Chapter 11
Exercises

1. If helium ions (mass number = 4) are accelerated with a voltage of 10 kV in a mass spectrometer, at what speed are they emitted from the source? Recall that 1 atomic mass unit (amu) = 1.66 × 10^-27 kg and the elementary charge is 1.602 × 10^-19 C. [Answer: 695 km/s]
2. We are trying to estimate the Rb concentration in a rock for the purpose of whole rock Rb-Sr dating. To this end, we use a spike with a Rb concentration of 7.5 ppm containing 99.4% ⁸⁷Rb and 0.6% ⁸⁵Rb (these are atomic abundances). We mix 3.5g of the spike with 0.25g of sample dissolved in 50g. The ⁸⁷Rb/⁸⁵Rb-ratio of the mixture is 1.55, as measured by mass spectrometry. What is the Rb concentration in ppm? Note that natural Rb comprises of 27.825% ⁸⁷Rb and 72.165% ⁸⁵Rb. [Answer: 120 ppm]
3. A biotite contains 465ppm Rb and 30ppm Sr with a ⁸⁷Sr/⁸⁶Sr-ratio of 2.50. Given an initial ⁸⁷Sr/⁸⁶Sr-ratio of 0.7035, what is the age of the biotite? Natural Rb has an atomic mass of 85.4678 and comprises 72.165% ⁸⁵Rb and 27.825% ⁸⁷Rb, which has a half life of t_1∕2 = 48.8 Gyr. Sr has an atomic mass of 87.62. Its non-radiogenic isotopes occur with the following abundances: ⁸⁴Sr/⁸⁶Sr = 0.056584 and ⁸⁶Sr/⁸⁸Sr = 0.1194. [Answer: 2.36 Ga]
4. What is the U-Th-Pb age of a zircon with the following composition: U = 792.1 ppm, Th = 318.6 ppm, Pb = 208.2 ppm. Atomic masses for U, Th and Pb in the zircon are 238.04, 232.04 and 205.94, respectively. The isotopic composition of the Pb is as follows: ²⁰⁴Pb = 0.048%, ²⁰⁶Pb = 80.33%, ²⁰⁷Pb = 9.00%, ²⁰⁸Pb = 10.63%. Assume the following initial Pb composition: 204 : 206 : 207 : 208 = 1.00 : 16.25 : 15.51 : 35.73. The decay constants for ²³⁸U, ²³⁵U and ²³²Th are given in Section 5. ²³⁸U/²³⁵U = 137.818. Calculate the ²⁰⁶Pb/²³⁸U, ²⁰⁷Pb/²³⁵U, ²⁰⁸Pb/²³²Th and ²⁰⁶Pb/²⁰⁷Pb-age of the zircon. Give an account of its formation history.
   [Answer: 1.405, 1.523, 1.284 and 1.689 Ga]
5. A biotite was separated from granite and dated with the K-Ar method. The analytical data are as follows: K₂O = 8.45 weight %, radiogenic ⁴⁰Ar = 6.015 × 10^-10 mol/g. What is the K-Ar age of the biotite? The atomic mass of K is 39.098 (and oxygen 15.9994), with an isotopic composition that comprises 93.258% ³⁹K, 6.730% ⁴¹K and 0.01167% ⁴⁰K, which has a half-life of t_1∕2 = 1.248 Gyr. Recall that only 10.72% of the ⁴⁰K decays to ⁴⁰Ar, with the remaining 89.28% turning into ⁴⁰Ca. [Answer: 47.7 Ma]
6. Consider a biotite with a conventional K-Ar age of 384Ma. A ⁴⁰Ar/³⁹Ar step-heating experiment yields the following data:

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   % 39Ar released	7	15	20	25	35	70	100
   40Ar*∕39Ar	2.27	4.97	6.68	9.58	10.25	10.10	10.26

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   The analysis was done using a co-irradiated 1.062 Ga biotite age standard yielding a ⁴⁰Ar^*/³⁹Ar-ratio of 27.64. Construct the ⁴⁰Ar/³⁹Ar age spectrum and use this to comment on the thermal history of the host rock. t_1∕2(⁴⁰Ar) = 1.248 Gyr.
   [Answer: 115, 243, 319, 442, 470, 463 and 470 Ma]

7. How many cm³ of helium does a rock weighing 1 kg and containing 2 ppm of uranium produce after 1 billion years? The molar volume of an ideal gas is 22.414 litres. Uranium has an atomic mass of 238.04 with ²³⁸U/²³⁵U = 137.818. Decay constants of U are given in Section 5. [Answer: 0.27 cm³]
8. Repeated analysis of the Fish Canyon zircon age standard (t=27.8 Ma) yields the following fission track data:

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   ρs	ρi	ρd
   (×105cm-2)	(×106cm-2)	(×105cm-2)
   36.56	6.282	2.829
   38.97	7.413	3.313
   56.53	7.878	2.457
   41.05	8.578	3.485
   45.87	6.985	2.482

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   Compute the average ζ-calibration factor and use this to calculate the zircon fission track ages of the following rocks:

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   	ρs	ρi	ρd
   	(×105cm-2)	(×106cm-2)	(×105cm-2)
   Tardree rhyolite	60.49	2.66	1.519
   Bishop tuff	6.248	1.299	0.081

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   The half-life of ²³⁸U is t_1∕2 = 4.47 Gyr.
   [Answer: Tardree – 57 Ma; Bishop – 643 ka]

9. The Dry Valleys of Antarctica represent one of the oldest landscapes in the world, with erosion rates as low as 2.5 cm/Myr. Cosmogenic ²¹Ne and ¹⁰Be accumulate in quartz at SLHL production rates of 20 at/g/yr and 4.5 at/g/yr, respectively. What is the expected ²¹Ne/¹⁰Be-ratio in these surface rocks? The rock density is 2.65 g/cm³ and the half-life of ¹⁰Be is 1.36 Myr. The attenuation length for cosmic ray neutrons is Λ=160 g/cm^-2. [Answer: 59.1]
10. A fossil mollusc has been found in a Quaternary beach formation and its activity ratio measured as A(²³⁰Th) / A(²³⁸U) = 0.6782. Determine the age of the fossil assuming that γ_∘ = 1.15 and given that the half lives of ²³⁰Th and ²³⁴U are 75,380 and 245,500 years, respectively. [Answer: 100kyr]