Notes for Lecture 4

Lecture 5, February 17; Christopher Chyba

The aim of the lecture is to determine how we date the events and the age of the Earth, Universe and life. It all has to do with radiation from atoms. Review of atomic structure from Lecture 4. Electromagnetic force is, like gravity, also 1/r^2. Consider two electrically charged objects, charges q_1 and q_2, separated by a distance r. The force between them is: F = k q_1 q_2/r^2. (The constant k ~ 10^10 Newton meter^2/coulomb^2). Notice charges come in positive and negative, so the force can be attractive or repulsive. The force of gravity is *much* weaker than that of electromagnetism. Consider the protons in an atomic nucleus: could their mutual gravity hold them together? (after all, the electrostatic force between them is pushing them apart). You can work it out: working out the ratio of the gravitational and the electrostatic force gives: Gm_p^2/kq^2 (notice r drops out!) where m_p is the mass of the proton, and q is the charge of a proton. Plugging in numbers gets the astonishingly small value of 10^{-39}. So gravity is 10^{39} times weaker than electromagnetism. The so-called "strong force" is the glue that holds the nucleus together. It is strong only on the scales of nuclei; it is negligible for two protons separated by a distance much larger than the a typical atomic nucleus. There is also a weak force, that drives the radioactive decay. There are thus 4 forces. The thrust in modern physics is to unify these forces, this may or may not succeed! Even though gravity is so weak, the dynamics of the universe is dominated by gravity; this is because in most cases, the material of the universe is electrically neutral, and has no net charge. A brief overview of the periodic table. The number of electrons in an atom determines its chemistry. The basic structure of atoms, with their nuclei and surrounding electrons, was described. A nucleus has both protons and neutrons. The type of the atom depends on the number of protons (which, for neutral atoms, is the same as the number of electrons); different *isotopes* of a given element will have different numbers of neutrons, but the same number of protons. An atom is almost entirely empty space. A proton has a radius of about 10^{-15} meters, while the electrons are whizzing around at a distance of 10^{-10} meters, i.e., 100,000 times further away. Experiments by Rutherford at Cambridge demonstrated this, by shooting alpha particles (the nuclei of helium atoms, emitted by a radioactive substance) at a thin foil of gold. The vast majority of the alpha particles go right through, but a small number will bounce back, because they hit something very hard, namely the nucleus. As far as we know, an electron has no intrinsic size; they represent a true mathematical point. Something unfamiliar to our everyday experience! So do the electrons also orbit in ellipses, just as we saw with planets? No. There is a real problem: an accelerated electron gives off energy in the form of light. So it loses energy, and will have no choice but to spiral into the nucleus (in a fraction of a second), destroying the atom. So how do atoms exist? The solution to this dilemma lay in the development of quantum mechanics. On the very small scales of atoms, nature works in very unfamiliar ways. "Radiation": any sort of emitted energy (in the form of waves or particles). For example, electromagnetic radiation (light), emission of charged particles by atomic nuclei. Radioactive decay refers to transformation of atomic nuclei from one type to another, usually with the release of energy (in the form of electromagnetic radiation, for example). Indeed, the fact that the interior of the Earth is extremely hot is largely due to the radioactive decay of various elements, and the interior would remain hot even if the Sun were to go out tomorrow. Radioactive heating drives plate techtonics and contributes to climate control on the Earth. Two isotopes of uranium: U238 (weakly radioactive) and U235 (unstable). Most Uranium is 238 and can't be used for bombs. Isotope separation is needed, and cannot be done chemically -- need power-intensive centrifuges. The mix of isotopes in a given substance often gives important clues about where the object came from. For example, you can look at the Deuterium/Hydrogen ratio in the water of the oceans, and compare that with ice in comets. They turn out not to be the same, at least suggesting that not all the water on Earth came from comet impacts. (Normal hydrogen has a single proton in the nucleus, while deuterium has a proton and a neutron in the nucleus). We can also use isotopes for radioactive dating. Consider Carbon; its most common isotope is Carbon-12 (6 protons, 6 neutrons), but there is also Carbon-13 (with 7 neutrons). Turns out life has a very slight preference to use Carbon-12 in its reactions. So the C13/C12 ratio in living objects is somewhat smaller than in non-organic objects. This has been used to determine whether some truly ancient rocks had carbon that was once incorporated into living objects. There is also Carbon-14 (8 neutrons). It is not stable: it decays with a half-life of 5700 years (i.e., after that time, half of the Carbon-14 will decay to some other element). So if you knew how much C14 you had initially in some object, and could measure how much you had in hand now, you can determine the age of the object. Carbon 14 (8 neutrons) decays with a half-life of 5,700 years. It is rare, making up about 1 atom in 10^12 carbon atoms in the atmosphere. I.e., after that time, half the carbon 14 in any given sample will decay. So where does the carbon 14 come from? It is produced by cosmic rays (highly energetic particles streaming through the galaxy) hitting the atmosphere, and producing (among other things) neutrons. Occasionally, the neutron will combine with Nitrogen 14 (very common in the atmosphere), giving off a proton, and leaving behind Carbon 14 (this balances the total charge, and total number of protons+neutrons). The carbon 14 decays via a process called beta decay, releasing an electron, and leaving behind Nitrogen 14 again. 7^N_14+n->p+6^C_14; Carbon 14 decays by beta-decay: n -> p + e- + nu^bar Decays of nuclei in which an electron is emitted is called 'beta decays' (an old name for electrons was beta rays). What is happening here is that one of the neutrons is decaying to a proton and an electron (and also something called a neutrino). Decays of nuclei in which a helium nucleus is emitted (two protons and two neutrons) is called an "alpha decay", as helium nuclei are also known as 'alpha particles'. Uranium 238 decays to Thorium 234, releasing an alpha particle (i.e., a Helium 4 nucleus). This process is very slow, with a half-life of ~4.5 billion years. Roughly 1 carbon atom in 10^{12} is carbon 14. This carbon 14 gets absorbed by living objects (e.g., plants take in carbon dioxide). Thus while the plant is alive, it has the full complement of Carbon 14, but after it dies, it doesn't take in more carbon 14, and the C14 decays, so you can use the ratio of the carbon 14 to the normal carbon in the plant as a measure the time since the plant died. Of course, if you are looking at a *really* old plant, all the C14 will decay away, and you can't measure it... To date really old things, we need a radioactive element with a substantially longer half-life. For dating we need to know the initial amount of radioactive material, and the rate of decay (half-life). For example, let's use Potassium and Argon. Potassium 40 (element 19) decays by positron emission into Argon 40 (element 18), with a half-life of 1.3 billion years. Argon is a noble gas, i.e., one which doesn't form molecules (and is a gas). Consider a lava flow (say from the early Moon). When the rock is liquid, the argon bubbles out. Once the rock solidifies, the argon is stuck inside. So the relative amounts of potassium and argon is a measure of the time that the rock solidified. At the beginning, there is no argon at all; it would have all evaporated out. In a simplified version of a more complicated radioactive decay scheme, after one half life, half the potassium has become argon, and the potassium/argon ratio is 1. After 2 half lives, you get a ratio of 1/3, and so on. So measuring the ratio tells you how old the rock is (i.e., the time since the rock solidified). This technique is used throughout geology and planetary science. Craters on the Moon have been filled in with (now solid) lava. We've brought some of these rocks back. We can also count the craters on the site from which a given rock came; the older the rock, the larger the number of craters. From studies of the relationship between number of craters and ages on the Moon, we infer that there was a period of *very* heavy bombardment early in the history of the solar system (~4 billion years ago). Most of the Moon's surface is very old, > 3.5 billion years old. This is because it is geologically dead; it cooled off much faster than did the Earth. Earth's surface is much younger, the vast majority is < 2.5 billion years old. This is because Earth has active geology, in particular lava flows and plate tectonics, and also has weather to erode things. The oldest fossils known on the Earth (albeit somewhat controversial) in the rare 3.5 billion year old rocks, are of single-celled cyanobacteria roughly 3.5 billion years old. You can also find fossil stromatolites from that epoch, which are layered colonies of bacteria. Stromatolites are rare today, as they are vulnerable to grazing creatures such as sea snails, and are only found in extremely salty environments, where these various grazing creatures can't survive. Interestingly, for most of the history of like on Earth (3.5 billion years to ~700 millions ago), life was only single-celled. The biggest craters on the Moon were caused by asteroids of diameter ~100 km, during the period of Heavy Bombardment. The Earth is a bigger target than is the Moon, so it must have received 20 times more impacts than did the Moon. The heavy bombardment period in the Solar System ended about 4 billion years ago. The earliest life we know of dates very soon thereafter. So life seems to have gotten started almost as soon as it possibly could have. The Earth was impact sterilized several times during the late bombardment. Notes for Lecture 6