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Chapter 4

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CHEM 222
Karine Auclair

4. The Condensation of our Sun and the Accretion of the Planets - The Big Bang created H, He, Li, Be, and little else - All the more massive nuclei were created in the nuclear fire of stars - From the dust of this nucleosynthesis, the elements of our Earth were formed and from these our Earth and Sun and planets condensed. 3.1 The Condensation of the Solar System - About 5 billion years ago (8 billion years after Big Bang), at some gravitational centre, material from the clouds of dust and gas left behind by supernoval explosions began to assemble the mass of our Solar System - All elements known to exist in our solar system, except Promethium (Pm) pre- existed in this condensed cloud • Half-life of Pm = 30 years. • All of the Pm would have been quickly lost to the cloud, and the now cool cloud wasn’t hot enough to produce its replacement. 1) Material from the clouds of dust and gas began to assemble 2) A great mass of gas (largely H and He) at the centre of this condensing cloud began to form a proto-sun 3) About the proto-sun, local centres of condensation formed orbits and concentrated the planets • These pro-planets were brought into orbit by angular momentum • As gravitational condensation increased and more material was attracted in, the angular momentum accelerated (just as a figure skater pulls in arms to spin faster) 4) Conserving angular momentum, the infalling dust and gas starts revolving faster • Angular Momentum ( ) is a conserved quantity of physics - We can’t account for the exact distribution of the planets about the Sun, but any condensation would have caused the planets to revolve around the gravitational central Sun in the same direction - Exceptions: Venus, Uranus, and Pluto, which all rotate about their own axis (one that is contrary to that of the Sun) Bode’s Law and the Titius-Bode Relationship - There seems to be some “order” to the distribution of planets Bode’s Law r = a + b 2k k Where k = planetary number counting from the sun a and b = parameters which best fit the planetary distribution from the Sun Titius-Bode Relationship k-1 rk= r o p Where r = 0.4AU = 6 x 10 km (the orbital distance of o Mercury from the Sun) p = 1.73 (best average fit through the whole planetary system when we count the belt of asteroids b/w Mars and Jupiter) 4.1.1 Gravitational Energy Retained as Heat in a Condensing Planet or the Sun - Von Helmholtz recognized that the gravitational energy contained within the Sun could account for its shining for between 20-40 million years - How do we estimate this energy? 1) Start from an extended, “absolutely” cold (0K) cloud 2) Somewhere a small mass M of radiuscr assembles (perhaps under electrostatic or magnetic forces) 3) Volume of centre (sphere) = (4/3)(r ) 3 4) Mass = pV, where p= density 5) Suppose that at some great distance R starta small element of mass, dm, is waiting to fall in upon this gravitating centre 6) Now, if our small element of mass were to fall in towards our condensation centre, it would accelerate, gaining velocity and kinetic energy of motion equal to its continuing loss of potential energy 7) Eventually it would – perhaps moving very fast – hit our central mass centre and release all of its kinetic energy in heat. 8) M iccreases slightly in volume 2 2 4 9) The energy contributed by the infalling dm is dE= G(16/3)(p  r ), where G is the universal Cavendish gravitational constant - Layer by layer, the Earth forms. - It becomes hotter and hotter as more gravitational energy is converted to heat. - There is a lot of energy largely contained as heat. 4.1.2 Internal Temperature of a Condensing Planet - The temperature of a material that is containing energy in the form of heat depends on its heat capacity - Water is one of the most efficient materials for holding heat • 1000 calories heats 1L of water 1C • Heat capacity = 1000cal/L/K • 1 calorie = 4.180 Joules of energy - The heat capacity of rocks and metals is quite a lot less than that of water • Rocks ~ 1000 J/kg/K - If the Earth had retained all the gravitational energy at condensation, its temperature would have started at 37000C - We now think that the interior of the proto-Earth was quite cool – at 37000C, all Earth materials would have vapourized, and all atoms and molecules dissociated into plasma. - We know that the Earth must have condensed quite cool. - It seems that more than 95% of the gravitational energy of condensation was re-radiated into space. • We have good evidence that Earth condensed cool and subsequently heated up. 4.2 The Accretion and Differentiation of Earth - The terrestrial planets condensed into orbits around the proto-sun about 4.54 billion years ago. - Most of the H and He from that primordial cloud condensed into the central Sun whose nuclear fires started to burn in its core. - Many lighter elements (H,He) and the elements which do not easily chemically combine (He, Ne) were not easily contained by the gravitational field of the condensing Terrestrial Planets, but were easily held by the enormous Sun. - The Terrestrial Planets (Mercury to Mars, then the asteroids) held the heavier elements that formed them as rocky-metallic bodies. - Beyond the Terrestrial Planets and the asteroids, the environment was much cooler in the early solar system • Lighter elements such as H and He, as well as H 0 were avai2able to condense into the formation of gas giants (Jupiter, Saturn, Uranus, Neptune) - Uranus and Neptune – water giants - Pluto – largely water-ice - Beyond Pluto – Kuiper Belt, then Oort Cloud • Oort Cloud – a spherical cloud of comet-like bodies – snowballs of water, ice, and original cosmic dust. - Hydrogen is the most abundant element in the solar system • Then He, O, Ne, N, C, Si, Mg…Fl Implications of Elemental Abundance - Almost all of the elements listed are produced in the nucleosynthetic fusion processes - Nickel and Cobalt (elements with nuclei more massive than Iron) are also quite abundant • Along with Iron, these are some of the most stable of all nuclei - Ni and Co are among the first elements to be produced in the r-process of neutron capture in supernoval explosions - The elements with massive nuclei – only produced by supernovae. Earth contains by mass… - 35% Fe - 30% O - 15% Si - 13% Mg - Combined in this ratio, these elements form the mineral olivine ([Mg,Fe]SiO 4 4.2.1 The Accretion (Growth) of a Terrestrial Planet – Earth - Birth of Earth – 4.54 billion years ago • Material attracted to a gravitational centre in orbit about the proto-Sun - Late in the formation (condensation) of Earth, one last large object (size of Mars?) crashed into proto-Earth • This happened before 4.44 billion years ago years ago • This catapulted up an enormous volume of material which began to orbit Earth – MOON! - Oldest zircons = 4.4 billion years old - Oldest rocks on moon – 4.44 billion years old The Earth at the Time… - Differentiation – Denser elements/materials sink to the centre and lighter ones rise to the surface - The moon contains much less Fe than Earth • But, the surface rocks on the moon contain more Fe than the surface rocks on Earth - Oldest rocks on the Moon are older than the oldest minerals and rocks on Earth (40 million years older than minerals, 400 million years for rocks) • The Moon solidified quickly after collision • The surface of the Earth remained largely molten for another 200+ million years. - The greater amount of iron in lunar rocks tells us something about the degree of differentiation of Earth that had already happened by the time of the collision Cold (Slow) Accretion Model - Cold Accretion Model (Hanks and Andersen) • The original temperature of proto-Earth never exceeded 2000C anywhere • Temperature of Earth’s core now = 6000C - The Cold Accretion Model suggests that the Earth was originally homogenous - Over time, the Earth began to differentiate and heat up How has the Earth heated up since its initial formation? 1) Heat from Gravitational Compression - Growing weight of matter to surface caused compression of the interior, which raises the temperature 2) The Big Whack - The collision that splashed the moon into orbit - The earth heated up as a result of this collsion 3) Radioactive Decay 26 26 + - Al decays into Mg by emitting a  particle - Aluminum is very abundant on Earth - Enough of 26Al condensed into Earth to produce sufficient heat to start the physical differentiation - Other isotopes (isotopes with short half-lives) of the lighter elements must have also condensed with the cloud and contributed to a rather rapid heating of the Earth • If the cloud had been formed in a supernoval explosion, it is very likely that there were many short-lived isotopes - Radionuclei now contribute significantly to the internal heating of Earth - The early heat has not yet been entirely radiated away from the Earth’s surface – the high internal temperature of the planet still partially derives from early radioactive heating. - Now, internal heating derives from the continuing geochemical differentiation and from the release of the latent heat of fusion of iron as the Earth’s core slowly freezes - 4K alloys with iron at
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