1 Lecture #02 - Earth History. 2 The Fine Structure of The Universe : The Elements Elements are a basic building block of molecules, and only 92 natural.

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1 Lecture #02 - Earth History

2 The Fine Structure of The Universe : The Elements Elements are a basic building block of molecules, and only 92 natural elements exist (109 total elements have been identified). The basic elements (H and He) were created during the Big Bang, while the heavier elements are created by stellar processes. The particular abundance of elements is yet another observation that can be used to test the Big-Bang hypothesis (it also passes this test).

3 Atoms & Atomic Numbers The fundamental unit of an element is an atom, which can be thought of as a nucleus of protons and neutrons, surrounded by electrons. The number of protons in the nucleus determines the type (name) of the element.

4 Isotopes If you add neutrons to a nucleus, you still have the same element, since the proton number is unchanged. To distinguish elements with different numbers of neutrons, we call them isotopes.

5 Radioactive Decay It turns out that some elements will spontaneously turn into other elements. This is called radioactivity and was discovered in 1896 by Henri Becquerel.

6 Radioactivity (Ex. 1) 238 U (an isotope of uranium) decays into 206 Pb (a lead isotope) and 4 He (a helium isotope): 238 U  206 Pb + 8 4 He This happens spontaneously over time. Note that mass is conserved.

7 Radioactivity (Ex. 1, cont.) The half-life of 238 U is about 4.5 billion years If we initially have 128 g of pure 238 U, after 4.5 billion years we will have 64 g of 206 Pb and 64 g of 238 U How much 238 U will there be after 18 billion years? How much 206 Pb?

8 Radioactivity (Ex. 2) Can we invert this process? Can we work backwards? Yes. In other words, if we are given 1) The amount of 238 U 2) The amount of 206 Pb 3) The half-life of the reaction Then, we can deduce the amount of time it took to get to this point. Then, we can deduce the amount of time it took to get to this point.

9 Radioactivity (Ex. 2, cont.) First we quantify the problem: N=N o e - t where, where, N = the present-day number (mass) of 238 U N o = the original number (mass) of 238 U  = the decay constant  = the decay constant t = time t = time

10 Radioactivity (Ex. 2, cont.) Step one is to determine Step one is to determine After one half-life there is half as many atoms of 238 U as there were originally In math, N=0.5N 0 when t=4.5 billion years, or: 0.5 = e - 4.5 Thus is 0.154 (in units of inverse billion years)

11 Radioactivity (Ex. 2, cont.) Thus, N=N o e -  t or, or, N/N o = e -0.154t or, or, ln(N/N o ) = -0.154 t ln(N/N o ) = -0.154 t or, or, t=ln(N/N o )/-0.154

12 Radioactivity (Ex. 2, cont.) So, N is the number of 238 U we observe in a rock N o is the original number of 238 U. We assume this to be the number of 238 U plus the number of 206 Pb (since the number of atoms is conserved over time) We plug these two observations into the previous equation and get the age (t) of the sample.

13 Radioactivity (Ex. 2, cont.) If we have a rock sample that has 8 atoms of 238 U and 120 atoms of 206 Pb, how old is it? t = ln(8/(128))/-0.154 t = ln(8/(128))/-0.154 t = ln(0.0625)/-0.154 t = ln(0.0625)/-0.154 t = 18 billion years old t = 18 billion years old

14 Radioactivity (Ex. 3) One of the most common radioactive elements used for dating is 14 C It decays into nitrogen by releasing an electron (referred to as a  particle): 14 C  14 N + 

15 Radioactivity (Ex. 3, cont.) The half-life for 14 C decay is only 30,000 years; thus it is useful for dating young objects. What is the decay constant,, for this reaction? N=N o e - t By definition of half-life, N=0.5N o when t=30,000 years, thus 0.5=e -30,000  or =2.3x10 -5 (yr -1 )

16 Radioactivity (Ex. 3, cont.) So, plugging back in to the original equation we have: 14 C today = 14 C original e -(2.3x10 -5 )t Solving this equation for t (time) we get, t = -43,280 x ln( 14 C today / 14 C original )

17 Radioactivity (Ex. 3, cont.) So, if we find a sample that has 90 14 C atoms and 10 14 N atoms, how old is it? t = -43,280 x ln(90/100) t = -43,280 x ln(90/100) t = -43,280 x (-0.1054) t = -43,280 x (-0.1054) t = 4,560 years t = 4,560 years

18 Age of the Earth (simplified) (1) Assume radioactive decay rates have been constant throughout time (there is actually good evidence for this). (2) For example the half-life of Uranium 238 is about 4.5 billion years. (3) Measure the ratio of Uranium 238 to its daughter product Lead (206) in a piece of rock (or even better a meteorite)

19 Age of the Earth (simplified) Use the observed ratio and the observed half-life to work backwards and get the time when there was only Uranium 238. Assume this time represents the formation of the rock. –Why? –Is this always true?

20 Earth Formation The definition of Earth formation is the delivery of 99% of the mass We need this definition because technically the Earth is still growing (accreting) by the influx of meteors and cosmic dust. It took the Earth a few tens of millions of years to form.

21 Earth Formation The Earth formed in two basic steps: –First was the condensation of a large number of moon-sized bodies from the dust of the solar nebula. This process occurred relatively quickly, probably over the time span of a few hundred thousand years. –Second was repeated collisions/impacts of these moon-sized planetary embryos. This process was much slower and took tens of millions of years.

22 Earth Formation One of the these collisions between the proto-Earth and a planetary embryo caused a large chunk of the proto-Earth to fly off from the main body. This material stayed in orbit around the Earth however, and accreted into the moon.

23 Earth Formation One of the these collisions between the proto-Earth and a planetary embryo caused a large chunk of the proto-Earth to fly off from the main body. This material stayed in orbit around the Earth however, and accreted into the moon.

24 Earth Formation

25 Earth Formation So: – Did the Earth’s iron core accrete first from a series of iron planetary embryos and then the mantle accrete next from a series of silicate planetary embryos? Or: –Did Earth accrete from planetary embryos consisting of both iron and silicate and then segregate into the present-day structure ?

26 Earth Formation The answer is the second case, which is known as homogeneous accretion The differentiation of the Earth into a metallic core surrounded by a silicate mantle probably occurred over a time space of 10-30 millions years.

27 Earth Formation The core formed because the Earth was extremely hot when it was accreting, especially after big impacts from planetary embryos. The heat caused a large portion of the Earth to become a magma ocean, out of which the core material (metals) sank because they were heavier than the surrounding silicate lava.

28 Earth Formation This process of differentiation between metals and silicates is common in planetary bodies from the inner solar system: Mercury, Venus, Earth, Mars (probably), Moon (possibly). We even have samples of meteorites that show asteroids have differentiated as well.

29 Earth’s Composition Ninety-eight percent of the continents are composed of eight elements. Seven elements (iron, silicon, magnesium, oxygen, sulfur, aluminum, and calcium) account for 97% of the entire planet.

30 Earth Dynamics

31 Summary of Earth Formation Earth has been formed by processes that we can now observe in other parts of the Universe. Our home is about 4.55 billions years old, and our Sun is a typical star, with an expected lifetime of about 10 billion years. Our system condensed from a second- or third- generation star, with some elements from at least one supernova. Earth is a dynamic planet with a hot, convecting interior. That convection is the driving force for the “tectonic” activity we see on the surface.

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