Atomic Model and Wave-Particle Duality

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To overcome these difficulties, Bohr made abold and daring hypothesis (postulate) :There are certain special states of motion (orbits), calledstationary states, in which the electron may exist withoutradiating electromagnetic energy.In the stationary states, theangular momentum L is given by:L= nh, n =1,2,3,....i.e. in the stationary states angular momentum Lis quantized in units of h !For circular orbits, r is always perpendicular to p.So the angular momentum L (= r x p), is simplyrp = mvr .h=h /2π46
The Bohr’s Atomic ModelThe postulate that angular momentum isquantized implies:mvr= nhFrom classical mechanics(F=ma), v and r are related by41vπε=0nhmrer22=mvr2Taken all together, r n isalso quantized!!!r n=4πεmeh022n2≡a0n2where a 0 is Bohr radius =0.0529nm47
Page 1 and 2: Atomic ModelandWave-Particle Dualit
Page 3 and 4: Mysterious Rays using Crookes Tubes
Page 5 and 6: Thomson’s Conclusions1. Cathode r
Page 7 and 8: Robert MillikanMillikan's oil drop
Page 9 and 10: Thomson and Millikan:electrons have
Page 11 and 12: Rutherford’s expectation and the
Page 13 and 14: The Scattering of α and β Particl
Page 15 and 16: SummaryAtoms: Electrons + Nucleus (
Page 17 and 18: Electromagnetic RadiationLight is a
Page 19 and 20: EM Waves: PowerAverage over one per
Page 21 and 22: Superposition of EM WavesEM waves o
Page 23 and 24: Thermal (Black Body) Radiation:Kirc
Page 25 and 26: Stefan-Boltzmann Law (1884)Maxwell
Page 27 and 28: Summaries for Emission by Black Bod
Page 29 and 30: Lord Rayleigh’s Attempt: UV Catas
Page 31 and 32: Planck’s ‘Act of Despair’ener
Page 33 and 34: Planck’s Quantum of LightEnergy e
Page 35 and 36: What can be measured?i) Rate of ele
Page 37 and 38: Einstein: “On a Heuristic Point o
Page 39 and 40: Photo-electron emission Einstein’
Page 41 and 42: Basic Properties of Atoms Small: ~
Page 43 and 44: Johann Balmer (1885) andJohannes Ry
Page 45: The Bohr’s Atomic ModelPotential
Page 49 and 50: E nSince the total energy of a circ
Page 51 and 52: Transition Energies An electron in
Page 53 and 54: The Bohr’s Atomic ModelSuccesses:
Page 55 and 56: Wave Properties of LightThere is no
Page 57 and 58: Compton ScatteringWith Bragg crysta
Page 59 and 60: Compton Scattering• Classically,
Page 61 and 62: Compton Effectλ’ -λ = (h/m e c)
Page 63 and 64: Problem: Is light Particle or Wave?
Page 65 and 66: De Broglie’s Matter Wave Hypothes
Page 67 and 68: De Broglie Wavelength of MovingObje
Page 69 and 70: Davisson and Germer (1926)e −φDc
Page 71 and 72: Neutron Diffraction ExperimentRecen
Page 73 and 74: Problem:Wave-Particle DualityHow sh
Page 75 and 76: Wave PacketNow, let’s assume that
Page 77 and 78: i.e.Wave PacketThe probability of f

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