Chapter 29 Nuclear Physics

General Physics Nuclear Physics Sections 1–4

General Physics Milestones in Nuclear Physics 1896 – the birth of nuclear physics Becquerel discovered radioactivity in uranium compounds 1911 Rutherford, Geiger and Marsden performed scattering experiments Established the point mass nature of the nucleus Nuclear force was a new type of force 1919 Rutherford and coworkers first observed nuclear reactions Naturally occurring alpha particles bombarded nitrogen nuclei to produce oxygen

General Physics History Becquerel – discovered radioactivity (1896) (from radiare = emit rays) Becquerel – discovered radioactivity (1896) (from radiare = emit rays) Curie – discovery of polonium and radium (1898) Curie – discovery of polonium and radium (1898) Rutherford – nuclear model Rutherford – nuclear model classified , ,  radiation,  particle = 4 He nucleus (nuclear transmutation) classified , ,  radiation,  particle = 4 He nucleus (nuclear transmutation) used  scattering to discover the nuclear model used  scattering to discover the nuclear model postulated ‘neutrons’ A=Z+N (1920); bound p + e - state? postulated ‘neutrons’ A=Z+N (1920); bound p + e - state? Mosley – studied nucleus via X-ray spectra Mosley – studied nucleus via X-ray spectra correlated (Z = charge of nucleus) with periodic table correlated (Z = charge of nucleus) with periodic table extra particles in nucleus: A = Z + ? extra particles in nucleus: A = Z + ? Chadwick – discovered neutron (1932) Chadwick – discovered neutron (1932) Pauli – postulated neutral particle from  -decay (1930) Pauli – postulated neutral particle from  -decay (1930) Fermi – theory or weak decay (1933) ‘neutrino’ Fermi – theory or weak decay (1933) ‘neutrino’ Fission – Hahn, Strassmann, (&Meitner!) (1938) Fission – Hahn, Strassmann, (&Meitner!) (1938) first reactor (chain reaction), Fermi (1942) first reactor (chain reaction), Fermi (1942) Bohr, Wheeler – liquid drop model Bohr, Wheeler – liquid drop model Mayer, Jensen – shell model (1949) Mayer, Jensen – shell model (1949) Hofstadter – electron scattering (1953-) Hofstadter – electron scattering (1953-) measured the charge density of various nuclei measured the charge density of various nuclei discovered structure in the proton (not point-like particle) discovered structure in the proton (not point-like particle)

General Physics Some Properties of Nuclei All nuclei are composed of protons and neutrons Exception is ordinary hydrogen with just a proton Atomic number, Z Number of protons in the nucleus Neutron number, N Number of neutrons in the nucleus Mass number, A Number of nucleons in the nucleus: A = Z + N Nucleon is a generic term used to refer to either a proton or a neutron in the nucleus The mass number is not the same as the mass

General Physics Symbolism Symbol: X is the chemical symbol of the element Example: Mass number: A = 27 nucleons Atomic number: Z = 13 protons Neutron number: N = 27 – 13 = 14 neutrons The Z may be omitted since the element can be used to determine Z

General Physics More Properties The nuclei of all atoms of a particular element must contain the same number of protons They may contain varying numbers of neutrons Isotopes of an element have the same Z but differing N and A values Example: See Appendix B – An Abbreviated Table of Isotopes RadioactiveStable Radioactive

General Physics Charge and Mass The proton has a single positive charge, +e e = x C The electron has a single negative charge, –e The neutron has no charge – difficult to detect unified mass unit: u 1 u = x kg Based on definition that mass of one atom of 12 C is exactly 12 u E = m c 2  1 u = MeV/c 2

General Physics Summary of Charges & Masses ChargesMasses ParticleCkguMeV/c 2 Proton x x Neutron x Electron– x x x

General Physics Binding Energy The total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons This difference in energy is called the binding energy of the nucleus It can be thought of as the amount of energy you need to add to the nucleus to break it apart into separated protons and neutrons

General Physics Binding Energy per Nucleon Except for light nuclei, the binding energy is ~ 8 MeV per nucleon The curve peaks in the vicinity of A = 60 Nuclei with mass numbers greater than or less than 60 are not as strongly bound as those near the middle of the periodic table The curve is slowly varying at A > 40

General Physics The Size of the Nucleus First investigated by Rutherford in scattering experiments He found an expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force The KE of the particle must be completely converted to PE

General Physics Size of the Nucleus, cont d gives an upper limit for the size of the nucleus Rutherford determined that For gold, he found d = 3.2 x m For silver, he found d = 2 x m Such small lengths are often expressed in femtometers where 1 fm = m Also called a fermi Active Figure: Rutherford ScatteringRutherford Scattering

General Physics Size and Density of Nuclei Since the time of Rutherford, many other experiments have concluded: Most nuclei are approximately spherical Average radius is r o = 1.2 x m or 1.2 fm The volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleons This suggests that all nuclei have nearly the same density Nucleons combine to form a nucleus as though they were tightly packed spheres

General Physics Z N A A=100 Z=N = A/2 Atomic element Nuclear isotope

General Physics N Z Nuclear decay modes:  ++ decay  ++ decay  - decay (isobar)  - decay (isobar)  + decay (isobar)  + decay (isobar)  electron capture (isobar)  electron capture (isobar) p decay (isotone) p decay (isotone) n decay (isotope) n decay (isotope)  decay (isomers)  decay (isomers) electron conversion (EC) electron conversion (EC) spontaneous fission (SF) spontaneous fission (SF) double beta decay (2  ) double beta decay (2  ) neutrino-less double beta decay (0  ) neutrino-less double beta decay (0  ) beta-delayed n,p,  decay beta-delayed n,p,  decay ISOBARS ISOTOPES ISOTONES ISOMERS

General Physics Chart of Nuclides – decay mode stable nuclide  - decay  , electron capture  decay p decay n decay spontaneous fission magic numbers

General Physics Chart of Nuclides – island of stability magic numbers

General Physics Nuclear Stability Very large Coulomb repulsive forces exist between the charged protons in the nucleus – the nucleus should fly apart Nuclei are stable because of the presence of another, short-range force, between nucleons called the nuclear force Light nuclei are most stable if N = Z Heavier nuclei are most stable when N > Z As the number of protons increase, the Coulomb force increases and more nucleons are needed to keep the nucleus stable No nuclei are stable when Z > 83

General Physics Radioactivity Radioactivity is the spontaneous emission of radiation Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei – 3 types Alpha particles The particles are 4 He nuclei Beta particles The particles are either electrons or positrons A positron is the antiparticle of the electron It is similar to the electron except its charge is +e Gamma rays The “rays” are high energy photons

General Physics The Decay Constant The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample ΔN = -λ N Δt λ is called the decay constant and determines the rate at which the material will decay The decay rate or activity, R, of a sample is defined as the number of decays per second

General Physics Decay Curve The half-life is also a useful parameter Defined as the time it takes for half of any given number of radioactive nuclei to decay The decay curve follows the equation Active Figure: Radioactive DecayRadioactive Decay

General Physics Decay Units and General Rules The unit of activity, R, is the Curie, Ci 1 Ci = 3.7 x decays/second The SI unit of activity is the Becquerel, Bq 1 Bq = 1 decay / second Therefore, 1 Ci = 3.7 x Bq When one element changes into another element, the process is called spontaneous decay or transmutation Conservation of charge, mass-energy, and momentum must hold in radioactive decay

General Physics Alpha Decay When a nucleus emits an alpha particle it loses two protons and two neutrons N decreases by 2 Z decreases by 2 A decreases by 4 Symbolically X is called the parent nucleus Y is called the daughter nucleus

General Physics Alpha Decay – Example Decay of 226 Ra Half life for this decay is 1600 years Excess mass is converted into kinetic energy Momentum of the two particles is equal and opposite Active Figure: Alpha Decay of Radium-226Alpha Decay of Radium-226

General Physics Beta Decay Beta– decay: a neutron is transformed into a proton, and an electron and antineutrino are emitted A stays the same, Z  Z+1 Beta+ decay: a proton is transformed into a neutron, and a positron and neutrino are emitted A stays the same, Z  Z–1 Symbolically Energy must be conserved is the symbol for the neutrino (carries away excess KE) is the symbol for the antineutrino (carries away excess KE)

General Physics Beta Decay – Example Radioactive Carbon-14 decay Used to date organic samples

General Physics Gamma Decay Gamma rays are given off when an excited nucleus “falls” to a lower energy state Similar to the process of electron “jumps” to lower energy states and giving off photons The photons are called gamma rays, very high energy relative to light The excited nuclear states result from “jumps” made by a proton or neutron The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission

General Physics Gamma Decay – Example Example of a decay sequence The first decay is a beta decay emission The second step is a gamma decay emission C* indicates the Carbon nucleus is in an excited state Gamma emission doesn’t change either A or Z

General Physics Medical Applications of Radiation Tracing Radioactive particles can be used to trace chemicals participating in various reactions Example, 131 I to test thyroid action Sterilization Radiation has been used to sterilize medical equipment Used to destroy bacteria, worms and insects in food Bone, cartilage, and skin used in graphs is often irradiated before grafting to reduce the chances of infection

General Physics Medical Applications of Radiation CAT scans Computed Axial Tomography Produces pictures with greater clarity and detail than traditional x-rays

General Physics Medical Applications of Radiation MRI scans Magnetic Resonance Imaging When a nucleus having a magnetic moment is placed in an external magnetic field, its moment precesses about the magnetic field with a frequency that is proportional to the field Transitions between energy states can be detected electronically to produce cross-sectional images

General Physics 3D-CRT Treatment Three-dimensional conformal radiation therapy uses sophisticated computers, CT scans and/or MRI scans to create detailed 3-D representations of a tumor and surrounding organs Radiation beams are then shaped exactly to treat the size and shape of the tumor – nearby normal tissue receives less radiation exposure Medical Applications of Radiation

General Physics 3D-CRT Treatment Planning 3D-CRT Treatment Planning