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UK PHY 213 - Lecture 23 Atomic Physics

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Physics 213 General PhysicsPowerPoint PresentationEarly Models of the AtomScattering ExperimentsSlide 5Early Models of the Atom, Rutherford ModelDifficulties with the Rutherford ModelBohr’s Assumptions for Hydrogen Part 1 -- ElectrostaticsBohr’s Assumptions for Hydrogen Part 1 – Electrostatics (derived)Quantization in Bohr’s Hydrogen ModelSlide 11Quantization in Bohr’s Hydrogen Model – Energy LevelsRadii and Energy of OrbitsBohr RadiusSuccesses of the Bohr TheorySlide 16Generalized EquationEnergy Level DiagramExamples of Emission SpectraSlide 20Quantum Mechanics and the Hydrogen AtomElectron CloudsElectron Clouds, contQuantum NumbersQuantum Number SummaryZeeman EffectShells and SubshellsSpin Magnetic Quantum NumberSlide 29The Pauli Exclusion PrincipleFilling ShellsThe Periodic TableAtomic Transitions – Stimulated AbsorptionAtomic Transitions – Spontaneous EmissionAtomic Transitions – Stimulated EmissionPopulation InversionLasersLaser Beam – He Ne ExampleProduction of a Laser BeamPhysics 213General PhysicsLecture 232Last Meeting: Quantum PhysicsToday: Atomic PhysicsEarly Models of the AtomJ.J. Thomson’s model of the atomA volume of positive chargeElectrons embedded throughout the volumeA change from Newton’s model of the atom as a tiny, hard, indestructible sphereScattering ExperimentsThe source was a naturally radioactive material that produced alpha particlesMost of the alpha particles passed though the foilA few deflected from their original pathsSome even reversed their direction of travel5Early Models of the Atom, Rutherford ModelRutherford, 1911Planetary modelBased on results of thin foil experimentsPositive charge is concentrated in the center of the atom, called the nucleusElectrons orbit the nucleus like planets orbit the sunDifficulties with the Rutherford ModelAtoms emit certain discrete characteristic frequencies of electromagnetic radiationThe Rutherford model is unable to explain this phenomenaRutherford’s electrons are undergoing a centripetal acceleration and so should radiate electromagnetic waves of the same frequencyThe radius should steadily decrease as this radiation is given offThe electron should eventually spiral into the nucleus, but it doesn’tBohr’s Assumptions for HydrogenPart 1 -- ElectrostaticsThe electron moves in circular orbits around the proton under the influence of the Coulomb force of attractionThe Coulomb force produces the centripetal accelerationBohr’s Assumptions for HydrogenPart 1 – Electrostatics (derived)Total energy is sum of KE and PECentripetal force = Coulomb attractionSolve for mev2 to find total energy.This is a bound state because < 0.0221222222rekErekrvmrekvmPEKEEeeeeeQuantization in Bohr’s Hydrogen ModelWhat keeps the kenetic energy from radiating away?*The quantization conditionQuantization in Bohr’s Hydrogen Model – Energy LevelsContinuous boundaryConditions for wave.n= 1, 2, 3, …Use with centripetal force relationSolve for rnPlug this into E to Determine EneVnrekEekmhnrrekrvmrmnhvvmhnrneneeneeee2222222226.132)2(22Radii and Energy of OrbitsA general expression for the radius of any orbit in a hydrogen atom isrn = n2 aoThe energy of any orbit isEn = - 13.6 eV/ n2Bohr RadiusThe radii of the Bohr orbits are quantized This is based on the assumption that the electron can only exist in certain allowed orbits determined by the integer nWhen n = 1, the orbit has the smallest radius, called the Bohr radius, aoao = 0.052 9 nm2 221, 2, 3,ne enr nm k e Successes of the Bohr TheoryExplained several features of the hydrogen spectrumCan be extended to “hydrogen-like” atomsThose with one electronZe2 needs to be substituted for e2 in equationsZ is the atomic number of the element16Generalized Equation For the Balmer series, nf = 2 For the Lyman series, nf = 1Whenever an transition occurs between a state, ni to another state, nf (where ni > nf), a photon is emittedThe photon has a frequency f = (Ei – Ef)/h and wavelength λ 22111ifHnnREnergy Level DiagramThe value of RH from Bohr’s analysis is in excellent agreement with the experimental valueThe generalized equation can be used to find the wavelengths of any spectral linesExamples of Emission Spectra20 ∞Quantum Mechanics and the Hydrogen AtomOne of the first great achievements of quantum mechanics was the solution of the wave equation for the hydrogen atomThe energies of the allowed states are in exact agreement with the values obtained by Bohr when the allowed energy levels depend only on the principle quantum numbersElectron CloudsThe graph shows the solution to the wave equation for hydrogen in the ground stateThe curve peaks at the Bohr radiusThe electron is not confined to a particular orbital distance from the nucleusThe probability of finding the electron at the Bohr radius is a maximumElectron Clouds, contThe wave function for hydrogen in the ground state is symmetricThe electron can be found in a spherical region surrounding the nucleusThe result is interpreted by viewing the electron as a cloud surrounding the nucleusThe densest regions of the cloud represent the highest probability for finding the electronQuantum Numbersn – principle quantum numberTwo other quantum numbers emerge from the solution of Schrödinger equationl – orbital quantum numberml – orbital magnetic quantum numberQuantum Number SummaryThe values of n can range from 1 to  in integer stepsThe values of ℓ can range from 0 to n-1 in integer stepsThe values of m ℓ can range from -ℓ to ℓ in integer stepsZeeman EffectThe Zeeman effect is the splitting of spectral lines in a strong magnetic fieldThis indicates that the energy of an electron is slightly modified when the atom is immersed in a magnetic fieldThis is seen in the quantum number m ℓShells and SubshellsAll states with the same principle quantum number, n, are said to form a shellShells are identified as K, L, M, …Correspond to n = 1, 2, 3, …The states with given values of m and l are said to form a subshellSpin Magnetic Quantum NumberSome spectral lines were found to actually be two very closely spaced linesThis splitting is called fine structureA fourth quantum number, spin magnetic quantum number, was introduced to explain fine structureSpin Magnetic Quantum NumberIt is convenient to think of the electron as


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UK PHY 213 - Lecture 23 Atomic Physics

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