L8GH09Small_SS_Bodies_II_Meteorites_and_

L8GH09Small_SS_Bodies_II_Meteorites_and_ - Small SS Bodies...

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January 29, 2009 asteroids Small SS Bodies II: Meteorites and Asteroids • Lecture topics: ¾ meteorites: ages, origins ¾ asteroids: shapes, rotation and composition, heating and cooling • Text readings: Chapter 7: esp. pp. 162-177
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January 29, 2009 asteroids Radioactive decay age measurement • Many elements have several isotopic forms, some of which are unstable and decay into other elements. • Radioactive decay obeys a simple law: the probability that a given isotope will decay into its “daughter” isotope is constant, independent of time and the original number of atoms. • Mathematically: dn/dt = - λ nwhere λ is the decay constant (units=#/sec). ¾ Integrating this from t=0 to t=t gives a classical exponential relation: n(t) = n(0)e - λ t . ¾ In a given sample we can measure n(t) and we know λ for a given decay process; if we can somehow determine n(0) we can find t.
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January 29, 2009 asteroids Radioactive decay age measurement •Consider two isotopes r (the radiogenic/unstable) and s (the stable decay product). •Initially (t=0) the sample will start with some atoms of the unstable isotope, r 0 , and some of the stable, s 0 . When we measure the sample at some later time (t) it contains 9 fewer atoms of the unstable isotope: 9 and more of the stable : t e r t r λ = 0 ) ( [ ] 1 ) ( ) ( 0 + = t e t r s t s
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January 29, 2009 asteroids Radioactive decay age measurement •If ±we ±measure ± s and r for different pieces of a given meteorite , we could make a plot which has (hopefully) a linear slope given by e λ t -1 ¾ However, we cannot be sure that r 0 and s 0 were the same throughout the sample. ¾ So compare the abundances to a stable isotope of the daughter (s), call it s . [] 1 ) ( ) ( ) ( 0 0 + = = t t e t r s t s e r t r λ 1 ) ( ) ( ) ( ) ( ) ( 0 + = t e t s t r t s s t s t s
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January 29, 2009 asteroids Rubidium-Strontium System •One common method uses isotopes of Rubidium and Strontium 87 Rb is a radioactive element that decays into 87 Sr with a half-life of 48.8 Gyr ¾ at t=t o , A,B,C have identical ratios of 87 Rb/ 86 Sr ¾ measure present abundances (A’,B’,C’ ) relative to the stable isotope 86 Sr ¾ slope = e λ t -1 => age [ ] 1 ) ( ) ( ) ( ) ( ) ( 0 + = t e t s t r t s s t s t s λ t=t o slope intercept
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January 29, 2009 asteroids Example 1993 observations of chondrules in the Allende meteorite, which fell as a 2 ton fireball in Mexico, 1969. > How can we estimate the age of the chondrules from these data?
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L8GH09Small_SS_Bodies_II_Meteorites_and_ - Small SS Bodies...

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