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Nuclear Physics This Lecture: Nuclear structure, Strong Force, Radioactivity Previous lecture: More on Atomic Physics Electron Spin and Exclusion Principle Emission and absorption spectra for atoms with more electrons Lasers Final Mon. May 12, 12:25-2:25, Ingraham B10 New material: Particle in a box (Ch 40.4-5, 40.10) Hydrogen Atom quantum numbers, wave functions, probability (Ch 41.1-2) Electron Spin and Pauli exclusion principle (Ch 41.3-6) Lasers (Ch 41.8) Nuclear Physics: nuclear structure (Ch 42.1-3) and Radioactivity (Ch 42.5-7) MTE1-3 material (see past lecture notes and Exam web page) Final Exam • Final is 25% of final grade • In the final about 30% on new material, rest is material in MTE1-3 • 2 sheets allowed (HAND WRITTEN!) Notify NOW any potential and VERY serious problem you have with this time From last lecture: building atoms 4 Measuring the Moon-Earth distance with a laser NASA Apollo Laser Ranging Experiment: begun 25 yrs ago when Apollo 11 deployed a reflector in the Sea of tranquillity Lunar ranging involves sending a laser beam through an optical telescope At the Moon's surface the beam is roughly four miles wide Highly collimated beam from stimulated emission, almost monochromatic 5 http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.html Nuclear Structure Neutron Size of electron orbit is 5x10-11 m Nucleus is 5,000 times smaller than the atom! Nucleus size ~10-14 m Proton 1 fermi = 10-15m Spacing between nucleons 10-15 m Neutron: zero charge (neutral) Proton: positive charge (equal and opposite to electron) 6 Nucleons are not building blocks of matter • We now know that protons and neutrons are not fundamental particles. • They are composed of quarks, which interact by exchanging gluons. 7 Notation for nuclei • Zero net charge -> # protons in nucleus = # electrons orbiting. • The number of electrons determines which element. – 1 electron → Hydrogen – 2 electrons → Helium – 6 electrons → Carbon A Z • How many neutrons? 6 3 Li Nucleus =Protons+ Neutrons nucleons A = # of nucleons= atomic mass number A=N+Z Z = atomic number (# of protons or # of electrons) 8 N = # of neutrons Example: Carbon •Carbon has 6 electrons (Z=6) •Zero net charge => 6 protons in the nucleus. •Most common form of carbon has 6 neutrons in the nucleus. 12 C 6 Another form of Carbon has 6 protons, 8 neutrons in the nucleus. This is 14C. 9 different mass Quiz Tritum is an isotope of hydrogen with three total nucleons: two neutrons and one proton. How many electrons does it have? A. One B. Two C. Three 10 Isotopes of Hydrogen D2O has 20 nucleons and H2O has 18. So heavy water is heavier than water by (20-18)/18= 10% Number of nucleons determines the mass of atoms 11 Women Nobel Prizes The only 2 female Nobel Prizes in Nuclear Physics! (we need more!!!) 1903 Marie Curie (with Pierre) in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel Maria Goeppert-Mayer 1963 Shell Model of Nucleus Nuclear Force (Strong Interaction) • So what holds the nucleus together? • Coulomb force? Gravity? • Coulomb force only acts on charged particles – Repulsive between protons, and doesn’t affect neutrons at all. • Gravitational force is much too weak. Showed before that gravitational force is much weaker than Coulomb force. Gravitational effects are negligible at atomic and nuclear level The Strong Nuclear Force • New attractive force. • Dramatically stronger than Coulomb force at short distances. • Doesn’t depend on sign of charge. • This is the ‘strong interaction’, one of the four fundamental interactions: electromagnetic interaction strong interaction weak interaction gravitational interaction 14 Estimating the Strong Force The Coulomb attraction energy (~10 eV) binds the hydrogen atom together. Protons in nucleus are 50,000 times closer together than electron and proton in hydrogen atom. Attractive energy must be larger than the Coulomb repulsion, so nuclear binding energies are at least A. 5000 eV B. 500,000 eV =0.5 MeV C. 5,000,000 eV Experimentally, nucleons bound by ~ 8 MeV / nucleon (8,000,000 eV / nucleon) 15 A convenient unit of Mass • It is convenient to use atomic mass units, u, to express masses – 1 u = 1.660 539 x 10-27 kg – mass of one atom of 12C = 12 u ⇒ 1 u = 1.66 x 10-27 kg • Mass can also be expressed in MeV/c2 – From rest energy of a particle ER = mc2 – 1 u = 931.494 MeV/c2 16 € Nuclear density • Experimentally, r0=1.2 fm – radius of nucleus r = roA1/3 (A=mass # = # nucleons) – says that volume V proportional to A. – says that nucleon density is constant • Nuclear matter is ~ incompressible – More nucleons -> larger nucleus – Nucleons ~ same distance apart in all nuclei ρ nuc m Au Au u 1.66 ×10−27 kg = = = = = = 2.3 ×1017 kg /m 3 V 4 πr 3 4 πr 3 A 4 πr 3 4 π (1.2 ×10−15 ) 0 0 3 3 3 3 Nuclear Binding Energy • Mass of nucleus is less than mass of isolated constituents! • Helium nucleus energy < energy isolated nucleons. mp=1.6726 x 10-27kg/1.66 x 10-27 kg/u= 1.0078u mn=1.6749 x 10-27kg/1.66 x 10-27 kg/u= 1.0087u • Energy difference is binding energy. 2 protons & 2 neutrons 1.0078u Helium nucleus 1.0078u Arises from E=mc2 Equivalence of mass and energy. 18 Binding energy Nucles mass mnucleus Mass of Z protons and N neutrons: Zmp + Nmn Experiment says: mnucleus < Zmp + Nmn • Binding energy: energy you would need to supply to disassemble the nucleus into nucleons: Ebinding = (Zmp+Nmn-mnucleus)c2 • Example: deuteron = 1 proton and 1 neutron bounded together • Free particles: mp = 1.0078u, mn= 1.0087u, mp+mn=2.01649u • Atomic mass of deuteron 2H = 2.01410u • Binding energy =0.002388u x 931.494MeV/u = 2.224MeV • Binding energy/nucleon = 2.224/2 19 Binding energy of different nuclei For nuclei smaller than Fe the binding energy increases with A: you have to supply more energy to win nuclear bounds. Fe with A = 56 nucleons has 8.79 MeV/nucleon (amount of energy to remove one nucleon from Fe nuclei) Peaks at 4He, 12C and 16O because these nuclei are more tightly bond. Nuclear force is short range: as nucleus grows nuclear bonds are saturated and nuclei interact only with neighbors => Ebinding almost constant 20 Binding energy released: fusion and fission Combine p and n to form 4He 7MeV/nucleon binding energy is released fusion of 2 light nuclei in a heavier one smaller energy is released in fission of a heavy nuclei into 2 lighter nuclei 21 Stable and Unstable Isotopes Isotope = same Z Isotone = same N Isobar = same A Stability of nuclei • Dots: naturally occurring isotopes. • Shaded region: isotopes created in the laboratory. • • • Light nuclei are most stable if N=Z Heavy nuclei are most stable if N>Z As # of p increases more neutrons are needed to keep nucleus stable • No nuclei are stable for Z>83 Radioactivity • Discovered by Becquerel in 1896 • spontaneous emission of radiation as result of decay or disintegration of unstable nuclei • Unstable nuclei can decay by emitting some form of energy • Three different types of decay observed: Alpha decay ⇒ emission of 4He nuclei (2p+2n) Beta decay⇒ electrons and its anti-particle (positron) Gamma decay⇒ high energy photons Penetrating power of radiation • Alpha radiation barely penetrate a piece of paper (but dangerous!) • Beta radiation can penetrate a few mm of Al • Gamma radiation can penetrate several cm of lead Is the radiation charged? • Alpha radiation positively charged • Beta radiation negatively charged • Gamma radiation uncharged • 232Th Decay: an exponential decrease −rt N(t) = N 0e has a half-life t1/2=14 x109 yr • Sample initially contains: N0 = 106 232Th atoms • Every 14 billion years, the number of 232Th nuclei goes down by a factor of two. N0 −rt1 / 2 N(t1/ 2 ) = = N 0e 2 N0 € N0/2 N0/4 N0/8 −rt1/ 2 = ln(1/2) ⇒ r = ln2 /t1/ 2 The Decay Rate • probability that a nucleus decays during Δt Prob(in Δt) = rΔt Constant of proportionality r = decay rate (in s-1) • number of decays (decrease)= NxProb=rNΔt = =-ΔN N=number of independent nuclei € N(t) = N 0e−rt ΔN = −rN Δt # radioactive nuclei at time t # rad. nuclei at t=0 The number of decays per second is the activity € € ΔN R= = rN Δt 1 τ= r time constant