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cphys351 c4:1 Chapter 4: Atomic Structure The Nuclear Atom The Atom as the smallest division of an element quantization of electric charge oil drop experiments q = ne e/m => mass of electrons neutral atoms as “natural” state “Plum Pudding” model BUT.....

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cphys351 c4:2 Rutherford scattering (alpha particles from heavy nuclei) = test of “plum pudding” model alpha particles emitted in some radioactive decays speeds ~ 2E7 m/s q = +2e, m ~ 8000 x m e ( is a He 4 nucleus) alpha source lead collimator thin foil light flash

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cphys351 c4:3 Expected (from plum pudding): small scattering angles, no back scattering Results: some larger scattering angles, including some back scattering The Nuclear Atom: small heavy nucleus (99.8% of atom’s mass) with positive electric charge ~ 1/100,000 radius of atom electron “cloud” => electrons orbit nucleus

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cphys351 c4:4 Rutherford Scattering (theoretical results):

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cphys351 c4:5 Rutherford’s ingredients: Newtonian Mechanics (F = ma) Coulomb Interaction => Distance of closest approach Example: The maximum KE of alpha particles from natural sources is 7.7 MeV. What is the distance of closest approach for a gold nucleus? (Z Au = 79)

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cphys351 c4:6 Electron Orbits: planetary models of the atom for the purposes of this discussion, take electron orbits to be circular Hydrogen: single electron atom Example 4.1: The ionization energy of Hydrogen is 13.6 eV (the energy required to liberate the electron from the atom). Find the orbital radius and speed of the electron in a hydrogen atom.

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cphys351 c4:7 Problems with the nuclear atom: accelerating charges radiate orbits cannot be stable!! considerable problems with atomic spectra

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cphys351 c4:8 Atomic Spectra emission line spectra (from thin, hot gas or vapor) spectrum tube contains rarified gas or vapor through which a high voltage is discharged screen or film prism collimating slit gas discharge tube Hydrogen Helium Mercury typical emission spectra emission spectra vs. absorption spectra 700nm400nm

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cphys351 c4:9 Hydrogen spectral series: patterns in the spectra

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cphys351 c4:10 Bohr Atom electron in orbit about nucleus atomic size ~ electron orbit radius (or see example 4.1) = 0.053 nm compare de Broglie wavelength with radius

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cphys351 c4:11 Bohr’s original hypothesis: quantize angular momentum of circular orbits... Bohr’s hypothesis justified by de Broglie wave theory

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cphys351 c4:12 Energy in the Bohr Atom E = 0eV n = E = -13.6eVn = 1 E = -3.40eVn = 2 n = 3... E > 0eV free electron

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cphys351 c4:13 Origin of Line Spectra Discrete Energy levels + conservation of energy + photons n f =1 -> Lyman, n f =2 -> Balmer, n f =3 -> Paschen, etc.

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cphys351 c4:14 Example 4.2: An electron collides with a hydrogen atom in its ground state(lowest energy) and excites it to a state of n = 3. How much energy was given to the hydrogen atom in this inelastic collision? Example 4.3: Hydrogen atoms in state of high quantum number have been created in the laboratory. (a) Find the quantum number of the Bohr orbit in a hydrogen atom whose radius is 0.0100mm. (b) What is the energy of a hydrogen atom in this state? Example 4.4: Find the longest wavelength present in the Balmer series of hydrogen

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cphys351 c4:15 The Correspondence Principle A new theory should encompass an old theory where the old theory was successful. Quantum theory approximates the results of classical mechanics when: quantum numbers are large h 0

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cphys351 c4:16 Classical treatment of radiation from “planetary” hydrogen: frequency of emitted light = frequency of orbits (+ harmonics) Quantum transition from n n p with p << n

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cphys351 c4:17 Refining the Bohr Atom nuclear motion: electron and nucleus orbit each other (each orbit center of mass). Two body problem => center of mass motion + relative motion (with reduced mass)

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cphys351 c4:18 Example 4.6: A “positronium” atom consists of an electron and a positron. Compare the spectrum of positronium to that of hydrogen Example 4.7: Muons are elementary particles with mass 207m e and + -e of charge. A muonic atom is formed by a negative muon with a proton. Find the radius of the first Bohr orbit and the ionization energy of the atom.

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cphys351 c4:19 Atomic spectra Atoms have discrete set of allowed energies ALL changes in atom’s energy have to be to an allowed state Absorption and emission spectra from conservation of energy Franck-Hertz Experiment: inelastic scattering of electrons by atoms ->atom only absorbs energy to E = e V EE h A VV VV

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cphys351 c4:20 The Laser: bright, monochromatic, coherent light source Excited State: state above ground state decays to lower states, with emission of photon (or other mechanism for energy transfer). Metastable State: “sort of stable” state state with a longer life time than ordinary excited states lifetime ~ 1E-3 s vs. 1E-8 s for ordinary states Three kinds of transitions EE h h h h h Induced Absorption Spontaneous Emission Induced Emission (Stimulated)

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cphys351 c4:21 pumping process fast emission to metastable state laser transition: stimulated emission h h h h ’ Energy levels for 4-level laser Light Amplification by Stimulated Emission of Radiation

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cphys351 c4:22 Other considerations: “recycling” inducing photons and selecting lasing transition: the laser cavity Fabret-Perot Interferometer = standing waves “Tunable” Dye Lasers Semiconductor Lasers Chemical Lasers

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cphys351 c4:23 Chapter 4 exercises:3,4,5,6,7,8,11,12,13,14,15,16,18,19,21,22,29,30,31,32,33,35

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E = hf E – energy of a quantum (Joules) h – Plank’s constant (6.626 x 10 -34 J s) f – frequency of absorbed or emitted EMR.

E = hf E – energy of a quantum (Joules) h – Plank’s constant (6.626 x 10 -34 J s) f – frequency of absorbed or emitted EMR.

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