Describe the structure of the nucleus Calculate nuclear binding energies Identify factors affecting nuclear stability

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1 Atomic and Nuclear Structure George Starkschall, Ph.D. Lecture Objectives Describe the atom using the Bohr model Identify the various electronic shells and their quantum numbers Recall the relationship between binding energy and atomic properties Describe the production of characteristic x-rays and Auger electrons Lecture Objectives Describe the structure of the nucleus Calculate nuclear binding energies Identify factors affecting nuclear stability 1

2 Bohr model (1913) Nucleus contains positive charge and most of mass Diameter around cm Electrons surround nucleus and revolve around nucleus Planetary model Equal numbers of protons and electrons Net charge of zero Bohr model (1913) Bohr model (1913) Two problems: According to classical physics Electrons in orbits should repel each other making atom unstable, and Electrons in circular orbits should radiate energy and spiral into nucleus 2

3 Bohr model (1913) Two postulates: Electrons revolve in specified orbits with fixed radii Electrons gain or lose energy only when they jump from one orbit to another Bohr model (1913) Orbits labeled with numbers quantum numbers Energy gain (or loss) given by Properties of electron Charge = coulomb Mass = kg Choose electron charge as practical unit of charge set electron charge to -1 3

4 Electronic energy levels Bohr theory gives specified orbits n is index of quantized orbit principal quantum number n = 1,2,3, Given n we can calculate radius of orbit and energy of orbit n identifies shell of atom Electronic energy levels How to fill electron shells: General principle: Any system tries to seek the lowest total energy state. Zero energy electron infinitely far from nucleus Energy of electron in orbit is negative Lowest energy is innermost orbit Maximum number of electrons in shell = 2n 2 Electronic energy levels 4

5 Electronic energy sublevels 3 additional quantum numbers Azimuthal quantum number (l) eccentricity of orbit l = 0,1,,n-1 Magnetic quantum number (m) orientation in magnetic field m = -l,,0,,+l Spin quantum number (s) intrinsic electron property s = ½ Pauli Exclusion Principle No two electrons can have the same set of quantum numbers. Binding energy (E b ) Energy required to remove electron completely from atom Normally E b < 0 energy must be supplied 5

6 Binding energy (E b ) E b (ev) n shell hydrogen tungsten 1 K ,500 2 L ,280 3 M ,810 4 N O Note dependence of binding energy on n, size of nucleus Binding energy (E b ) Dependence on n Closer electron is to nucleus, stronger the attractive force from nucleus Closer electron is to nucleus, less shielding of nuclear charge by other electrons Dependence on Z Greater the number of protons in nucleus, stronger the attractive force from nucleus Electron transitions Photon or electron interacting with inner shell electron gives it enough energy to remove it from atom Leaves vacancy called hole Probability of producing a hole is probability of interaction occurring 6

7 Electron transitions Outer shell electron moves into inner shell vacancy loss of energy Energy given off as radiation characteristic radiation Energy used to eject another electron Auger electron Valence electrons Electrons in outermost shell No more than 8 electrons in outermost shell Valence electrons determine chemical properties of elements Explain periodic table periodicity of like chemical behavior Nuclear structure Nucleus composed of protons and neutrons nucleons mass = kg for both protons and neutrons charge = C for proton no charge for neutron Note that proton charge same as electron charge but of opposite sign 7

8 Mass number atomic number Mass number (A) -- number of nucleons (protons + neutrons) in nucleus Gives some indication of mass of nucleus Atomic number (Z) -- number of protons in nucleus and number of electrons in neutral atom Neutron number (N) -- number of neutrons in nucleus relationship: A = Z + N Atomic mass unit Unit of mass atomic mass unit (amu) defined as mass of carbon nucleus with 6 protons and 6 neutrons 1 amu = kg (Note: Some sources say carbon atom, rather than nucleus.) Atomic mass unit Masses: electron proton neutron = amu = amu = amu 8

9 Models of nuclear structures Liquid drop model (Bohr) Nucleus composed of closely-packed nucleons Shell model (Mayer) Discrete energy levels in nucleus Analogous to electron shells as evidenced by stability of Z =2, 8, 20, 82, 126, suggesting filled nuclear shells n/p ratio used as measure of stability Stability of nuclei Nuclei with even numbers of protons or neutrons are more stable than those with odd numbers Pairing of nuclear spins gives rise to lower energy # of protons # of neutrons # stable isotopes Even Even 165 Even Odd 57 Odd Even 53 Odd Odd 6 9

10 Indicators of stability Magic numbers 2,8,20,28,50,82,126 filled shells Line of stability N = Z for low Z Even vs odd Even more stable than odd Nuclear force Protons should repel each other in nucleus due to electrostatic repulsion Require short range force to hold nucleus together Short range force is approximately 100 times stronger than electromagnetic force Nuclear binding energy Mass of nucleus is less than sum of masses of nucleons in nucleus -- mass defect Mass defect represents energy in binding nucleons according to Einstein formula E=mc 2 Generally express masses in terms of rest energies: 1 amu = 931 MeV In these units 1 electron mass = MeV 10

11 Example Mass of 6 protons = 6 x amu = amu Mass of 6 neutrons = 6 x amu = amu Mass of 12 nucleons of 12 C = amu Example Mass of 12 nucleons of 12 C = amu Mass of 12 C nucleus = amu Mass defect = amu Example Binding energy of 12 C nucleus = amu x 931 MeV/amu = 89.0 MeV Average binding energy/nucleon = 89.0 MeV/12 nucleons = 7.42 MeV/nucleon 11

12 Plot binding energy/nucleon vs mass number Note low values for small A, rising to maximum in range A = 60-80, then gradually decreasing Nuclear fission Splitting of high A nucleus after absorbing slow neutron 235 U + slow neutron 92 Kr Ba + 3n + energy Energy released approximately 200 MeV per fission Nuclear fission Neutrons produced can cause fission in other U nuclei giving rise to chain reaction Uncontrolled chain reaction atomic bomb Controlled chain reaction nuclear reactor Chain controlled by absorbing some of the neutrons produced in fission 12

13 Nomenclature Isotope same Z, different N 12 C, 14 C Isotone same N, different Z 3 H, 4 He Isobar same A, different Z,N 18 O, 18 F Isomer same Z,N, different nuclear energy states 99 Tc, 99m Tc 13

Basic Nuclear Theory. Lecture 1 The Atom and Nuclear Stability

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