Chapter 32 - Nuclear Physics and NuclearRadiation1 The Constituents and Structure of NucleiThe nucleus of an atom consists of positively-charged protons and neutral neutrons.Protons and neutrons are called “nucleons.” We characterize nuclei by the numberof protons and neutrons they contain:• atomic number (Z): the number of protons in a nucleus• neutron number (N): the number of neutrons in a nucleus• mass number (A = Z + N): the total number of nucleonsThe notation we used to represent the composition of the nucleus is:AZX, where Xrepresents the symbol for a particular element. For example, the symbol for hydro-gen is H, the symbol for carbon is C, the symbol for sodium is Na. Since you aregiven A and Z in this notation, you can find N = A − Z.All nuclei of a given element have the same number of protons (same atomic num-ber). However, they may have different numbers of neutrons. Nuclei of the sameelement (same atomic number Z) that have different numbers of neutrons are called“isotopes.” For example,126C and136C are isotopes of carbon.There is a unit of mass called the “atomic mass unit” (u), defined such that oneatom of126C is exactly 12 u.1u = 1.660540 × 10−27kg.A proton has a mass of 1.007276 u, and a neutron has a mass of 1.008665 u.The average radius of a nucleus of mass number A isr = (1.2 × 10−15m)A1/3(1)L. Whitehead 1 Phys 13021 fermi = 1 femtometer (fm) = 10−15m. (Named after Enrico Fermi.)Using the radius of a nucleus, we can find an expression for the density (ρ) of anucleus. We’ll use the approximation that the proton and neutron have the samemass ≈ 1u = 1.67 × 10−27kg.ρ =MV=A(1.67 × 10−27kg)43πr3=A(1.67 × 10−27kg)43π(1.2 × 10−15mA1/3)3=A(1.67 × 10−27kg)43π(1.2 × 10−15m)3A=1.67 × 10−27kg43π(1.2 × 10−15m)3= 2.3 × 1017kg/m3(2)The density is independent of the mass number - all nuclei have approximately thesame density.Protons in the nucleus exert repulsive electric forces on each other. What keeps thenucleus from flying apart? There must be another stronger force that overcomesthe electric force. The force that holds the nucleus together is the strong nuclearforce. It is a short range force, only acting over a range about the size of the nu-cleus. It is an attractive force for protons and neutrons, but does not act on electrons.2 RadioactivityEinstein’s famous equationE = mc2(3)indicates that mass is a form of energy.We can use this expression to get a conversion factor between atomic mass units (u)L. Whitehead 2 Phys 1302and electron-volts (eV). The energy equivalent of 1 atomic mass unit is:E = mc2= (1u)c2= (1.660540 × 10−27kg)(2.998 × 108m/s)21eV1.6022 × 10−19J= 9.315 × 108eV = 931.5MeV(4)So we can write:931.5MeV = (1u)c21u = 931.5MeV/c2(5)Energy per c2is a unit of mass!Some nuclei are unstable, and will decay by emitting a particle and changing itscomposition or its state. The particles that are emitted in a decay are known asradioactivity.The law of conservation of energy applies to decays. The total energy of the systembefore the decay (the mass of the original nucleus) has to be equal to the total energyof the system after the decay (the mass of the new nucleus plus the energy of the otherparticles that are emitted.) Thus when a decay happens, the mass of the final nucleuswill be less than the mass of the original nucleus. The difference in mass between thenuclei appears as a release of energy. A nucleus cannot decay into a heavier nucleus- it is energetically forbidden (i.e. it would disobey the law of conservation of energy).Alpha DecayAn alpha particle is a helium nucleus (42He). When a nucleus decays by emittingan alpha particle, it loses two protons and two neutrons, so it’s atomic number Zdecreases by 2, and its mass number A decreases by 4. An alpha decay can be writtenthis way:AZX →A−4Z−2Y +42He (6)We call X the parent nucleus, and Y the daughter nucleus. Note that the totalatomic number on the left side is equal to the sum of the atomic numbers on theL. Whitehead 3 Phys 1302right. Ditto for the mass number.Smoke detectors use alpha decay.Beta DecayEvery particle has a corresponding antiparticle. Antiparticles have the same mass,but opposite charge of particles (neutral particles have neutral antiparticles. Theantiparticle of the electron e−is called the positron (e+). All the ordinary matteraround us is made of matter, but antimatter is produced (in only small quantities)in decays and other particle interactions.The basic process in beta decay is the conversion of a neutron to a proton, with theemission of an electron and particle called a neutrino - in particular, an electron-typeantineutrino (the bar above indicates it is an antiparticle).10n →11p + e−+ ¯νe(7)Notice that charge is conserved - a neutron is neutral, and the total charge on theright hand side is also zero.When the above decay happens inside a nucleus, it looks like this:AZX →AZ+1Y + e−+ ¯νe(8)A similar decay in which a positron is emitted can also happen:AZX →AZ−1Y + e++ νe(9)Note that an isolated proton cannot decay into a neutron, because the proton islighter than the neutron.The electron is also known as a beta particle. We write β−for an electron and β+for a positron.Beta decay is how the neutrino was discovered. The results of experiments thatlooked at the energy of the outgoing electrons indicated that there must be anotherparticle present. In addition, angular momentum wasn’t conserved. Wolfgang Paulihypothesized that there was a new type of very light neutral particle that was so farunknown. Fermi named it neutrino, Italian for “little neutral one.” Neutrinos wereobserved for the first time in the 1950’s, more than 20 years after Pauli proposedL. Whitehead 4 Phys 1302their existence.Gamma DecayA nucleus in an excited state can emit a photon when decaying to a lower energylevel, just as in atoms. Because energies are much greater at the nuclear scale thanthe atomic scale, the photons are very high energy, in the gamma portion of the EMspectrum. They are called gamma (γ) rays. We write such a decay in this way:AZX∗→AZX + γ (10)where the * indicates an excited state. The composition of the nucleus doesn’t changein this type of decay.What is the daughter nucleus when146C undergoes β−decay?146C →147Y + e−+ ¯νeLooking at the periodic table (Appendix E in your book), we see that nitrogen hasan atomic number of 7.146C →147N + e−+ ¯νeHow much