Problem set · Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (2007) · Answers →
Use the equations given in Chapter 4 to generate the Rayleigh fractionation curves shown in Fig. 9.5.
The Chapter 4 interactive Rayleigh plot implements the same equations.
The fractionation during ammonium assimilation by aquatic algae spans a very large range, with Δ15N ranging from −27 to 0‰. How would the availability of NH3 ultimately affect the δ15N value of the algae?
In downhole hydrology tests of an aquifer “downstream” from an agricultural center, dissolved nitrate content and δ15N values of nitrate in each sample were measured. Assume that the concentration and δ15N value of the water were initially the same and that nitrogen is lost via denitrification only by Rayleigh loss of N2 gas. Consider the following table:
| Sample | NO3− concentration | δ15N |
|---|---|---|
| 1 | 37.4 | 7.36 |
| 2 | 18.4 | 32.4 |
| 3 | 4.7 | 83.0 |
| 4 | 28.9 | 16.4 |
| 5 | 20.6 | 28.5 |
| 6 | 39.7 | 5.25 |
What is the average denitrification enrichment factor (Δ15N between product N2 gas and dissolved nitrate)? (Hint: graph the Rayleigh fractionation equation for different values of α and see what fits.)
Work the problem directly in the grid below. Cells accept Excel-style formulas beginning with =, with cell references (B1), ranges (G1:G6), and the named parameter cells shown above the grid. For example, =B1/CINIT in D1 gives F for sample 1, =(DINIT+1000)*D1^(ALPHA-1)-1000 in E1 gives the Rayleigh prediction for a trial α, and =E1-C1 in F1 the residual. For the linearized route, put =LN(D1) in G1 and =LN((C1+1000)/(DINIT+1000)) in H1, fill the rows, and =SLOPE(H1:H6,G1:G6) in row 7 returns α − 1 directly.
[Worksheet constructed for the modernization; it is not part of the 1st-ed. problem. Data as printed.]
A local grocer claims that the apples he sells are “organic”, that is, only natural fertilizers are used. You don’t trust him and decide to measure the nitrogen isotope ratio of the apple to see if he’s telling the truth. The δ15N value of your apple is +16‰. What do you conclude?
If the δ15N value of air is 0‰, but the discrimination associated with denitrification was +20 (instead of negative), what would the average δ15N value of the ocean be?
On the basis of Fig. 9.9, where on the diagram would you expect an Eskimo community to plot? Assume a diet of seal and occasional polar bear.
Fig. 9.9 (not reproduced here; see the 1st ed.) plots δ13C vs δ15N of bone collagen from Native American communities: (a) Western Anasazi, Southern Utah (A.D. 1–1300); (b) Nantucket Island, Massachusetts (A.D. 1000–1600); (c) Northwest coast Haida and Tlingit salmon fishers (historic); (d) Southern California coastal (A.D. 1400–1800); (e) Plains Arikara, South Dakota (A.D. 1650–1733); (f) Southern Ontario, Middle Woodland period (A.D. 1–400); (g) Modern Chicago, United States. Compilation and references from Martin (1999) and Schoeller et al. (1986).
Does the contamination of an N2 sample by CO cause an apparent increase or decrease in the measured δ15N value? (Hint: check out Table 1.4.)
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.