1 THE NATURE OF LIGHT Light is also known as electromagnetic radiation Light is emitted by oscillating charges Oscillating charges create oscillating electric and magnetic fields Light is very peculiar in that it is a particle and a wave at the same time Our physical intuition tells us that this is impossible Waves are spread out as in ocean waves Particles are in one place localized as in a bowling ball Q How can something be spread out and localized at the same time A Who knows It is a mystery of nature THE WAVE NATURE OF LIGHT Light moves at a constant speed through a particular medium c speed of light in a vacuum air c 2 997 x 108 m s 670 000 000 mi hr Waves have two components wavelength Greek lambda distance between wave crests 1 1 0 5 sin x 0 0 5 1 1 0 0 5 10 x 15 20 18 85 frequency Greek nu how often wave crest moves up and down at a single point number of beats per second Hertz Hz 1 Hz 1 s 1 s 1 think of a boat bouncing up and down on waves Frequency and wavelength are related c 2 if we know we can calculate Example If light has a frequency of a mercury vapor lamp is 6 879 x 1014 Hz what is the wavelength of the light if we know we can calculate Example If a medical x ray coming from tungsten metal has a wavelength of 2 09 10 11 m what is the frequency of the light THE PARTICLE NATURE OF LIGHT light comes as particles called photons energy of a photon is proportional to frequency E h h Planck s constant h 6 626 x 10 34 J s Example How much energy does a photon coming from the KVNO radio tower with a frequency of 90 7 x 106 Hz have Photoelectric Effect Light shining on a metal surface may cause electrons to be ejected from the surface e Frequency of light needs to be above threshold frequency to induce to escape from the surface of the metal Albert Einstein proposed that the electrons are knocked off the surface with a particle of light Nobel 1921 The photoelectric effect can be explained as a collision between an electron and a photon 3 ELECTROMAGNETIC SPECTRUM Name Radio Microwave Infrared Visible Ultraviolet X ray Gamma Wavelength 300 km to 0 3 m 30 cm to 1 mm 1 0 mm to 780 nm 780 nm to 390 nm 390 nm to 1 nm 10 to 0 06 1 5 to 0 3 ym Frequency Hz 103 109 109 3 1011 3 1011 4 1014 4 1014 8 1014 8 1014 3 1017 3 1017 5 1019 2 1018 1033 LINE SPECTRA OF THE ELEMENTS The light emitted by pure elements has specific energies Therefore light of only specific wavelengths can be seen i e different colors can be seen This emitted light is called a line spectrum pl spectra Line spectra tell us that atoms can only have certain energy levels The atoms cannot have any arbitrary value of energy ATOMIC STRUCTURE HISTORY Review Thomson discovered cathode rays i e electrons Milliken found charges come in discrete units charge of electron is fundamental Rutherford found that atom has a very small yet very heavy nucleus BOHR S MODEL OF THE HYDROGEN ATOM History Scientists before Bohr knew atom was made of nucleus and electrons They didn t know where the electrons were or how they behaved They also knew each element had a distinct line spectrum 1913 Model Bohr assumed electrons traveled in orbits around nucleus Bohr also assumed that electrons could only have specific orbits Specific orbits were labeled with a quantum number Energies of orbits are 1 E n R H 2 n 1 2 3 4 n RH Rydberg constant for hydrogen 2 18 x 10 18 J Won Nobel Prize 1922 4 SCHEMATIC OF BOHR MODEL Orbits are quantized Electrons can not exist between defined orbits Using the Bohr Model to Calculate Spectra Spectra result from light being emitted or absorbed when atom changes energy i e when electron goes to different orbit emission energy of atom decreases i e electron orbits closer to nucleus absorption energy of atom increases i e electron orbits further from nucleus Change in energy is all or nothing Electron can not be in between energy levels ground state lowest possible energy state excited state any other state when energy in an atom changes we can calculate the change as E Ef Ei E R H 1 1 1 1 2 RH 2 RH 2 nf ni n i n 2f also consider that since E is the energy of the photon emitted or absorbed Ephoton Eatom Ef Ei h 5 an equation for the frequency of the photon can be written as 1 1 h RH 2 2 ni n f RH 1 1 2 2 h ni nf Example What frequency of light is emitted when the H atom changes its electron energy level from n 6 to n 3 Note Negative sign relates that radiation was emitted Frequencies usually reported as positive THE DUAL NATURE OF MATTER Bad News The Bohr model is wrong Electrons don t behave like planets Electrons have a wave nature that makes them spread out We have seen that light can behave as a wave and a particle This dual nature of light is also true for matter All matter behaves as a particle and a wave I e an electron an atom or a baseball all behave like a wave 6 DE BROGLIE WAVES MATTER WAVES All moving particles have a wavelength Wavelength of particle is inversely proportional to particle s momentum Recall Momentum is defined as mass velocity p m v or 1 p Thus proportionality is note smaller p implies higher higher p implies smaller The proportionality constant is Planck s constant Therefore the wavelength of a particle is h p De Broglie s Relation Picture of a de Broglie wave 0 981 1 0 5 f x 0 0 5 0 981 1 3 2 99 2 1 0 x 1 2 3 2 99 note that the wave is localized somewhat as wavelength decreases wave becomes more localized Note momentum has increased 0 976 1 0 5 g x 0 0 5 0 976 1 3 2 999 2 1 0 x 1 2 3 2 999 In the macroscopic world objects do not have large enough wavelengths to exhibit wave like behavior Only in the microscopic world as in the atom do objects exhibit wave like behavior 7 Let us illustrate with a couple of examples Example Calculate the wavelength of an electron when the electron is moving 2 18 x 106 m s me 9 109 x 10 31 kg h 6 626 x 10 34 J s 34 h h 6 626 x10 J s J s 3 34 x10 10 3 34 x10 10 6 31 p m v 9 109 x10 kg 2 18 x10 m s kg m 2 m2 2 s …