Geol. 656 Isotope Geochemistry

Geol. 656 Isotope GeochemistryProblem Set 4 Solutions Due March 6, 2000r = 143.95Bm V eWe solve this to find r 2 = 30.1047, so the collector spacing is 1.047 mm6. Suppose you measure a 87 Sr/ 86 Sr ratio of 0.70734 with a mass spectrometer. To monitor massfractionation, you also measured 86 Sr/ 88 Sr and found a value of 0.11992. Assume the true value of86 Sr/ 88 Sr is 0.11940.a. What is the true 87 Sr/ 86 Sr ratio according to the linear mass fractionation law?87⎛ Sr⎞⎜ 0 7073487 ⎟ = .⎝ ⎠Srmeas⎛According to the linear mass fractionation law: ⎜⎝So:87⎛ Sr⎞⎜ 0 70888087 ⎟ = .⎝ ⎠Srtrue8787Sr⎞Sr87Sr⎟ = ⎛ ⎞187⎠ ⎝ ⎜ ⎜Sr⎠truemeas⎜⎛⎟ +⎝0.11992− 1⎞0.1194 ⎟2⎟⎠⎝ b. What ⎠ ⎝ ⎠trueis the true 87 measSr/ ⎜86 Sr ratio according ⎟ to the power mass fractionation law?⎝⎠For power law fractionation: α = ⎡ ⎣ ⎢RRNuvMuv1 / ∆m uv− 1 / 2⎤⎥ − = ⎡ 0.119401⎦ ⎣ ⎢ ⎤0.11992⎦⎥α = R N 1/∆m uv–1=uv0.11940 –1/2– 1 = 0.00426227R M 0.12042And since R C i,j=R M i,j[1+α] ∆m i,j87⎛ Sr⎞⎜ 0 70887987 ⎟ = .⎝ ⎠Srtrue− 1 = 0.002175193