GEOL360 Homework 1 : Elements and Isotopes

Transcription

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) by 6 pm on Monday February 12 th. There will be harsh penalties for late submission, and no credit will be given for answers that are not accompanied by calculations. Some questions use results from other questions I will be giving a lot of partial credit even if the final answer is wrong (as long as you provide clear explanation of your calculations) ========================================================== Q1: 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? Use simplified atomic weights (Si 28, O 16, Na 23). (Hint: compare abundances and atomic weights of Na and Si) weight percent Q2: 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? (Hint: recall the definition of residence time and rearrange the 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 1 and 2a to calculate the percentage of sodium in the Earth s crust which is cycled through the oceans each year? % of total sodium in the crust

2 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 2/5 Q3: The decay constant for 87 Rb 87 Sr is 1.42 x y -1. (a) How many 87 Rb half-lives have elapsed since the formation of the Earth at about x 10 9 years ago? half-lives (b) 87 Rb currently makes up 27.8 weight % of naturally occurring rubidium (the other 72.2 weight % is stable 85 Rb). What was the 87 Rb/ 85 Rb ratio of the Earth when it formed, assuming no change in the abundance of 85 Rb since that time? Be sure to use at least four significant figures, or two decimal places in percentage terms, throughout your calculation. (hint: first of all change weight percent into atomic abundances, then use N = N 0 e -λt ) Q4: 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? 18 O V-SMOW = Q5: 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? α QUARTZ-ANORTHITE = (b) Use the graph over the page to determine the temperature recorded by this thermometer, and say whether you think it records the temperature of crystallization of the granite, or some other process (explain your answer briefly) T = C Brief interpretation of this temperature:

3 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 3/5 Graph for question 5 (from Brownlow, Fig. 2-19). Data from Kieffer (1982) and O Neil (1986) Q6: 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/ Nd Nd/ Nd whole-rock mineral mineral (a) From the data above, construct an isochron plot as accurately as possible on the diagram on the next page (b) What is the age recorded by this data? (The decay constant for 147 Sm Nd is 6.54 x y -1 ). Age = Ma (c) What was the initial Nd/ Nd ratio of these samples? ( Nd/ Nd) initial =

4 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 4/ Question Nd/ Nd Sm/ Nd (d) From the following data, what is the CHUR model age of this rock? Data for CHUR: Nd/ Nd CHUR, today Sm/ Nd CHUR, today Useful formula: Nd Nd 147 Nd Sm t = e 1 Nd Nd sample today + sample t λ,, sample, today where t is an arbitrary time in the past Hint: first you need to derive the formula for T CHUR, recalling that ( ) ( Nd/ Nd) sample = ( Nd/ Nd) CHUR at the time corresponding to the model age. Please derive this formula in full (show all working)

5 GEOL360 HOMEWORK 1: TOPICS 1 AND 2 5/5 Formula: T CHUR = Answer: T CHUR = Ma (e) Briefly discuss the implications of your answers for parts (b) and (d) for the protolith (the source rock) of this rock. (Hint: could the immediate protolith of this rock have been CHUR?)