Chapter. 3 Wave & Particles I

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1 Announcement Course webpage Textbook PHYS-3301 Lecture 7 HW2 (due 9/21) Chapter 2 63, 65, 70, 75, 76, 87, 92, 97 Sep. 19, 2017 Outline: Chapter. 3 Wave & Particles I M- Waves behaving like Particles Blackbody Radiation (Plank; 1900; 1918*) The Photoelectric ffect (instein; 1905; 1921*) The Production of X-Rays (Rontgen;1901; 1901*) The Compton ffect (Compton; 1927; 1927*) Pair Production (Anderson; 1932; 1936*) Is It a Wave or a Particle? à Duality? Newton(1704): light as a stream of particles. Historical Development Descartes (1637), Huygens, Young, Fresnel (1821), Maxwell: by mid-19 th century,the wave nature of light was established (interference and diffraction, transverse nature of M-waves). Physics of the 19 th century: mostly investigation of light waves Physics of the 20 th century: interaction of light with matter One of the challenges understanding the black body spectrum of thermal radiation Black body: In physics, a black body is an idealized object that absorbs all incident &M radiation. No &M radiation passes through the black body and none is reflected. Because no light is reflected or transmitted, the object appears black when it is cold. An approximate realization of a black body as a tiny hole in an insulated enclosure

2 Newton(1704): light as a stream of particles. Historical Development Descartes (1637), Huygens, Young, Fresnel (1821), Maxwell: by mid-19 th century,the wave nature of light was established (interference and diffraction, transverse nature of M-waves). Physics of the 19 th century: mostly investigation of light waves Physics of the 20 th century: interaction of light with matter One of the challenges understanding the black body spectrum of thermal radiation Black body: In physics, a black body is an idealized object that absorbs all incident &M radiation No &M radiation passes through it and none is reflected. Because no light is reflected or transmitted, the object appears black when it is cold. However, a black body emits a temperature-dependent spectrum of light. (see Fig.) This thermal radiation from a black body is termed black-body radiation. Black Body Radiation (Max Planck 1900) xperiment shows that as frequency increases, the blackbody spectral energy density reaches a max. then fall off. But, classical theory predicts a divergence!! Do we need a new theory? As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. (More in Appendix C) Historical Development In 1900, Planck suggested a solution based a revolutionary new idea: mission and absorption of &M radiation by matter has quantum nature: i.e. the energy of a quantum of &M radiation emitted or absorbed by a harmonic oscillator with the frequency f is given by the famous Planck s formula = h f,where h is the Planck s constant Also, in terms of the ω = 2π f =hω where h = angular frequency 2 h at odds with the classical tradition, where energy was always associated with amplitude, not frequency h π J s h J s The Planck s Black-Body Radiation Law: The nergy () in the electromagnetic radiation at a given frequency (f) may take on values restricted to = nhf where: n = an integer h = a constant h ( Planck Constant ) J s

3 Blackbody Radiation: A New Fundamental Constant Plank s spectral energy density is the critical link between temperature and &M radiation. Interestingly, although the assumption = nhf might suggest M radiation behaving as an integral number of particles of energy hf, he hesitated at the new frontier - others carried the revolution forward. For the discovery, Plank was awarded the Nobel prize in 1918!! xperimental Fact: = nhf BUT Why should the energy of an lectromagnetic wave be Quantized? (n= integer) No xplanation until 1905 Albert instein The Photoelectric ffect A wave is a Continuous Phenomenon The Photoelectric ffect (Albert instein 1905) The Photoelectric ffect (Albert instein 1905) Albert instein postulated the existence of quanta of light -- photons -- which, when absorbed by an electron near the surface of a material, could give the electron enough energy to escape from the material. ven With Very strong light of low frequency metal Phenomenon observed long time before instein, and something very strange was observed: metal Contradicting Classical Wave Physics NO electrons

4 The Photoelectric ffect (Albert instein 1905) Planck s Law ( = nhf) Photoelectric ffect (Threshold frequency) ven With Very-Very weak light intensity, but of high enough frequency lectrons Albert instein proposed: The light is behaving as a collection of particles called photons each of them having energy = hf The Photoelectric ffect (Albert instein 1905) xample (1): Very intensive light beam, low frequency light ven With Very-Very weak light intensity, photon beam but of high enough frequency = hf = nhf lectrons What happens is that 1 PHOTON ejects 1 LCTRON photon beam = hf = nhf SMALL (below the threshold) LARG (n is large) There is no PHOTON capable of ejecting an LCTRON NO lectrons

5 xample (2): SINGL PHOTON Very weak light beam of high frequency nergy Conservation: photon beam = hf = photon = nhf LARG (above the threshold) 1 electron photon = hf K max = hf "! The PHOTON ejects 1 LCTRON! Also known at that time: To free an electron from the metal, one has to pay a certain amount of energy the Work Function! = 380nm " =?! f max min =? =? Repels electrons Determine the max. wavelength light that can eject electrons from this metal. U < 2Volts

6 lectrons are from plate 1 with a certain max. K. If none have enough K to surmount the electrostatic P difference (qv), no electrons will reach place 2. qv ((=1.6x10-19 C) (2V) = 3.2 x J = 2 ev) is the max. that can be surmounted, so the max K must be 2 ev. Determine the max. wavelength (λ ) light that can eject electrons from this metal. The limit of ejecting electrons occurs when an incoming photon has only enough energy to free an electron from the metal, with none left for K. Using the equation, Problems 1. The work function of tungsten surface is 5.4eV. When the surface is illuminated by light of wavelength 175nm, the maximum photoelectron energy is 1.7eV. Find Planck s constant from these data. c Ke = hf W = h W λ Problems 1. The work function of tungsten surface is 5.4eV. When the surface is illuminated by light of wavelength 175nm, the maximum photoelectron energy is 1.7eV. Find Planck s constant from these data. 7 ( Ke + W) λ ( 1.7eV + 5.4eV) m 15 c h= = = ev s 8 Ke = hf W = h W c 3 10 m/ s λ = ev s J / ev = J s 2. The threshold wavelength for emission of electrons from a given metal surface is 380nm. (a) what will be the max kinetic energy of electrons when lis changed to 240nm? (b) what is the maximum electron speed? (b) (a) c h W c c c 1 1 K = h W = h h = hc = 1.9eV λ = e 0 λ1 λ1 λ0 λ1 λ0 2K 2 e 5 Ke = mv e /2 v= = m/ s me

7 The Production of X-Rays (Wilhelm Roentgen 1901) (The opposite of the Photoelectric ffect) We use the name X-rays for M radiation whose wavelengths are in the 10-2 nm to 10 nm region of spectrum The Production of X-Rays (Wilhelm Roentgen 1901) (The reverse of the Photoelectric ffect) X-rays can be produced by smashing highspeed electrons into a metal target. When they hit, these decelerating charge produce much radiation, called Bremsstrahlung CLASSICAL physics: Radiation covers entire spectrum Photon = wave Bremsstrahlung SURPRIS: xperiments indicate a cutoff wavelength: SURPRIS: xperiments indicate a cutoff wavelength: Oops!!! Not entire spectrum!! Frequency f, nergy =hf There is no classical explanation for so sharp a termination of the spectrum 1 photon -> 1 electron (?) 1 electron -> 1 photon (?) Frequency f INDD: If the radiation is quantized, the minimum allowed at f is hf (single photon). We can t produce half a photon, so if multiple electrons don t combine their s into a single photon, no photon could be produced of > K of a single electrons. Setting the K of an incoming electron = of one photon

8 Frequency f INDD: 1 electron -> 1 photon