PHY138Y Nuclear and Radiation Professor Tony Key MP401 key@physics.utoronto.ca You can hear Tom Lehrer s Elements at http://www.privatehand.com/flash/elements.html Van Kranendonk Prize for an Outstanding TA (tutor or lab demo) Nominations to ugchair@physics.utoronto.ca Professor David Bailey, MP301 OR Dr Savaria, MP129 with a brief statement Announcements Pre-class quiz #2 will be posted at noon MP N&R PS #1 due Friday midnite Questions - Remember our Runner! Ardavan E-mails Mon, Tues, Wed, Thu morning, Sunday - if no reply within 24 hours Send them again! Today Complete the story of the atom Highlights of SNI Review of Monday s Lecture Boltzmann molecular explanation for thermodynamics Thomson discovery of the electron The Nucleus and the Planetary model Rutherford A worked problem (time permitting) 1
α Alpha Scattering Experiment α Х EXPERIMENTAL OBSERVATION Review of Monday s Lecture Boltzmann atomic explanation for thermodynamics Thomson discovery of the electron The Nucleus and the Planetary model Rutherford Planetary Model problems electromagnetic radiation line spectra Planck and his black body Bohr s hypotheses Important for you to know! 1. E-M radiation : an accelerating charge emits electromagnetic waves So does an accelerating magnetic pole! The Electromagnetic Spectrum 2. Elements emit Line Spectra James Clerk Maxwell The Bohr Atom Electrons exist in a finite number of nonradiating orbits, each with a fixed energy Radiation is emitted when an electron jumps from a higher to a lower energy state The energy of the radiation is given by E n -E m Where E n = - 13.6/n 2 ev Energy Level Diagram for Hydrogen E n -E m = energy of radiation 2
Photons Check out Dr Harrison s excellent Flash diagram on the Bohr Model and Line Spectra This man studied the Photo-electric Effect to prove that Light comes in Lumps (called photons) : E = hf Who is he? Who is he? A. Ludwig Boltzmann B. Karl Marx C. Albert Einstein D. Max Planck E. Ernest Rutherford Photons Albert Einstein Nobel Prize 1921 Photons The Photo-electric Effect Light comes in lumps (called photons) E = hf Energy Level Diagram for Hydrogen E n -E m = hf 3
Max. = c!! E = hf!!?? Particles are also waves Quantum Theory Uncertainty Principle 1913 Otto Stern ( Einstein s student) and Max von Laue (Planck s student) "If this nonsense of Bohr should in the end prove to be right, we will quit physics!" Erwin Schroedinger Werner Heisenberg Atoms, electrons, protons, neutrons, are like nothing we have ever seen before! No reasonable definition of reality could be expected to permit this. A. Einstein Atoms, electrons, protons, neutrons, are like nothing we have ever seen before! "If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet." N. Bohr 4
Yet...Quantum Mechanics is the most accurate theory N Neutrons (neutron number) The Nucleus (!) Z Protons (proton number) e.g. the Magnetic moment of the electron: Measured value = 1.001 159 652 19 Calculated value = 1.001 159 652 14 A = N+ Z (mass number) Dimensions ~ 10-15 m A ZX The Nucleus Question Why does the nucleus stay together?? A very strong force the strong nuclear force comes into play at very short distances to overcome the Coulomb force between the protons. Neutrons and protons experience this STRONG force equally. Three electrons orbit the nucleus of a neutral 6 Li atom. How many electrons orbit the nucleus of a neutral 7 Li atom? A. 1 B. 2 C. 3 D. 4 E. 0 Question Three electrons orbit the nucleus of a neutral 6 Li atom. How many electrons orbit the nucleus of a neutral 7 Li atom? A. 1 B. 2 C. 3 D. 4 E. 0 Question What are isotopes? 5
Isotopes are nuclei that have: A. the same mass number but different atomic numbers B. the same atomic number but different mass numbers C. the same neutron number but different atomic numbers D. the same neutron number but different mass numbers E. None of the above Isotopes are nuclei that have: A. the same mass number but different atomic numbers B. the same atomic number but different mass numbers C. the same neutron number but different atomic numbers D. the same neutron number but different mass numbers E. None of the above Basic Nuclear Properties Nuclide a particular nuclear species with given A and Z, e.g. 12 C, 16 O Element has a specific value of Z e.g. H, He, Li, Be, B, C, N, O Isotopes of an element have the same Z value, but different N and A values. e.g. 12 C, 14 C : 1 H, 2 H, 3 H Size of Nucleus Radius = r 0 A 1/3 r 0 = 1.2 x 10-15 m Unit of Mass (1 - u) Mass : kg too large a unit, so. define the atomic mass unit, u. Definition: the mass of an atom of 12 C is exactly 12 u 1u = 1.660 559 x 10-27 kg (approximately the mass of a nucleon) Unit of Mass (2 MeV/c 2 ) Einstein s most famous equation: E = mc 2 Means that the mass of one unified mass unit (1 amu) 1u = 1.660 559 x 10-27 kg = 931.494 MeV/c 2 (Remember 1 ev = 1.6 x 10-19 J) E.g the mass of the proton m p = 938.3 MeV/c 2. etc. Avogadro s Number Avogadro s number is the number of atoms contained in 12 g of 12 C : N A = 6 x 10 23 1 mole is that quantity of a substance that contains exactly N A atoms 6
Molar Mass 1 molar mass of A ZX A gram Mass of A Z X atom A u EXACTLY = only for 12 C SO the number of atoms in 1 gram N A /A The molar mass of A ZX is not exactly equal to A gm BUT... it s pretty *#@% close!! See Worked Problem 1.4 (i) Calculate the mass of 1 mole of 23 11 Na A. B. C. D. E. Nuclear Binding Energy minimum The Binding Energy is the ^ energy required to break the nucleus into its component parts A. B. C. D. E. ENERGY NUCLEUS INDIVIDUAL PROTONS AND NEUTRONS B + m nucleus = Z m p + N m n Nuclear Binding Energy The Binding Energy is the energy required to break the nucleus into its component parts ENERGY NUCLEUS INDIVIDUAL PROTONS AND NEUTRONS Calculate the Binding Energy of 12 C B + m nucleus = Z m p + N m n So... B = ( Z m p + N m n ) - m nucleus 7
Worked Example Binding Energy of 12 C ATOMIC MASS 1u = 1.660 559 x 10-27 kg = 931.494 MeV/c 2 8