A 1 . 5 × 10 9 years old rock contains U 238 which disintegrates to form Pb 206 . Assume that there was no lead in the rock initially and it is the only stable product formed by the decay. Calculate the ratio of the number of nuclei of lead to that of uranium. [Given, half-life of U 238 = 4 . 5 × 10 9 years, 2 1 3 ≈ 1 . 26 ]

Step-by-step solution

Let N 0 be the initial number of uranium nuclei. After time t , let N U be the number of uranium nuclei and N Pb be the number of lead nuclei. The number of half-lives passed is n = t T half = 1 . 5 × 10 9 4 . 5 × 10 9 = 1 3 N U = N 0 1 2 n = N 0 1 2 1 3 N Pb = N 0 - N 0 1 2 1 3 N Pb N U = 2 1 3 - 1 = 0 . 26