Chapter 28Slide 2Importance of Hydrogen AtomSir Joseph John ThomsonEarly Models of the AtomRutherford’s Scattering ExperimentsRutherford Model of the AtomRutherford Model, ProblemsEmission SpectraEmission Spectrum of Hydrogen – EquationSpectral Lines of HydrogenAbsorption SpectraApplications of Absorption SpectrumNeils BohrThe Bohr Theory of HydrogenBohr’s Assumptions for HydrogenBohr’s Assumptions, contBohr RadiusQuantized EnergiesRadii and Energy of OrbitsSpecific Energy LevelsEnergy Level Diagram & EquationBohr’s Correspondence PrincipleSuccesses of the Bohr TheoryModifications of the Bohr Theory – Elliptical OrbitsModifications of the Bohr Theory – Zeeman EffectModifications of the Bohr Theory – Fine StructureSlide 28Atomic Transitions – Stimulated AbsorptionAtomic Transitions – Spontaneous EmissionAtomic Transitions – Stimulated EmissionPopulation InversionLasersLaser Beam – He Ne ExampleProduction of a Laser BeamHolographyHolography, contChapter 28Chapter 28Atomic PhysicsAtomic PhysicsGeneral PhysicsAtom PhysicsAtom PhysicsSections 1–4Sections 1–4General PhysicsImportance of Hydrogen AtomHydrogen is the simplest atomEnables us to understand the periodic tableIdeal system for performing precise comparisons of theory with experimentMuch of what we know about the hydrogen atom can be extended to other single-electron ions For example, He+ and Li2+General PhysicsSir Joseph John Thomson“J. J.” Thomson1856 - 1940Developed model of the atomDiscovered the electronDid extensive work with cathode ray deflections1906 Nobel Prize for discovery of electronGeneral PhysicsEarly Models of the AtomNewton’s model of the atom was a tiny, hard, indestructible sphere J.J. Thomson’s model of the atomA volume of positive chargeElectrons embedded throughout the volumeGeneral PhysicsRutherford’s Scattering ExperimentsThe source was a naturally radioactive material that produced alpha particles (He++)Most of the alpha particles passed though the gold foilA few deflected from their original pathsSome even reversed their direction of travelActive Figure: Rutherford ScatteringGeneral PhysicsRutherford Model of the AtomRutherford, 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 sunGeneral PhysicsRutherford Model, ProblemsAtoms 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 at a frequency related to their orbital speedThe radius should steadily decrease and the speed should steadily increase as this radiation is given ofThe electron should eventually spiral into the nucleus, but it doesn’tThe radiation frequency should steadily increase – should observe a continuous spectrum of radiation at progressively shorter and shorter wavelengths, but you don’tGeneral PhysicsEmission SpectraWhen a high voltage is applied to a gas at low pressure, it emits light characteristic of the gasWhen the emitted light is analyzed with a spectrometer, a series of discrete bright lines is observed - emission spectrumEach line has a diferent wavelength and colorGeneral PhysicsEmission Spectrum of Hydrogen – Equation The wavelengths of hydrogen’s spectral lines experimentally agree with the equationRH is the Rydberg constantRH = 1.0973732 x 107 m-1n is an integer, n = 3, 4, 5, 6, …The spectral lines correspond to diferent values of n22Hn121R1General PhysicsSpectral Lines of HydrogenThe Balmer Series has lines whose wavelengths are given by the preceding equationExamples of spectral linesn = 3, λ = 656.3 nmn = 4, λ = 486.1 nmn = 5, λ = 434.1 nmn = 6, λ = 410.2 nmGeneral PhysicsAbsorption SpectraAn element can also absorb light at specific wavelengthsAn absorption spectrum can be obtained by passing a continuous radiation spectrum through a vapor of the gasThe absorption spectrum consists of a series of dark lines superimposed on the otherwise continuous spectrumThe dark lines of the absorption spectrum coincide with the bright lines of the emission spectrumGeneral PhysicsApplications of Absorption SpectrumThe continuous spectrum emitted by the Sun passes through the cooler gases of the Sun’s atmosphereThe various absorption lines can be used to identify elements in the solar atmosphereLed to the discovery of heliumGeneral PhysicsNeils Bohr1885 – 1962Participated in the early development of quantum mechanicsHeaded Institute in Copenhagen1922 Nobel Prize for structure of atoms and radiation from atomsGeneral PhysicsThe Bohr Theory of HydrogenIn 1913 Bohr provided an explanation of atomic spectra that includes some features of the currently accepted theoryHis model includes both classical and non-classical ideasHis model included an attempt to explain why the atom was stableGeneral PhysicsBohr’s Assumptions for HydrogenThe electron moves in circular orbits around the proton under the influence of the Coulomb force of attractionThe Coulomb force produces the centripetal accelerationOnly certain electron orbits are stableThese are the orbits in which the atom does not emit energy in the form of electromagnetic radiationGeneral PhysicsBohr’s Assumptions, contRadiation is emitted by the atom when the electron “jumps” from a more energetic initial state to a lower stateThe frequency emitted in the “jump” is related to the change in the atom’s energyIt is generally not the same as the frequency of the electron’s orbital motionThe size of the allowed electron orbits is determined by a condition imposed on the electron’s orbital angular momentumLn = me v r = n ħ where n = 1, 2, 3, …General PhysicsBohr RadiusThe 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 nWhen n = 1, the orbit has the smallest radius, called the Bohr radius, aoao = 0.0529 nm2 221, 2, 3,ne enr nm k e hKGeneral PhysicsQuantized EnergiesThe total energy of the atom Using the radius equation for the
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