Problem set · Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (2007) · Answers →
Large isotopic variations have been found in hydrogen, carbon, nitrogen, and oxygen in meteoritic material. The explanation for the large range differs for each element. Review the mechanisms that have been proposed to explain the large isotopic range for each element.
What is self-shielding, and how can it explain the CCAM mixing line?
It has been proposed that the δ18O value of the Sun is either very heavy (δ18O > +20‰) or very light (δ18O < −60‰). On what basis have these values been obtained, and what are the implications in terms of explaining the CCAM line?
If the CCAM line intersected the TFL at +50‰ and passed through pure 16O at its lower end, what is its slope?
We generally think of the relationship from equation (13.1),
and the equation δ17O = 0.52·δ18O as equivalent, but strictly speaking, they are not. Graph δ17O vs δ18O over a range of 0 to 1,000‰, assuming first that equation (13.1) is correct and then that δ17O = 0.52·δ18O is correct.
The Chapter 3 triple oxygen interactive plot explores exactly this distinction between the power-law and linear forms.
The six problems below are constructed additions to the 1st-ed. set, written for this modernization; they are not from the printed book. Parameter cells holding literature values are editable, and their defaults are representative placeholders to be set from the preferred references.
Problem 3 of the printed set poses the Sun’s δ18O as either very heavy or very light. The Genesis mission measured the solar wind directly in both 18O/16O and 17O/16O, but the solar wind is mass-dependently fractionated from the photosphere. Take the measured solar-wind composition, assume the Sun lies on the slope-1 line, and correct the solar wind back along a mass-dependent slope λ to find the Sun. How far below the slope-1 line does the measured solar wind sit, what is the Sun’s composition in both δ17O and δ18O, and which of the printed Problem 3’s alternatives survives?
[The solar-wind values, slope-1 intercept, and λ are editable; set them from the Genesis literature (McKeegan et al., 2011). The Sun is the intersection of the slope-1 line with the mass-dependent line through the solar wind.]
Mass-dependent fractionation laws relate the two isotope-ratio pairs of a three-isotope system through an exponent λ that depends on the masses and on the process. For O (17/16 and 18/16), S (33/32 and 34/32), and Si (29/28 and 30/28), compute the high-temperature equilibrium exponent λeq = (1/m₁ − 1/m₂)/(1/m₁ − 1/m₃) and the kinetic exponent λkin = ln(m₁/m₂)/ln(m₁/m₃). Why do measured arrays that fall off these slopes demand either a different process or an inherited (non-mass-dependent) component?
[Isotope masses from standard tables. Compare with the printed Problem 5 and the Chapter 3 triple oxygen plot.]
Meteorites divide into non-carbonaceous (NC) and carbonaceous (CC) groups in nucleosynthetic-anomaly space such as ε54Cr vs ε50Ti. Using the two endmembers in the parameter cells, and assuming for simplicity equal Cr and Ti concentrations in both, build the mixing line, find the CC fraction needed to carry the NC endmember to ε54Cr = 0 (the terrestrial value), and check what ε50Ti that mixture predicts. What does a mismatch with the terrestrial ε50Ti of 0 tell you about the equal-concentration assumption or the endmembers?
[Endmember values are representative placeholders; set them from a preferred compilation. The equal-concentration assumption is the flagged simplification under test.]
The mineral data below (constructed) come from one igneous inclusion. Fit the internal isochron of δ26Mg* against 27Al/24Mg, convert the slope to the initial 26Al/27Al of the inclusion, and date it relative to the canonical early-solar-system value using the 26Al half-life. The trial-isochron model curve lets you fit by eye before regressing.
[Data constructed to be exact; slope → (26Al/27Al)₀ uses the 26Mg/24Mg of the parameter cell.]
Free evaporation of K fractionates kinetically with α = √(m39/m41). Compute that α, build the Rayleigh curve for the δ41K of the residue as a function of the K fraction remaining, and then invert it, what fraction of K could a planetary body have lost this way if its bulk δ41K sits only at the target value in the parameter cell? What does that imply about free evaporation as the cause of planetary K depletions?
[The target δ41K is an editable placeholder for the planetary value of interest. The same worksheet structure applies to Cl, Fe, or any volatile system by swapping the masses.]
A reservoir of solar-like composition (δ17O = δ18O = 0) is mixed with a small fraction of presolar oxide grains whose composition is given in the parameter cells. Tracking both 17O/16O and 18O/16O, compute the mixture for each grain fraction, and the slope of the mixing trajectory in δ17O vs δ18O space. How does that slope distinguish inheritance from any mass-dependent process (λ ≈ 0.52) and from the slope-1 line?
[The grain endmember is a representative placeholder (Group-1-like); equal O concentrations in grain and reservoir assumed, a flagged simplification.]
Transcribed from Z. Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (Pearson Prentice Hall, 2007), end-of-chapter problem set (published source). Reference-scale names are written VSMOW, VPDB and VCDT where the original used SMOW, PDB and CDT, with the original numerical constants unchanged; historical usages (e.g. Craig's definition of SMOW) are kept as printed.
The source PDF's text layer scrambles mathematics, so equations and some values were reconstructed during transcription. Bracketed notes and anything tagged reconstructed or check vs print are editorial (constructed), not part of the original, and the warn-tagged items should be verified against the print copy.