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Physics Chapter 22 Notes New book Atoms are composed of protons, neutrons and electrons (except for Hydrogen, which has no neutron). Protons and neutrons of an atom are called nucleons. Due to the fact that the nuclei of atoms are really small, usually about 10 -15 m, the femtometer, fm, or Fermi is 10- 15m is used to describe sizes of atoms. 27 Al For Aluminum, the mass number, A, is 27. This is the total number of nucleons in the nucleus. For Aluminum, the atomic number, Z, represents the number of protons in the nucleus. For aluminum, the neutron number is determined by subtracting the Z number from the A number= 14 n 1 2 3 H (hydrogen) H (deuterium or heavy hydrogen) H (tritium or heavy heavy hydrogen) 1 1 13 A X Z 1 Nuclei, being composed of protons and neutrons have about the same density for every element: 2.3 EE 17 kg/m 3 . Because electrons are so tiny, only the protons and neutrons are counted in the mass of the atom. The protons are called unified mass units or atomic mass units (amu). Electrons are about 2000 times lighter than protons. Isotopes are different flavors of an element which are different because they have different numbers of neutrons. For instance, Carbon-12 has 6 neutrons and Carbon-14 has 8 neutrons. If like charges repel, then why do nuclei, loaded with positive particles (protons) remain together; why do they not fly apart? There is something called a strong force that binds nucleons together in the nucleus. The strong force overcomes the repulsive force of the protons and keeps the nucleus compact. The strong force is the same for protons or neutrons (it is independent of charge) and is limited to distances of 10-15 m. Distances greater than 10-15 m are out of the reach of strong forces. Neutrons help keep nuclei stable. Heavy nuclei are only stable when they have more neutrons than protons. For a Z number greater than 83, the repulsive forces between protons cannot be compensated by the addition of more neutrons. Elements that contain more than 83 protons do not have stable nuclei. In real life, unstable nuclei decay until they become stable. CH 22 Subatomic Physics Dr. Barnes 1 The binding energy is the energy released when unbound nucleons come together to form a stable nucleus, which is equivalent to the energy required to break the nucleus into individual nucleons. Conversion of 1 u of mass into energy would produce about 931.9 MeV. The mass of the nucleons when unbound minus the mass of the nucleons when bound is called the mass defect. Weirdly, the mass of a nucleus is smaller than the mass of the sum of all of the individual protons and neutrons combined. The mass of the unbound nucleus is equal to the sum of the individual nucleon masses and the mass of the bound nucleus is about equal to the atomic mass minus the mass of the electrons. The binding energy for elements with an atomic number less than 20 is smaller than for those elements with more protons. The average binding energy per nucleon is about 8 MeV for elements greater than atomic number 20. So, the bigger the element, the more energy is takes to hold it together. Atoms that are not stable break apart. The process of an atom breaking apart is called nuclear decay. The decay may be spontaneous or artificially induced and usually energy is released in the form of particles, photons or both. The emission o f particles and photons is called radiation and the process is called radioactivity. The nucleus before decay is called the parent nucleus and the nucleus remaining after decay is called the daughter nucleus. In all nuclear reactions, the energy released is measured with the formula E = mc2. There are three types of decay that can be emitted by a nucleus as it undergoes radioactive decay: alpha, beta and gamma radiation. In alpha decay, the emitted particles are helium nuclei. A helium nucleus involves a mass loss with a new element produced. A helium nucleus has a composition of 2 protons and 2 neutrons and has a charge of +2. Alpha particles can usually be stopped by a piece of paper. 238 92 U-> 234 Th 90 + 4 He 2 Rules for nuclear decay: The total of the atomic numbers on the left is the same as the total on the right because the charge must be conserved. The total of the mass numbers on the left is the same as the total on the right because nucleon number must be conserved. CH 22 Subatomic Physics Dr. Barnes 2 Beta decay involves the loss of electrons or positrons (positively charged particles with a mass equal to that of the electron). Electrons are -1 and positrons are +1, but the loss of either involves no change in mass number because neither are considered to have a significant mass. Beta decay, however can result in a new element formed. Beta decay can penetrate a few millimeters of aluminum. 14 C 6 12 14 N + 7 N 7 12 0 e (electron lost) -1 C + 6 0 e (positron lost) 1 Beta decay transforms neutrons and protons: 1 n 0 1 1 1 p + 1 p 1 0 0 e -1 n + 0 e 1 In the Carbon-14 equation listed earlier, it was noticed in the mid-1900’s that energy is not conserved in this equation. Pauli reasoned that there must be another particle, a neutrino, involved in this decay which would account for the disparity in energy conservation in the decay of Carbon-14. The Greek letter nu (v) is used to represent a neutrino. When a bar is drawn above the nu, an antineutrino or the antiparticle of a neutrino is represented. The neutrino has no electric charge and its mass is very small. Due to this discovery, the rule is: In beta decay, an electron is always accompanied by an antineutrino and a positron is always accompanied by a neutrino. CH 22 Subatomic Physics Dr. Barnes 3 14 C 6 12 14 N + 0 7 N 7 12 e + bar nu e + nu -1 C + 0 6 1 Gamma radiation is composed of high energy photons with a release of energy only. Gamma rays can penetrate several centimeters of lead. Gamma rays often result from an alpha or beta decay in which the nucleus becomes more excited. It releases energy in the form of a gamma ray to return to its ground state. In gamma decay, energy is emitted but the parts of the nucleus are left unchanged. Nuclear reactions: Any process that involves a change in the nucleus of an atom is called a nuclear reaction. Nuclear reactions include fission, in which a nucleus splits into two or more lighter nuclei and fusion, in which two or more nuclei combine. For fission to occur to occur naturally, the nucleus must release energy. The nucleons in the daughter nuclei must be more tightly bound and therefore have less mass than the nucleons in the parent nucleus. This decrease in mass appears as released energy in the form of photons or kinetic energy. Since fission produces lighter nuclei, the binding energy per nucleon must increase with decreasing atomic number. This is only possible for atoms in which A>58. Fission, therefore only occurs with heavy atoms. Below is a typical fission reaction caused by bombarding an Uranium with a neutron. 1n 0 + 235U 92 -> 140Ba 56 + 93Kr + 36 3 1n 0 Notice how the numbers balance from side-to-side in the equation. The energy released in the fission of one atom is about 100 million times the amount released in a single molecule of gasoline (octane). CH 22 Subatomic Physics Dr. Barnes 4 When Uranium-235 undergoes fission, the extra neutrons released can cause a chain reaction if the reaction is uncontrolled. If the energy in 1 kg of Uranium-235 were released, it would equal the energy in about 20,000 tons of TNT. This is the idea behind nukes. The original atomic bomb dropped by the USA on Japan in 1945 was a tremendous nuclear fission reaction. Nuclear reactors are designed to maintain a controlled, self-sustained chain reaction, for the production of energy. At this point, all nuclear reactors are fission reactors. Bad news: The radioactive by-products of nuclear energy have half-lives of 10,000 years or longer. Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus. As with fission, the product of a fusion event must have a greater binding energy than the original nuclei for energy to be released. Since the binding energy per nucleon must increase as atomic number increases, atomic fusion only occurs for atoms with atomic numbers less than 58. Because water is plentiful, it is considered the preferred fuel for future fusion reactors. The chief problem with a controlled fusion process is that to impart enough kinetic energy to the nuclei, the fuel must be heated to about 10 8 K or about 10 times greater than the interior temperature of the sun. That’s really hot and very expensive. The fusion reaction in 90% of stars fuse hydrogen and probably helium. The released energy is carried by gamma rays, positrons, and neutrinos. The energy-liberating fusion reactions are called thermonuclear fusion reactions. The hydrogen or fusion bomb was first detonated in 1952. Particle physics is all about discovering the ultimate structure of matter: elementary particles. Following is an explanation called the standard model. Elementary particles do not appear to be divisible and have neither size nor structure. Originally, it was thought that electrons and protons were the fundamental particles. Since 1945, over 300 new particles have been catalogued in the search for this grail. The four fundamental interactions of particles include: strong, electromagnetic, weak and gravitational. All of these interactions are mediated by particles and are categorized in broad categories: leptons and hadrons. The only particle of the four forces following that has not been detected is the graviton. The strong interaction is responsible for binding protons and neutrons in the nucleus. The strong force is the “glue” that holds that holds the nucleons together. The strong force is very short-ranged and is negligible for separations greater than about 10-15 m (the approximate size of a nucleus). The strong interaction is mediated by gluons. The electromagnetic interaction is about 1/100 the strength of the strong interaction, is responsible for the attraction of unlike charges and the repulsion of like charges. It is a long-range interaction that decreases in strength according to the inverse square rule. The electromagnetic force is mediated by photons. CH 22 Subatomic Physics Dr. Barnes 5 The weak interaction is a short-range that is involved in beta decay. It is about 10-13 times the interaction of the strong force. The weak interaction is mediated by W and Z bosons. The gravitational attraction is a long-range interaction with a strength of only about 10-38 that of the strong interaction. It holds solar systems and galaxies together but is real weak on the subatomic level. The gravitational attraction is proposed to be mediated by gravitons. Hadrons are particles that participate in the four interactions, but leptons participate in all forces except the strong force. Electrons and neutrinos are both leptons. Leptons have no measurable size and do not seem to break down into smaller units; therefore, leptons appear to be truly elementary. The six leptons are: electron, muon, tau, each paired with a neutrino. Each of the six leptons has an antiparticle. Hadrons can be divided into mesons and baryons. Baryons are protons and neutrons, which compose everyday matter. Mesons are unstable and are not part of ordinary matter. Hadrons are thought to be composed of charged quarks (fractionally) which are in pairs (up and down, top and bottom and charm and strange). Associated with each quark is an antiquark of opposite charge. Mesons are composed of one quark and one antiquark. Baryons are composed of three quarks. Antibaryons are composed of three antiquarks. Despite many efforts, no isolated quark has ever been observed. Some physicists believe that quarks are permanently confined inside ordinary particles by the strong force. This is called the color force, which is the property of quarks that allows them to attract one another and form composite particles. It is thought that up until 3-7 x 105 years after the big bang, most of the energy in the universe was in the form of radiation rather than matter. Evolutionists believe that matter resulted as the energy cooled after the initial explosion. CH 22 Subatomic Physics Dr. Barnes 6 22A Binding energy The nucleus of the deuterium atom, called the deuteron, consists of a proton and a neutron. Given that the atomic mass of deuterium is 2.014102 u, calculate the deuteron’s binding energy in MeV. Atomic number = Z 1 1 H Mass number = A A 1 H 1.007 2.104 2 H Z 1 H 1 atomic mass of deuterium = 2.014102u atomic mass of H Z = 1 N = 1 = 1.007825u CH 22 Subatomic Physics Dr. Barnes 7 mn = 1.008665u c = 3.00 Ebind = ? Ebind = Δmc2 Binding energy = x 108 m/s mass defect x (speed of light)2 The energy of 931.48MeV/u can be substituted for c2 in the equation above. M = Z(atomic mass of H) + Nmn - atomic mass M in the equation above is mass defect. The total mass of a stable nucleus (mbound) is always less than the sum of the masses of its individual nucleons (munbound). Mn is the mass of a neutron. Ans: In order for a deuteron to be separated into its constituents-a proton and a neutron-2.224MeV of energy must be added. CH 22 Subatomic Physics Dr. Barnes 8 22B Nuclear Decay The element radium was discovered my Marie and Pierre Curie in 1898. One of the isotopes of radium, 226 Ra 88 decays by alpha emission. What is the resulting daughter element? Hint: show a Helium nucleus on the right side of the equation 4 He 2 Ans: 226 88 Ra -> 222 86 Rn + 4 He 2 (find the new element in Appendix G of your book) CH 22 Subatomic Physics Dr. Barnes 9 22C Measuring nuclear decay The half-life of the radioactive radium (226Ra) is 5.0 x 1010 s. A sample contains 3.0 x 1016 nuclei. What is the decay constant for this decay? The half-life for a nucleus is: T1/2 = 0.693 λ Half-life = 0.693 Decay constant First find wavelength: λ= 0.693 = 0.693 = 1.4 X 10-11/S 5.0 x 1010 s T1/2 How many radium nuclei, in curies, will decay per second? Activity=λN = 1.4 x 10-11 x 3.0 x 1016 nuclei =415800 nuclear decays S s One curie (Ci) is equal to 3.7 x 1010 decays/second. 415,800 decays S x 1 curie = .000011 Ci 3.7 x 1010 decays CH 22 Subatomic Physics Dr. Barnes 10 S CH 22 Subatomic Physics Dr. Barnes 11