In an ore containing uranium, the ratio of U238 to Pb206 is 3. Calculate the age of the ore, assuming that all the leas present in the ore is the final stable product of U238. Take the half-life of U238 to be 4.5×109 yr.
Correct answer: (c)
Solution: Let the initial mass of uranium be M0 Final mass of uranium after time t,M=43M0 According to the law of radioactive disintegration. M0M=(21)t/T⇒MM0=(2)t/T ∴log10(MM0)=Ttlog10(2) t=Tlog10(2)log10(MM0)=log10(2)Tlog10(34) =log10(2)Tlog10(1.333)=4.5×109(0.30100.1249) ⇒t=1.867×109yr.