Quantum Physics

940 Chapter 29 Nuclear PhysicsERNEST RUTHERFORD,New Zealand Physicist(1871 – 1937)Rutherford was awarded the Nobel Prize in1908 for discovering that atoms can bebroken apart by alpha rays and for studyingradioactivity. “On consideration, I realizedthat this scattering backward must be theresult of a single collision, and when I madecalculations I saw that it was impossible toget anything of that order of magnitude unlessyou took a system in which the greaterpart of the mass of the atom was concentratedin a minute nucleus. It was then thatI had the idea of an atom with a minutemassive center carrying a charge.”Definition of the unified mass unit u TIP 29.1 Mass Number is notthe Atomic MassDon’t confuse the mass number A withthe atomic mass. Mass number is aninteger that specifies an isotope andhas no units—it’s simply equal to thenumber of nucleons. Atomic mass isan average of the masses of theisotopes of a given element and hasunits of u.North Wind Picture Archives29.1 SOME PROPERTIES OF NUCLEIAll nuclei are composed of two types of particles: protons and neutrons. The onlyexception is the ordinary hydrogen nucleus, which is a single proton. In describingsome of the properties of nuclei, such as their charge, mass, and radius, wemake use of the following quantities:• the atomic number Z, which equals the number of protons in the nucleus,• the neutron number N, which equals the number of neutrons in the nucleus,• the mass number A, which equals the number of nucleons in the nucleus(nucleon is a generic term used to refer to either a proton or a neutron).AThe symbol we use to represent nuclei is Z X, where X represents the chemical27symbol for the element. For example, 13 Al has the mass number 27 and the atomicnumber 13; therefore, it contains 13 protons and 14 neutrons. When no confusionis likely to arise, we often omit the subscript Z, because the chemical symbol can alwaysbe used to determine Z .The nuclei of all atoms of a particular element must contain the same numberof protons, but they may contain different numbers of neutrons. Nuclei that arerelated in this way are called isotopes. The isotopes of an element have the same Zvalue, but different N and A values. The natural abundances of isotopes can differ11 12 13 14substantially. For example, 6 C, 6 C, 6 C, and 6 C are four isotopes of carbon. Thenatural abundance of the12 13 6 C isotope is about 98.9%, whereas that of the 6 C isotopeis only about 1.1%. Some isotopes don’t occur naturally, but can be producedin the laboratory through nuclear reactions. Even the simplest element, hydrogen,12 3has isotopes: 1H, hydrogen; 1 H, deuterium; and 1 H, tritium.Charge and MassThe proton carries a single positive charge e 1.602 177 33 10 19 C, the electroncarries a single negative charge e, and the neutron is electrically neutral.Because the neutron has no charge, it’s difficult to detect. The proton is about1 836 times as massive as the electron, and the masses of the proton and the neutronare almost equal (Table 29.1).For atomic masses, it is convenient to define the unified mass unit u insuch a way that the mass of one atom of the isotope 12 C is exactly 12 u, where1u 1.660 559 10 27 kg. The proton and neutron each have a mass ofabout 1 u, and the electron has a mass that is only a small fraction of an atomicmass unit.Because the rest energy of a particle is given by E R mc 2 , it is often convenientto express the particle’s mass in terms of its energy equivalent. For one atomicmass unit, we have an energy equivalent ofE R mc 2 (1.660 559 10 27 kg)(2.997 92 10 8 m/s) 2 1.492 431 10 10 J 931.494 MeVIn calculations, nuclear physicists often express mass in terms of the unitMeV/c 2 , where1 u 931.494 MeV/c 2TABLE 29.1Masses of the Proton, Neutron, and Electron in Various UnitsMassParticle kg u MeV/c 2Proton 1.6726 10 27 1.007 276 938.28Neutron 1.6750 10 27 1.008 665 939.57Electron 9.109 10 31 5.486 10 4 0.511