In an ore containing uranium, the ratio of U²³⁸ to Pb ²⁰⁶ is 3. Calculate the àge of the ore, assuming that all the lead present in the ore is the final stable product of U²³⁸ . Take the half-life of U²³⁸ to be 4.5 10⁹ yr .

Step-by-step solution

Let the initial mass of uranium be M ₀ Final mass of uranium after time t M = 3 4 M ₀ According to the law of radioactive disintegration. array l M M ₀ = ( 1 2 )^ t / T M ₀ M =(2)^ t / T ₁₀ ( M ₀ M )= t T ₁₀(2) t = T ₁₀ ( M ₀ M ) ₁₀(2) = T ₁₀ ( 4 3 ) ₁₀(2) = T ₁₀(1.333) ₁₀(2) =4.5 10⁹ ( 0.1249 0.3010 ) t =1.867 10⁹ yr . array