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 10^8 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 10^9 years; _c 2=0.693 ]
A. A
_ 92 U ^ 238 _ 82 ~Pb ^ 206 +8 _2 He ^4+6_ -1 ^0 t =0 ~N _0= ( 1 238 + 7 206 ) moles t = tN _ t = 1 238 moles x = 7 206 moles Life of sample \( t\) years \([A]_0 \) Initial mole of \( U -238\) \([A]]_t \) Final mole of U-238 \( aligned & |A|_0 |A|_t = 1 228 + 7 206 1 238 \\ & = 0.0042+0.0340 0.0042 \\ & =9.1 \\ & = 2.303 2 t 4.5 10^9 =2.303 9.1 \\ & t=14.27 10^9 years \\ & =142.7 10^8 years \\ & P=142.7 \\ & P=143 aligned \)
Related: Chemistry — Chemical Kinetics · All PYQ Banks