In a sample of rock, the ratio of ${ }^{206}\mathrm{Pb}$ to ${ }^{238}\mathrm{U}$ nuclei is found to be 0.5. The age of the rock is (Given half life of ${\mathrm{U}}^{238}$decay to $=4.5\times {10}^9$ year and answer if initially the rock had equal nuclei of${ }^{206}\mathrm{Pb}$ and ${ }^{238}\mathrm{U}$)