Lecture #1: Quantum Mechanics Historical Background Photoelectric Effect. Compton Scattering

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1 561 Fall 2017 Leture #1 page 1 Leture #1: Quantum Mehanis Historial Bakground Photoeletri Effet Compton Sattering Robert Field Experimental Spetrosopist = Quantum Mahinist TEXTBOOK: Quantum Chemistry, 2 nd Edition, D MQuarrie, University Siene (2007) Reommended: Spetra and Dynami of Small Moleules, R W Field, Springer, 2015 GRADING: 3 Thursday evening 50 minute exams (7:30 9:00 PM) tentatively Otober 5, 26, and November 30 One Leture anelled for eah exam ~9 problem sets usually posted online Friday and usually due 3:00 PM the following Friday There will be no graded problem set due the week of eah exam Points 300 (100 eah) 100 3Hour Final Exam during Exam Week (Deember 1821) 200 TOTAL 600 The Leture shedule is tentative The Leture Notes will be posted on the website, usually several days before the lass Revisions, usually printed in red, will be posted usually the day after the lass Leture Notes are pseudotext Everything in them is examrelevant Let s begin: Chalk demonstration Trajetory x(t), p(t): an predit endpoint x end, p end, t end, after observation of short segment of trajetory at early t Derease mass of thrower, halk, and target by 100 without modifying observers What happens? Derease by fator of What happens? How sure are you? Quantum Mehanis is a theory that desribes unexpeted phenomena in the mirosopi world without requiring any hange of our understanding of the marosopi world

2 561 Fall 2017 Leture #1 page 2 Quantum Mehanis is based on a theory of (in priniple) measurement without knowledge being allowed of what goes on between measurements Everything you an know must be the result of a (possible) measurement Key ideas of Quantum Mehanis to be seen in first few letures * lak of determinism: probabalisti * wavepartile duality for both light and matter * energy quantization and line spetra some of this should really bother you TODAY: Light is both wave and partile What are the familiar properties of light that make us believe that light is wavelike (as opposed to partilelike)? * refration, prism and lens * diffration; grating and pinhole * twoslit experiment Many wave phenomena involve interferene effets Add two waves (amplitude vs spatial oordinate): x + n Waves have + and amplitudes x x = n The result is perfet destrutive interferene Destrutive and Construtive Interferene What s nu? = / frequeny (s 1 )? speed of light in vauum (m/s) 6 wavelength (m) Return to this in next leture on wave harateristis of matter

3 561 Fall 2017 Leture #1 page 3 Two simple but surprising experiments that demonstrate the partile harater of light: photons * photoeletri effet * Compton Sattering A Photoeletri Effet Hertz 1886, Einstein 1906 What do you expet for light impinging on a flat metal surfae? Light is known to be eletromagneti radiation: * transverse osillating eletri and magneti fields * Intensity (Watts/m 2 ) ε 2 (Volts/m) 2 eletri field What do you expet the osillating eletri field of radiation, ε(t), to do to the e in a metal target? What effet does an eletri field have on a harged partile? 1 #e /se = urrent z} { i q {z} e eletron harge Observations vs intensity, I: i q e UV IR Why no ejeted e for IR light regardless of I?

4 561 Fall 2017 Leture #1 page 4 2 e /se vs frequeny at onstant I i/q e z} { {z} sudden onset of e prodution at ν 0 0 /h onset work funtion of metal (energy required to remove? one eletron from the bulk) HY Harbitrary onstant 3 KE of ejeted e vs ν at onstant I Measure by asking how high a potential energy hill an the ejeted e just barely limb? E stop = q e V stop > 0 ( q e < 0, V stop < 0) e must limb hill of height q e V stop This is the energy required to anel the KE of the ejeted e vs the frequeny of the inident light V stop 0 0 ν 0 ν * straight line with positive slope * onset at ν 0, slope independent of I * slope independent of whih metal Experimental results are desribed by the following equation:

5 561 Fall 2017 Leture #1 page 5 E stop (ν) = q e V stop (ν) = h(ν ν 0 ) = hν φ Plank s onstant is diretly measured by slope of E stop vs ν Leads us to think of light as omposed of disrete pakets of energy alled photons Energy of photon is E = hν Is this the only sensible explanation of all of the experimental observations? Another property of photons: B Compton Sattering 1923 Plank s onstant Same for every metal! work funtion of metal (Different for eah metal) Xrays photons parafin blok (mostly e ) Observe angular distribution of sattered Xray radiation as well as that of the e ejeted from the parafin target This experiment provides evidene that light ats as a billiardlike partile with definite kineti energy (a salar quantity), KE, and momentum (a vetor quantity), p The sattering is explained by onservation of KE and p We start with the idea, suggested by the previously disussed photoeletri effet, that light onsists of photons with kineti energy KE KE = E(ν) = hν Hypothesize that photons also have momentum: p = E = hν = h λ ( E / has units of momentum) Use observation of onservation of E and p to predit features of the sattering that ould only be explained by the partile nature of light

6 561 Fall 2017 Leture #1 page 6 p out θ large θ, large p out p out p e pin = p out + p e (billiards) p out θ small θ, small p out p out p e Sine photon transfers some of its energy to e, the sattered photon will have less energy (longer λ) than the inident photon Can show that λ in λ = 2h sin2 θ 2 0 red shift The wavelength shift depends on the diretion of the sattered photon θ = 0 (forward) λ = 0 θ = π (bakward) λ = 2h h = Å Compton λ of e Sattered light at θ 0 is always redshifted Dependene of λ on θ is independent of λ in

7 561 Fall 2017 Leture #1 page 7 Experimental Verifiation: Use Xray region (short λ) so that λ λ measure aurately Light passes all tests for both partilelike and wavelike harater Derive Compton formula for θ = π NONLECTURE is large enough to Conservation of p = p out + p e λ = 2h for photon p =E/= hν = h λ bak sattering unit vetor pointing in +z diretion Momentum removed from photon is transferred to the eletron Conservation of p: 1 h + 1 λ in = p e h 2 λ (It is not neessary to make this approximation) Conservation of E: λ λ in + 2

8 561 Fall 2017 Leture #1 page 8 2 hν in = hν out + p e h λ in = h 2 + p e 1 1 = p 2 e λ in 2h λ in = p 2 e λ in 2h 2 2 insert onservation of p result λ in λ 2 = h 2 λ 2h 2 λ in = λ = 2h 4h2 2h = 2h for θ = π (red shift) A beautiful demonstration of Compton sattering is an e, photon oinidene experiment Cross and Ramsey, Phys Rev 80, 929 (1950) Measure sattered the single photon and the single sattered e that result from a single event The sattering angles are onsistent with E,p onservation laws END OF NONLECTURE Today: we saw two kinds of evidene for why light ats as a partile * photoeletri effet: light omes in disrete pakets with E = hν * Compton sattering: light paket has definite momentum NEXT LECTURE: evidene for wave nature of e 1 Rutherford planetary atom a lot of empty spae Why no radiative ollapse of e in irular orbit? 2 Diffration of Xray and e by metal foil 3 Bohr model * Bohr assumed that angular momentum is quantized * de Broglie showed that there are integer number of e wavelengths around a Bohr orbit

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