GEOL360 Homework 1 : Elements and Isotopes

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1 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 1/5 GEOL360 Homework 1 : Elements and Isotopes Name: Fill in the final answers in the blank spaces provided after each question. Note carefully the units which I want the answer in (especially check ppm, weight %, etc). Staple all other pieces of paper which you have used to this page, and put in my mailbox (outside room 245) or give it to me in person by the end of class on Tuesday February 12 th. There will be harsh penalties for late submission. No credit will be given for answers that are not accompanied by calculations. Some questions use results from other questions I give partial credit even if the final answer is wrong (as long as you provide a clear explanation of your calculations). Numbers for each question given in brackets. Total points available is 35 for this homework. Some guidelines for homeworks Use multiplication signs, not dots these can be confused with decimal points by both you and me. Be very careful with factors of 10: remember there are (100 x 100 x 100) = or 10 6 cm 3 per m 3, and likewise there are 10 9 cubic meters in a cubic kilometer Be careful to copy the same answer if you need it again in a later question do not misread 10 8 as 10 6, for example (if this happens frequently I suggest you write neater!) Write out the formula you started with, and the formula you used to get the final answer (often this will be the first formula rearranged slightly). Then you and I will know whether the mistake was made on the calculator (bad but not too serious) or whether it was a mistake in algebra (bad but not too serious) or a misunderstanding of the terms involved (more serious). If you are reading something off a graph, do not pretend that you can measure to the nearest micron I would much rather you put 280 ± 5 C than C after all, who has a thermometer that accurate! I will deduct points in future for too many decimal places Conversely, if you are given information (especially isotope ratios) which have 5 decimal places, please quote your answer to five decimal places. All rocks have present-day 143 Nd/ 144 Nd ratios between 0.50 and 0.52 basalts vary between about and , so the fourth and even the fifth decimal place are very important. When reporting isotopic values in delta notation, always say or 5.6. The difference between positive and negative can be very important, especially when we get on to thermodynamics. Diagrams can be useful in explaining your interpretation for example, a diagram of Nd ratios against time is a good way of describing your interpretation of crystallization ages and model ages.

2 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 2/5 Q1: The sun's mass is 1.99 x kg, three-quarters of which is hydrogen. The mass of a hydrogen atom is 1.67 x kg. How many hydrogen atoms does the sun contain? Use scientific notation (powers of ten). [2] The sun contains hydrogen atoms Q2: The abundance of sodium in the continental crust is 1.17 x 10 5, relative to silicon = 10 6 atoms (Table 1-5, Brownlow). Assuming that the SiO 2 content of the continental crust is 60% by weight, what is the sodium content of the continental crust in weight percent? [3] Use simplified atomic weights (Si 28, O 16, Na 23). (Hint: compare abundances and atomic weights of Na and Si) weight percent Q3: The volume of the Earth s oceans is about 1,370,000,000 km 3. Seawater has a sodium concentration of ppm (parts per million) by weight, and sodium has a residence time of about 260 million years in the ocean (Table 1-11, Brownlow). Assume seawater density is approximately 1.0 g/cm 3 (a) What is the mass of sodium transferred to and from the oceans each year, assuming that the concentration of sodium in seawater remains constant? [3] (Hint: Residence time T = A / (da/dt), where A is total amount of species in reservoir, da/dt is net influx or outflux of species. Now rearrange this equation) kg y -1 (b) The mass of the crust (continental and oceanic combined) is 2.4 x kg. Assuming (roughly) that sodium is a similar weight fraction of both continental and oceanic crusts, use your answers to question 2 and 3a to calculate the percentage of sodium in the Earth s crust which is cycled through the oceans each year? [3] % of total sodium in the crust

3 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 3/5 Q4: The decay constant for 87 Rb 87 Sr is 1.42 x y -1. How many 87 Rb half-lives have elapsed since the formation of the Earth at about x 10 9 years ago? [3] half-lives Q5: The two commonly used reference standards for reporting the 18 O/ 16 O ratio of samples are V-SMOW ( 18 O/ 16 O = x 10-6 ) and PDB ( 18 O/ 16 O = x 10-6 ). If a sample has 18 O PDB = -23, what is the 18 O V-SMOW of the sample? [3] 18 O V-SMOW = Q6: I have two different powdered rock samples, A and B. Powder A contains 100 ppm strontium (1 ppm is weight percent), and has an 87 Sr/ 86 Sr ratio of Powder B contains 200 ppm strontium, and has an 87 Sr/ 86 Sr ratio of (a) What weight proportions of A and B would mix together to give a powder with an 87 Sr/ 86 Sr ratio of ? [4] (Hint: use the equations on your handout, page 5) In weight proportions, % of A and % of B (b) What would the concentration of strontium be in this powder? Give your answer in ppm. [2] [Sr] = ppm

4 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 4/5 Q7: In an attempt to measure the crystallization temperature of a granite, a geochemist analyses the oxygen isotope ratios of coexisting quartz (SiO 2, qtz) and anorthite (CaAlSi 3 O 8, an). The results are 18 O V-SMOW (qtz) = +10, and 18 O V-SMOW (an) = +4.4 (a) What is the fractionation factor, α QUARTZ-ANORTHITE? [2] α QUARTZ-ANORTHITE = (b) Use the graph to determine the temperature recorded by this thermometer. T = C [2] (c) Given that granites crystallize at about 640 to 650 C, does this temperature it records the crystallization of the granite, or some other process? [1] Graph for question 5 (from Brownlow, Fig. 2-19). Data from Kieffer (1982) and O Neil (1986)

5 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 5/5 Q8: Below is a table containing Sm-Nd isotopic data for two mineral separates and a whole-rock sample of a basalt: Basalt data 147 Sm/ 144 Nd 143 Nd/ 144 Nd whole-rock mineral mineral (a) From the data above, construct an isochron plot as accurately as possible on the diagram below [3] (b) What is the age recorded by this data? (The decay constant for 147 Sm 143 Nd is 6.54 x y -1 ). [3] Age = Ma (c) What was the initial 143 Nd/ 144 Nd ratio of these samples? [1] ( 143 Nd/ 144 Nd) initial = Question Nd/ 144 Nd Sm/ 144 Nd

GEOL360 Homework 1 : Elements and Isotopes

GEOL360 HOMEWORK 1: TOPICS 1 AND 2 1/5 GEOL360 Homework 1 : Elements and Isotopes Name: Fill in the final answers in the blank spaces provided after each question. Note carefully the units which I want