Chapter 25 Modern Optics and Matter Waves This image of the individual atoms in a silicon crystal was made by exploiting the wave properties of electrons Matter and light behave like particle and waves This is an important result of quantum physics Chapter Goal To explore the limits of the wave and particle models 2 4 09 1 Chapter 25 Modern Optics and Matter Waves Topics Spectroscopy Unlocking the Structure of Atoms X Ray Diffraction Photons Matter Waves Energy is Quantized 2 4 09 2 Does a photon of red light have more energy or less energy than a photon of blue light A More energy B Less energy 2 4 09 3 Does a photon of red light have more energy or less energy than a photon of blue light A More energy B Less energy 2 4 09 4 Spectroscopy Unlocking the Structure of Atoms There are two types of spectra continuous spectra and discrete spectra Hot self luminous objects such as the sun or an incandescent light bulb emit a continuous spectrum of light at every possible wavelength In contrast the light emitted by a gas discharge tube such as those used to make neon signs contains only certain discrete individual wavelengths Such a spectrum is called a discrete spectrum 2 4 09 5 Spectroscopy examples 2 4 09 6 There is some sort of pattern here 2 4 09 7 The Spectrum of Hydrogen Hydrogen is the simplest atom with one electron orbiting a proton and it also has the simplest atomic spectrum The emission lines have wavelengths which correspond to two integers m and n Every line in the hydrogen spectrum has a wavelength given by 2 4 09 8 Why the discrete atomic spectrum Electrons are bound to atomic nuclei as standing waves In normal atoms the electrons vibrate in the fundamental mode Excitations correspond to harmonic modes each corresponding to an integer Light is emitted or absorbed when an electron changes mode the light frequency determined by the difference frequency The spectrum of an atom is a representation of the music of electron motion in the atomic world A continuous spectrum corresponds to noise a jumble of overlapping signals at various frequencies What you learn in acoustics and optics applies to atoms 2 4 09 9 The fundamental dilemma of quantum physics Light appears normally to be a wave phenomenon Interference and diffraction provide the evidence But light has a particle aspect simultaneously Light energy and momentum appears in chunks quanta called photons Matter appears to be a particle phenomena Electrons nuclei atoms can be counted kerplink kerplank kerplunk But matter has a wave aspect simultaneously Matter energy and momentum is observed to exhibit interference and diffraction We know now light is one of several massless bosonic quantum fields while matter is comprised of massive fermionic quantum fields 2 4 09 10 The particle aspect of light The discrete particle nature of light is discovered at low intensity Photography illustrates amplification of quantum events at the atomic level 2 4 09 11 Photochemistry Crystals of Silver Bromide before and after development The Fundamentals of Photography by C E K Mees 1 Exposure Single photons break silver halide AgBr bonds in dispersion of AgBr crystals 2 Development and fixing Silver on photoactivated crystals deposited as black grain others removed 2 4 09 12 The Photon Model of Light 1 Light consists of discrete massless units called photons A photon travels in vacuum at the speed of light 3 00 108 m s 2 Each photon has energy where f is the frequency of the light and h is a universal constant called Planck s constant The value of Planck s constant is h 6 63 10 34 J s 3 The superposition of a sufficiently large number of photons has the characteristics of a classical light wave 2 4 09 13 Evidence for Photon Model of Light The universal Planck formula E hf was first developed By Planck to explain the shape of the continuous spectrum emitted by hot objects Einstein made the bold step of postulating the particle model to explain features of the energy spectrum of electrons ejected from metals by light For given light wavelength and frequency the energy imparted to electrons in atoms in all sorts of processes is governed by the universal Planck formula More in later chapters 2 4 09 14 EXAMPLE What frequency and photon energy corresponding to light of wavelength 550 nm This frequency and energy is typical of electron motion in atoms Compare radio frequencies 1 MHz 1e6 Hz 2 4 09 15 EXAMPLE A light bulb emits 1 Watt 1 Joule s of visible light energy How many photons per second are emitted That is not a number a human can count 2 4 09 16 Extreme light X rays are photons created by for example energetic electrons in the cores of heavy atoms and first appeared to be neutral penetrating particles The wave nature of X rays was discovered with a 3 D diffraction grating of extremely fine pitch corresponding to their wavelength being of order interatomic dimensions 0 1 0 2 nm a crystal 2 4 09 17 X Ray Diffraction Bragg condition Constructive interference from parallel planes if the interplane path length difference is a multiple of a wavelength Diffraction from a known crystal gives wavelength If the wavelength is known crystal structure may be determined 2 4 09 18 Evidence for matter waves In 1927 Davisson and Germer discovered electrons incident normal to a crystal face at a speed of 4 35 106 m s exhibited a diffraction pattern similar to X ray scattering and from the Bragg condition deduced an electron wavelength for that speed 2 4 09 19 The de Broglie Wavelength De Broglie had already boldly postulated that a particle of mass m and momentum p mv has a wavelength where h is Planck s constant This wavelength for material particles is now called the de Broglie wavelength The same formula applies to light and massless photons De Broglie guessed the quantum features and conundrum of light were universal 2 4 09 20 EXAMPLE 25 4 The de Broglie wavelength of an electron Tah dah 2 4 09 The story of how the electron mass is measured comes later 21 Confined particle standing waves Consider a particle of mass m confined inside a rigid box of length L In the wave picture reflections create a standing wave The wavelength of a standing wave is related to the length L of the confining region by 2 4 09 22 Energy of confined particles is quantized The discrete values of wavelength imply discrete values of momentum and discrete levels of energy E p2 2m A confined particle can only have certain energies This is called the quantization of energy The
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