The age of rocks collected from the moon on the Apollo 16 mission has been determined from the 87Rb — Physical Chemistry Chemistry Question
Dating moon rock
The age of rocks collected from the moon on the Apollo 16 mission has been determined from the 87Rb / 86Sr and 87Sr / 86Sr ratios of different minerals found in the sample.
Mineral 87Rb / 86Sr 87Sr / 86Sr
A (Plagioclase) 0.004 0.699
B (Quintessence) 0.180 0.709
87Rb is a β– emitter, write down the equation of nuclear decay. The half-life for this decay is 4.8 × 10^10 years.
Model Answer
87 37 Rb → 87 38 Sr + 0 -1 β
Calculate the age of the rock. You can assume that the initial 87Sr / 86Sr is the same in A and B and that 87Sr and 86Sr are stable.
Model Answer
87Srnow = 87Srt=0 + 87Rbt=0 – 87Rbnow
87Rbnow = 87Rbt=0 exp(-λ t)
87Rbt=0 = 87Rbnow exp(λ t)
87Srnow = 87Srt=0 + 87Rbnow (exp(λ t) – 1)
(87Srnow / 86Srnow) = (87Srt=0 / 86Srnow) + (87Rbnow / 86Srnow) (exp(λ t) – 1)
y = c + x(m)
(87Srt =0 / 86Sr ) same for A and B using assumption given in question
m = (0.709 – 0.699) / (0.180 – 0.004) = 0.0568 = (exp(λ t) – 1)
λ t = (ln 2) / t1/2 × t
t1/2 = 4.8×10^10 years
t = (4.8×10^10 / ln 2) × ln 1.0568 = 3.8×10^9 years