How to Build a Habitable Planet Summary Chapter 1 The Setting The universe as we know it began about 15 billion years ago with an explosion that is called the big bang. There is no record of any prior event. A paradox that existed before the big bang theory was how to explain the black night sky. If the universe was infinite, then light should be coming from everywhere and the sky should be quite bright. Two possible explanations: (1) Finite universe, so the black seen between stars represents the void beyond the universe. (But a finite universe would undergo gravitational collapse upon itself). (2) Clouds of nonluminous matter between the stars. (This should produce a dull glow like what is seen from approaching headlights through a fog.) In 1927 George Lemaitre proposed that the universe began with the explosion of a cosmic "egg". The outward momentum from the explosion would defeat the effects of gravitational collapse in a finite universe. In 1929 Edwin Hubble reported that a shift toward the red in the spectra of light from distant stars and galaxies suggested that the universe was expanding at a terrific rate. (The shift is actually in the positions of the characteristic dark absorption bands in the light from the stars.) The further away the light source, the greater the shift, meaning the faster the speed. The fastest objects are on the opposite side of the universe from Earth, and the slowest objects are near us. By assuming that the velocities are constant, then by estimating the distance to the different galaxies (based upon their brightness assuming they all have the same intrinsic brightness to begin with) we can determine the location of the big bang and when it occurred. Wilson and Penzias demonstrated that the background radiation of the universe is equivalent to a temperature of 2.76 K. This is roughly equal to the computed temperature of the universe assuming a big bang 15 billion years ago. We estimate the volume of the universe, and multiply that by the energy in 2.76 K, and this gives us the total energy of the universe, i.e. the energy of the big bang.
Recently, (summer of 2001) it has been shown that the universe is actually accelerating in its expansion. This experimental evidence is under close scrutiny and if it holds up to be true, then the whole picture of the universe will have to be modified. Remember that an acceleration can only be produced by a force, so what is the source of the force that is accelerating the expansion of the universe? Shortly after the big bang the universe consisted of only 2 elements, H and He with no electrons around them, it was too hot. 100,000 years after the big bang the temperature dropped enough to allow electrons to orbit around the nuclei and so H and He gases were formed. The gas clouds continued to rapidly expand, but space was not homogeneous. The clouds eventually began to break up into clusters which formed galaxies through gravitational collapse. These large clusters subsequently broke up into smaller ones that eventually formed stars. There were no planets, since only H and He existed. The formation of these clouds is related to electronic forces that came into existence once the electrons became bound to the nuclei. Chapter 2 The Raw Material: Synthesis of Elements in Stars The big bang only produced H and He, the first 26 elements were formed in the interior of stars. Some stars, called red giants, eventually explode to cast their debris throughout their neighborhoods in an event called a supernova, during which the rest of the elements are created. These events happen at a rate of about once per galaxy per century and so far they have converted ~1% of the primordial H and He into heavier elements. (This small amount is why we can use the average background temperature to estimate the total energy of the universe, we can compute a number that has only at most 1% error. Earth consists primarily of 4 elements, Fe, Mg, Si and O and it is a relatively new object. Stars form from the gravitational collapse of H and He clouds and therefore their composition must resemble the composition of the parent cloud. We assume that our sun is completely typical of the composition of the universe. The composition is determined by the positions and intensities of characteristic spectroscopic absorption lines. This composition is given in terms of the relative abundance of the elements using 1 million atoms of Si as the reference.
Note, the graph shows that H and He are the most abundant and that there is a general decline in abundance with atomic number. There are two large anomalies: (1) Fe is 1000 times more abundant and (2) Li, Be, and B are much less abundant than would be expected for a smooth declining curve. Furthermore, there is a saw-toothed appearance to the plot such that elements with an odd number of protons are less abundant than their neighbors with an even number of protons. These features provide the clues to determining the origin of the elements that are heavier than H and He. An understanding of the nucleus of an atom is necessary to understand the origin of the heavy elements. Each atom has a nucleus made of neutrons and protons. This nucleus is 10-13 cm in diameter and contains most of the atom's mass. To create heavy elements from H and He requires nuclear reactions in the form of fusion. The energy required to create a nuclear reaction is on the order of 50x10 6 K and the only natural furnace with this sort of temperature is in the interior of a star. Only certain combinations of neutrons and protons are stable, the largest is 209 Bi. All nuclei with more than 209 particles are radioactive. From the figure it is apparent that more neutrons are needed to stabilize a nucleus than protons, the neutrons act as the glue that holds the nucleus together.
All stable nuclides are found in nature, and thus all must have been produced from H and He in the interior of stars. The production of the heavier elements occurs in many steps. Carbon only requires two steps, Fe requires a few more, Bi requires quite a few steps, that is why the elemental abundance trend in the star decreases with atomic number. Some common ways to convert one element into another are: (1) Alpha decay: the emission of a He nucleus which consists of 2 protons + 2 neutrons. An example is 238 U 234 Th + 4 He. The He particle is called an alpha particle and a stream of alpha particles is called alpha radiation. (2) Beta decay: one nucleus changes into another of the same mass number but different proton number by neutron proton + electron + antineutrino or proton neutron + positron + neutrino with the electrons or positrons being emitted (they are called beta particles) and with streams of beta particles called beta radiation. An example is 14 14 6 C 7 N + e - + ν.
(3) Electron capture: where the nucleus captures an electron from an inner orbital and the electron then combines with a proton to form a neutron, emitting X-rays as the vacancy is filled by an outer shell electron. An example is 40 40 19 K 18 Ar. (4) Neutron capture: Because the neutron is neutral it can enter any nucleus, regardless of its speed. This reaction can occur at room temperature. The big bang event primarily produced neutrons which decayed, with a half-life of 12 minutes when outside of a nucleus, to protons and electrons. This means that 12 minutes after the event, half of the matter in the universe consisted of protons and half of neutrons. Due to the intense heat and density, there were plenty of nuclear collisions which produced He. A complicated series of 2 particle collisions created the He nucleus (starting with 4 protons and ending up with 2 of the original protons plus 2 neutrons that were formed by the other 2 protons combined with 2 electrons). Elements heavier than He were rare because they require at least 3 particles to simultaneously merge. This is a very improbable event, so rare that for all practical purposes only H and He existed. An example of a 3 particle event would be the production of 6 Li, needing 4 He + 2 protons. By the first day there was 24% He by mass, or 60 He/1000 H. Gravitational collapse of H and He clouds creates the stars because of the incredible heat associated with the collapse. This heat causes the nuclei to fly at each other with sufficient velocity to overcome the proton repulsion and to hit each other. Thus more He is formed from H. However, the mass of He is a little smaller than the mass of 4H. This difference in mass is converted to energy in the form of more heat. The outward pressure created by the escaping heat stabilizes the size of the collapsing star and it burns smoothly for a long time. For instance our sun is 4.6 billion years old and will burn for several billion more years. The stars are continuing the process of conversion of H to He that was started during the big bang. If the star is quite large, then the supply of H is used up in about 1 million years. Gravitational collapse then starts again, causing the core temperature to rise. Eventually the ignition temperature of He is reached (higher temperature because of 2-proton repulsion per atom needs to be overcome) The collisions of 3 4 He form 12 C. There is a little mass lost
in this collision that is converted to heat so the size again stabilizes. Four 4 He can also combine to form one 16 O. This process continues, and when He is used up the star collapses again till C starts to burn to form Mg, and so on. During each collision heat is produced to stabilize the star, until Fe is created. Elements that have more mass then Fe are larger than the collective masses of the atoms that formed them, so additional energy is actually required to form elements heavier than Fe. Thus no elements heavier than Fe are formed by the methodical aging of a star. The structure of such a star can be pictured like an onion with different layers burning different elements, the hottest towards the center. Fuel Products Temperature H He 60 x 10 6 K He C, O 200 x 10 6 K C O, Ne, Na, Mg 800 x 10 6 K Ne O, Mg 1500 x 10 6 K O Mg to S 2000 x 10 6 K Mg to S elements near Fe 3000 x 10 6 K For stars that are not so massive, like our sun, there is only sufficient mass to generate temperatures high enough for He to burn. In this case after the He has burned the star will collapse into a very dense object that will slowly cool until it gives off only a dull glow. Once this has happened, the star is called a white dwarf. Once a massive star has consumed all of its core's nuclear fuel (and the last fuel is Fe) then it undergoes one final collapse. This collapse becomes an implosion, called a supernova, which tears the star into pieces that scatter though space. During the implosion a series of nuclear reactions occur that produce neutrons. The interior of the star is so dense that neutron capture occurs before neutron decay. Since Fe is so prevalent, many Fe atoms become heavier till the nucleus cannot take any more neutrons. This is followed by beta decay during which a neutron becomes a proton + electron (the electron is immediately emitted) and Fe turns to Co. Co absorbs neutrons till it is saturated and then it decays to Ni. This sequence occurs over and over again with all possible nuclei being formed (even past Bi). The creation of all these heavy elements is very fast, it occurs during the explosion of the star. As soon as the neutron source is depleted the nuclei can start to decay, emitting electrons as the neutrons turn to protons until a stable neutron-to-proton ratio is achieved. Elements
heavier than Bi emit alpha particles, as well as electrons, as they turn into Pb isotopes. This decay is called the r-process because it is so rapid. For elements with several isotopes the r-process only makes the one with the most neutrons. There is also another process that makes heavy elements out of lighter ones, called the s-process because it is slower. During regular nuclear burn the star releases neutrons. These are not released as frequently as during the r-process, and so the nuclei that are struck have time to undergo radiodecay. The last method for producing heavy elements is due to impacts with protons that are released during regular stellar burning. This creates isotopes that are several orders of magnitude less abundant then those created by the r- and s-processes. Evidence supporting this theory for the synthesis of elements heavier than He are: 1. The only conceivable source of energy to keep stars burning is nuclear. 2. Explosions of large stars has been observed. 3. The element technetium (Tc) is not present in the earth, nor is its spectra observed in the sun (because it has no stable isotopes), but its spectrum is observed in the remnants of supernovae explosions. Tc has two isotopes, 97 Tc (2.6 x 10 6 years) and 98 Tc (4.2 x 10 6 years). Therefor it can exist for millions of years after a supernova explosion, but it would not be on earth since it is 4.5 x 10 9 years old. 4. Calculations of theoretical relative abundances of various nuclides produced by red giants match what is observed. For instance, the abundance of Fe, and the scarcity of B, Be and Li, and the prominence of nuclides with mass numbers divisible by 4 (He, C, O, Mg, Si and Fe) because of being direct aggregates of 4 He. Another property of nuclei that affects their abundance is called the neutron-capture cross section. This property is a measure of the size of the nucleus as it appears to incoming neutrons. Nuclei with small cross sections are not hit as often as nuclei with larger cross sections. This property is a function of the number of neutrons in the nucleus, so the nucleus has a different cross section before a hit then after a hit. Elements with an even number of protons are more abundant than elements with an odd number. Here is the reason for this. When an element undergoes radioactive decay it releases energy and thus loses some mass. This means that of those elements with the same number of
nuclear particles (protons + neutrons), also called an isobar, it is the ones with the lowest mass that are the most stable. There is a hierarchy of masses that depend upon whether the particle numbers are even or odd. An odd number of protons + an odd number of neutrons is most massive, and odd-even combination is less so, and an even-even combination is least massive and so most stable. Therefore, an element with an even numbers of protons is guaranteed to be less massive than an element with an odd number, and therefore more stable and so more abundant. Furthermore, elements with an even number of protons have several isotopes, while those with an odd number of protons generally only have one isotope. Chart of the nuclides
Odd-even particle number systematics