A) \[2.25\times {{10}^{9}}\]years
B) \[13.5\times {{10}^{9}}\]years
C) \[9.0\times {{10}^{9}}\]years
D) \[4.5\times {{10}^{9}}\]years
Correct Answer: D
Solution :
One atom of\[_{92}P{{b}^{238}}\]produces one atom of\[_{82}P{{b}^{206}}\]on decay. Therefore, the number of atom of \[{{U}^{238}}\]and\[P{{b}^{206}}\]in a rock sample is equal only when half of the number of\[~{{U}^{238}}\] originally present decay to give same number of\[P{{b}^{206}}\]. Thus the time elapsed will be equal to the half-life period of\[{{U}^{238}}\]
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