Chemical Kinetics And Nuclear Chemistry

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into $\mathrm{Pb}-206$ while the rest of it remains undisintegrated.

When the age of the sample is $\mathbf{P} \times 10^8$ 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; $\log _e 2=0.693$ ]