Question

9 Question (1 point) See page 978 Uranium-lead (U-Pb) dating of geological samples is one of the oldest and most refined radiometric dating methods, able to determine ages of about 1 million years to over 4.5 billion years with precision in the 0.1-1% range. The U-Pb dating method relies on two separate decay chains, one of which is the uranium series from 238 to 206Pb, with a half-life of 4.47 billion years. 5th attempt w See Periodic Table See Hint Geologists unearth a sample of zircon that appears to be a closed system. They find 0.706 microgram of 206Pb for 1.000 microgram of 238 U present. Approximately how old is the sample? 3.85 yrs

Answer 1

half-life = 4.47 billion years

decay constant = 0.693 / half life

                          = 0.693 / 4.47 x 10^9

                         = 1.55 x 10^-10 year-1

moles of lead = 0.706 / 206

                        = 3.427 x 10^-3 umol

moles of U = 1.00 / 238

                 = 4.20 x 10^-3 umol

total moles of U initially = 0.0042 + 0.0034 = 0.00763 umol

k = 1/t ln (Ao / At)

1.55 x 10^-10 = 1 / t ln (0.00763 / 0.0042)

t = 3.85 x 10^9 years

age = 3.85 x 10^9 years