A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into Pb-206 while the rest of it remains undisintegrated. When the age of the sample is P 108 years, the ratio of mass of Pb-206 to that of U-238 in the sample is found to be 7. The value of P is . [Given: Half-life of U-238 is 4.5 109 years; e 2 = 0.693]
Answer
143
Solution
Convert the mass ratio to a mole ratio: nPbnU = 7 238206 = 8.087
Initial U = U left + U decayed (= Pb formed) N0N = 1 + 8.087 = 9.087
t = t1/20.693 N0N = 4.5 1090.693 9.087
9.087 = 2.207 t = 6.494 109 2.207 = 1.433 1010 years = 143.3 108 years
Answer: 143