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ASTR 209
Ian Lovatt

Page 1 of 7 Astr 209 Lecture 3c October 2 2010 Details about the fusion of hydrogen in the Sun The 4 H → He has three stages. The nucleus of a hydrogen atom is also called a proton (p). + + + + p + p → pn ( ) + e +ν (2 of these) (1) (pn + + p → ppn )++ +γ (2 of these) (2) ++ ++ ++ + + (ppn ) + ppn ) → ppnn ) + p + p (3) Equation (1) requires considerable description (a, b, c, and d below). a) the protons The two hydrogen nuclei have a property called electrical charge. You can at least become aware of the effects of this property by playing with long strips of adhesive tape. i) Stick one long strip to the top of a table. Stick another strip on top of the first. Rip the bottom piece off the table, so that the two strips of tape are still stuck together. Pull the two strips apart, and hold them far apart. Now bring them closer together; they are attracted to each other. This is the same behavior exhibited by clothes that you take out of a dryer when you have forgotten to use a sheet of Fleecy. Notice also that, if you are taking the laundry out of the dryer in the dark, when you pull the socks off your shirt you see sparks and hear crackling. Light and sound involve the transfer of energy. ii) Stick a fresh piece of tape to a table-top. Stick another piece to a different part of the table-top. Pull both strips off the table, and hold them apart. When you bring the strips close to each other, they repel each other. These two strips are analogous to the two protons in step (1) above. MANY observations like (i) and (ii) have convinced us that there are two (and only two) types of electrical charge. In case (i), you have done something different to the two strips, so they have different properties Page 2 of 7 (different types of charge). It turns out that when two objects carry different types of charge, they attract each other. In case (ii), you have done the same thing to the strips, so they have the same property (same type of electric charge). It turns out that two objects with the same type of electrical charge repel each other. (What sort of observation might you expect if there are more than two type of charge? This isn’t an idle question. It turns out that the constituents of protons and neutrons [called QUARKS] have a property analogous to electric charge. We call this property “color” - American spelling for an American idea. “Color” is just the name of a property; it has nothing to do with the everyday meaning of colour. A quark can have one of two types of electric charge (positive, negative); a quark can have one of three colors (call them red blue, and green if you like). The quark-quark interactions are considerably more complicated than proton- proton interactions.) One source of electrons is a hot wire, like a toaster filament. (J. J. Thomson in 1897 actually discovered electrons by studying what is somehow emitted by hot wires.) In the late 1800s and very early 1900s we learned that electrons are natural “parts” of matter. It turns out that electrons all carry the same amount of one type of charge (called negative). When electrons are emitted by (expelled from) matter, what remains carries the other type of charge (called positive). We have found that this division of charge applies to individual atoms. (The smallest amount of an element is an atom.) A hydrogen atom is the simplest atom; it is composed of one negative electron and one positive proton. (J.J. Thomson in 1906 discovered that a hydrogen atom has only one electron.) If you can figure out how to strip electrons from matter, you have removed electrons from individual atoms. In the case of hydrogen, each atom has become a proton. Two protons carry the same type of charge, so they repel each other. To get them close to each other, you must somehow make the protons travel very rapidly towards each other; as the inter-proton distance decreases, the speed decreases. This is another example of POTENTIAL energy increasing, and KINETIC energy decreasing. (In this case ELECTRICAL potential energy increases as two similarly-charged protons get closer to each other. Recall that you must push two similarly- charged strips of tape together.) It turns out that the temperature of something tells you about the average speed of that thing’s atoms and molecules. For instance, the speed of sound is higher on a hot day than on a cold day. The sound energy is conveyed from one molecule (oxygen, nitrogen) to the next in a collision. That means that the speed of sound is determined by the speeds of the molecules. Page 3 of 7 Another example. On a hot day, your molecules are vibrating back and forth, in place, a little faster than on a cold day. If protons must be travelling very fast to fuse, the temperature at the core of the Sun must be very high. It turns out that the temperature must be at least 10 million kelvins (10 K). Fusion therefore can only happen in the core of the Sun. Why does the core have a high temperature? The outer layers of the Sun push on the inner layers, so that 11e pressure in the core is very high. We calculate a pressure of about 10 time the pressure of Earth’s atmosphere. Using more-or-less the IDEAL GAS LAW that describes familiar gases on Earth, we calculate that the temperature in the core is about 15 million K. This is more than the minimum required for proton-proton fusion. (This doesn’t prove that fusion happens, just that the right conditions are present in the core.) When two protons get “close enough”, they are actually attracted to each other, and stick together. In the process, one of the protons turns into a + neutron (n), a positron ( e ) and a neutrino (v; the symbol is the Greek letter “nu”, the equivalent of our letter “n”). The protons sticking together is an example of what has come to be called the strong nuclear force: “strong” because the attractive force is stronger than the repulsive electric force, and “nuclear” because this force is only important when distances are as small as a nucleus (about 10 -15m, almost 1 millionth the size of an atom, so we don’t need to understand nuclear forces to understand atoms). The transformation of a proton into a neutron, a positron, and a neutrino is an example of the weak nuclear force. “Weak” in this case means the reactions are slow compared with reactions involving the strong nuclear force. b) the neutron (a vague description): It is “like” the proton, but with a mass 0.1% larger than the proton’s mass. It has no charge The bound state of a proton and a neutron is called a deuteron, a type of (an ISOTOPE of) hydrogen. The Greek word “deuteros” means “second, as in Deuteronomy, the second book of the bible; deuterium is the second- heaviest nucleus. c) the positron: Page 4 of 7 It is identical to the electron (e ), except that it has the SAME type of charge as the proton (which we call positive). It is an example of anti- matter. When a positron collides with one of the electrons in the Sun, the electron and positron disappear, and two particle of light are produced. We call particles of light” PHOTONS, and use the symbol γ , the Greek letter “gamma”. e + e →γ +γ The energy associated with these photons (and the photons from reaction (2) above) is absorbed, emitted, and scattered MANY times between the core and the Sun’s photosphere. This energy takes approximately a million years to get out of the Sun. If the nuclear reactions were to stop today, energy would continue to filter out of the Sun, and we wouldn’t know anything was wrong for several hundreds of thousands of years. The conversion of the positron and the electron into 2 photons reminds us that matter and energy are really the same quantity. We use kilograms to measure the mass-energy of the positron and the electron, and joules to measure the particles’ kinetic energy, and the energy of photons.
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