A sample initially contains only \(\mathrm{U}-238\) isotope of uranium. With time, some of the \(\mathrm{U}-238\) radioa…

A sample initially contains only \(\mathrm{U}-238\) isotope of uranium. With time, some of the \(\mathrm{U}-238\) radioactively decays into \(\mathrm{Pb}-206\) while the rest of it remains undisintegrated. When the age of the sample is \(P\times {10}^{8}\) years, the ratio of mass of \(\mathrm{Pb}-206\) to that of \(\mathrm{U}-238\) in the sample is found to be 7. The value of \(\mathbf{P}\) is
[Given: Half-life of \(\mathrm{U}-238\) is \(4.5\times {10}^{9}\) years; \({\log }_{e}2=0.693\) ]