A rock sample contains traces of^238 U, ^235 U, ^232Th, ^208 Pb, ^207 Pb, and^20

Question

A rock sample contains traces of^238 U, ^235 U, ^232Th, ^208 Pb, ^207 Pb, and^206 Pb. Careful analysis shows that the ratio of^238 U to^206 Pb is 1.874. (a) Use this information to determine the age of the rock. Age = 2.78e 9 years (b) What should be the ratios of^235 U to^207 Pb and^232 Th to^208 Pb so that they would yield the same age for the rock? Neglect the minute amount of the intermediate decay products in the decay chains. Note that this form of multiple dating gives reliable geologic dates. N_U235/N_pb207 = 0.68 N_Th232/N_pb208 = 6.72

Explanation / Answer

assume initial mass of U235 to be M kg.

half life of 235 U to 207 Pb decay (called the actinium series) is 710 million years.

decay equation i.e. mass of U235 remaining after t years=M*exp(-lambda*t)

where lambda*half life=ln(2)

==>lambda=ln(2)/half life=9.7626*10^(-10)

so after 2.78*10^9 years, mass of U235 remaining=M*exp(-9.7626*10^(-10)*2.78*10^9)= 0.066271*M

so mass of Pb 207=M-0.066271*M

=0.93373*M

ratio=0.066271/0.93373=0.070974

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.