The analysis of a mineral of uranium reveals that ratio of moles of ²⁰⁶Pb and ²³⁸U in sample is 0.2. If effective decay constant of process  ${ }^{238}U{\to }^{206}Pb$ is  $\lambda$ then age of rock is(assuming the only source of Pb in the mineral is U).

• A

  $\frac{1}{\lambda }\ln \frac{5}{4}$

• B

  $\frac{1}{\lambda }\ln \left(5\right)$

• C

  $\frac{1}{\lambda }\ln 4$

• D

  $\frac{1}{\lambda }\ln \frac{6}{5}$