)` years

Explanation

What this implies is that in the time since the ore was formed, `(eta)/(1+ eta)U^(238)` nuclei have remained undecayed. Thus
`(eta)/(1_eta)= e^(-txx(In2)/(T_(1//2))`
or `t= T_(1/2)(In (1+eta))/((eta)/(In2))`
Substituting `T_(1/2)= 4.5xx10^(9)years, eta= 2.8`
we get `t=1.98xx10^(9)`years.