Announcements. A test of General Relativity. Gravitational Radiation. Other Consequences of GR

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1 Announcements HW1: Ch.2-70, 75, 76, 87, 92, 97, 99, 104, 111 *** Lab start-up meeting with TA This Week *** Lab manual is posted on the course web *** Course Web Page *** Lecture Notes, HW Assignments, Schedule for thephysics Colloquium, etc.. A test of General Relativity! Can test to see if the path of light appears curved to us! Local massive object is the sun! Can observe apparent position of stars with and without the sun 2 Other Consequences of GR! Time dilation from gravity effects! Gravitational Radiation!! Created when big gravity sources are moved around quickly! Similar to the electromagnetic waves that were caused by moving electron charges quickly! Black Holes! xpanding Universe (although instein missed the chance to predict it! He didn t believed) 3 Gravitational Radiation! When a mass is moved, the curvature of space-time changes! Gravitational radiation carries energy and momentum and wiggles mass in its path 4

2 vidence for Gravity Waves! In 1974, Joseph Taylor and his student Russell Hulse discovered a binary neutron star system losing energy as expected from gravitational radiation Direct Detection of Gravity Waves LIGO is a collection of large laser interferometers searching for gravity waves generated by exploding stars or colliding black holes 5 Phy107 Fall Nobel Prize in 2006! For the universe to start small and expand space and time must be thing that can expand(or contract)! General relativity was key physics needed to understand that process! However, a simple model of that would predict such a universe would not have clumps of matter(stars, galaxies)! Unless those clumping were present very early on! 2006 Nobel prize was given to the people who designed the COB experiment which was sensitive enough to see those clumping in the CMB v/c Maxwell s quations of electromagnetism (1873) Relativistic mechanics, l.-mag. (1905) Classical physics Newtonian Mechanics, Thermodynamics Statistical Mechanics Conclusion Relativistic quantum mechanics (1927-) Quantum mechanics (1920 s-) h/s Question: Should we use relativistic or classical approach to describe the motion of an electron in H atom?

3 Outline: Lecture 6 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?! 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 blackbody spectrum of thermal radiation Black body: In physics, a black body is an idealized object that absorbs all &M radiation that falls on it. " 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. As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. 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? 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,where h is the Planck s constant - at odds with the classical tradition, where energy was always associated with amplitude, not frequency Also, in terms of the angular frequency where (More in Appendix C)

4 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 ( Planck Constant ) 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 1918 Nobel prize!! 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 RMINDR:: Waves (based on PHYS 1408/2401) Wave equation in one dimension for any quantity!: Solution: a plane wave traveling in the negative (positive) direction x with velocity v: v the phase velocity Harmonic plane wave traveling in the positive direction x: angular frequency lectromagnetic waves: (transverse in free space) wave number! A 0 -A 0! A 0 -A 0 t = 0 t = t 0! T vt 0 x x t

5 The Photoelectric ffect (Albert instein 1905) Photoelectric ffect Historical Note: The photoelectric effect was accidentally discovered by Heinrich Hertz in 1887 during the course of the experiment that discovered radio waves. Hertz died (at age 36) before the first Nobel Prize was awarded. Observation: when a negatively charged body was illuminated with UV light, its charge was diminished. J.J. Thomson and P. Lenard determined the ratio e/m for the particles emitted by the body under illumination the same as for electrons. The effect remained unexplained until 1905 when 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. metal Phenomenon observed long time before instein, and something very strange was observed: Robert Milliken carried out a careful set of experiments, extending over ten years, that verified the predictions of instein s photon theory of light. instein was awarded the 1921 Nobel Prize in physics: "For his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." Milliken received the Prize in 1923 for his work on the elementary charge of electricity (the oil drop experiment) and on the photoelectric effect. The Photoelectric ffect (Albert instein 1905) The Photoelectric ffect (Albert instein 1905) ven With Very strong light of low frequency metal Contradicting Classical Wave Physics NO electrons ejected ven With Very-Very weak light intensity, but of high enough frequency lectrons ejected

6 Planck s Law ( = nhf) Photoelectric ffect (Threshold frequency) The Photoelectric ffect (Albert instein 1905) Albert instein proposed: The light is behaving as a collection of particles called photons each of them having energy = hf ven With Very-Very weak light intensity, photon beam but of high enough frequency = hf = nhf lectrons ejected What happens is that 1 PHOTON ejects 1 LCTRON xample (1): Very intensive light beam, low frequency light xample (2): SINGL PHOTON Very weak light beam of high frequency photon beam = hf = nhf SMALL (below the threshold) LARG (n is large) photon beam = hf = photon = nhf LARG (above the threshold) NO lectrons ejected 1 electron ejected There is no PHOTON capable of ejecting an LCTRON The PHOTON ejects 1 LCTRON

7 nergy Conservation: Also known at that time: photon = hf K max = hf "!! To free an electron from the metal, one has to pay a certain amount of energy the Work Function! = 380nm Repels electrons U < 2Volts " =?! f max min =? =?

8 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. 2. The threshold wavelength for emission of electrons from a given metal surface is 380nm. (a)! what will be the max kinetic energy of ejected electrons when "is changed to 240nm? (b)! what is the maximum electron speed? 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. 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 2. The threshold wavelength for emission of electrons from a given metal surface is 380nm. (a)! what will be the max kinetic energy of ejected electrons when "is changed to 240nm? (b)! what is the maximum electron speed? (a) (b) X-rays can be produced by smashing highspeed electrons into a metal target. When they hit, these decelerating charge produce much radiation, called Bremsstrahlung

9 The Production of X-Rays (Wilhelm Roentgen 1901) (The reverse of the Photoelectric ffect) SURPRIS: xperiments indicate a cutoff wavelength: There is no classical explanation for so sharp a termination of the spectrum Frequency f, nergy =hf CLASSICAL physics: Radiation covers entire spectrum Bremsstrahlung 1 photon -> 1 electron (?) 1 electron -> 1 photon (?) SURPRIS: xperiments indicate a cutoff wavelength: 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. Frequency f INDD: Setting the K of an incoming electron = of one photon Frequency f INDD: 1 electron -> 1 photon

10 The Compton effect (Arthur Compton 1927) Momentum & nergy when a photon strike a free electron Is this true? Compton provided the 1 st experimental evidence!! momentum energy Hypothesis: xperiment? Before Collision: A photon approaches an electron at rest Momentum & nergy when a photon strike a free electron Momentum & nergy when a photon strike a free electron After Collision: The electron scatters at speed u, angle #. A photon of wavelength " scatters at angle $ nergy and Momentum Conservation

11 X-ray detector The Compton ffect X-ray tube target (light atoms, e.g. graphite) Photons carry momentum like particles and scatter individually with other particles indeed, the wavelength shift is independent of the target material and the initial photon wavelength. e -