Download 1 ES 6216 – Isotope Geochemistry Problem Set 2 Distributed 9/11

ES 6216 – Isotope Geochemistry
Distributed 9/11/12
Due 9/25/12
Problem Set 2
1. a. What magnetic field strength would be required to focus a beam of CO2+ ions on
a collector of a mass spectrometer whose analyzer tube as a radius of 31.45cm,
assuming a voltage of 1000V?
b. Change your magnetic field strength by -10%, what voltage puts the CO2 ions
into the collector?
2. Estimate the Earth’s potassium content in ppm by weight from data for Ar in the atmosphere.
[helpful numbers: mass atmosphere = 5.3 x 1021g, Ar = 1.29% of atmosphere]
3. Calculate the K-Ar age for a feldspar sample which yielded the following data:
K = 0.157 wt. %
40
Ar = 7.37 x 10-7 cc STP/g
[helpful number: 1 mole of gas = 22.4 liters at STP]
4. The data in the table below are for various mineral and chemical separates from the
Shergotty meteorite, which is believed to be a fragment ejected from Mars. Shergotty has an
igneous texture, and the age information from various radioactive decay systems is believed
to reflect the time of crystallization of this material on Mars. Construct an isochron and
determine the age and initial ratio of Shergotty. Express the intial ratio in terms of both molar
ratios and ∈Nd(t). Assuming that Sm/Nd for Mars is similar to that for Earth, what does this
say about the source materials from which the Shergotty magma was derived? Use CHUR
isotope ratios provided in lecture notes.
Sample #
1
2
3
4
5
6
7
8
9
10
11
147
144
Sm/ Nd
0.31489
0.31510
0.29640
0.26490
0.07660
0.37700
0.33600
0.28000
0.32070
0.14180
0.20930
143
144
Nd/ Nd
0.512420
0.512420
0.512370
0.512250
0.511810
0.512530
0.512450
0.512227
0.512410
0.512010
0.512090
5. What was the 235U/238U ratio when the earth formed 4.6 billion years ago?
6. Assuming the activity ratio (234U/238U) in seawater has not changed over the past few hundred
thousand years, what is the (234U/238U) activity ratio in an undisturbed coral with an age of
85,000y and a U concentration of 2.8ppm?
1
b) Assuming that no Th was incorporated into its skeleton when it precipitated, how
many 230Th atoms does a 1g sample of this coral contain?
c) The analytical precision for a U-Th age is typically limited by measurement of the
230
Th atoms, and typically one is lucky to recover 0.05% of the total 230Th atoms during
a typical mass spec run. What will be a minimum 2σ relative error on the U-Th age for
your 1g coral sample?
7. Suppose a radioactive gaseous element in the atmosphere has a half-life of 6yrs. Its daughter,
also radioactive, has a half-life of one month. Because the daughter is not gaseous, it adsorbs
onto aerosol particles and is removed by physical processes, mainly precipitation. If the
activity ratio for these two isotopes (daughter/parent) in the atmosphere is observed to be 0.3
in steady state, what is the lifetime of the daughter with respect to physical removal from the
atmosphere?
8. The following activity ratios were measured in a manganese nodule. Estimate the growth rate
of the nodule, assuming that the amount of U-supported 230Th is negligible.
230
Depth (mm)
0-0.3
0.3-0.5
0.5-0.85
232
Th/ Th
43.7± 1.8
26.2 ± 0.6
10.4 ± 0.3
2