CHAPTER 8 QUANTUM MECHANICS WAVE PARTICLE DUALITY AND THE SINGLE ELECTRON ATOM Electromagnetic waves can possess particle behavior o Same with electrons Einstein the Photon and the Union of Planck and the Photoelectric Effect Emitted electrons photoelectrons o Were liberated from metal surface by light Threshold for photoelectron release determined by the frequency of the radiation o Below threshold no photoelectrons are emitted no matter how long the light is on the metal surface Kinetic energy of the emitted photoelectron is directly proportional to the frequency of light striking the surface of the metal Emission of electrons Independent of the intensity of radiation Planks formula resolved disputes E h Energy of light was delivered to the metal surface as particles of light energy aka photons Einstein Surface left with Kinetic Energy equal to the difference between the original energy of the incident photon E hv and the threshold energy E0 hv0 required to free the electron o KE hv hv0 h v v0 o KE 0 for v v0 for v v0 Threshold is different for every metal work function of metal Momentum of the Photon E mc2 o Mass refers to the inertial mass of the photon result of the energy possessed by the photon Momentum of photon p mc h photon Photon has rest mass of zero but has a defined momentum Photon can collide like a projectile yet interfere like a wave Spectroscopy and the Study of Light Emission from Atoms Spectroscopy study of light emitted by atoms and molecules and separated into specific wavelengths Was the series of discrete separated emission lines of limited number from a given element that began to suggest that the pattern of the emission lines could be quantitatively deciphered Emission lines vary for each element Used to calculate wavelength o RH Rydberg constant 1 097 x 107 m 1 o n integer common to each series of spectral lines Brought quantitative foundation to studies of molecular structure o Also showed that science can t explain why this works Bohr Model of the Hydrogen Atom Assertions of Hydrogen Model o Hydrogen atom consists of negatively charged electron that can occupy several circular orbits around nucleus o Atoms have only certain allowable energy levels stationary states corresponds to orbit quantum number n o When atom is in stationary state doesn t emit electromagnetic radiation unless it jumps to a stationary state of a lower energy level or if it absorbs a photon and jumps up to a higher state o Each stationary state has a specific En o Jumping from one stationary state to another via absorbing or emitting a photon of energy equal to the difference between the energy of two stationary states E Eupper final Elower initial o Atoms will seek the lowest energy state Provided a basis for applying the laws of physics to the motion of the electrons in orbits Angular momentum of electron L mvr Calculate energy level of hydrogen atom As electron is drawn into attractive electrostatic field of nucleus energy DECREASES Electron jumps down energy levels more negative Energy atom becomes more stable The de Broglie Wavelength of the Electron Electron is confined to spatial scales on the order of the atomic size photon h mv h pphoton o Same with electron o Shows that if waves can be particles then particles could also be waves Nature of Waves and the Wave Equation Wavelength of electrons confined to spatial domain surrounding nucleaus Wavefunction connects amplitude and wavelength o o o Uncertainty in the Position of the Electron in the Square Well Potential Cannot accurately locate the particle within the envelope of it wavelength Attempting to increase the accuracy of determining the position of the particle by shrinking the dimension of the box uncertainty in the momentum of the particle increases proportionately Werner Heisenberg idea that measuring the position of an electron disturbs its momentum and measuring the momentum of an electron can result in altering its position CONCLUSIONS o N integer values energy of particle is quantized restricted to series of o Particle in a contained space cannot have zero energy can never be motionless discrete values called energy levels Must have energy if it is to exist The Schr dinger Equation The allowed quantized energies of the electron result form the boundary conditions imposed on the solution by the square well potential The Hydrogen Atom Energy of an electron in the Coulomb field of a single proton for hydrogen Energy Levels of the Hydrogen Atom Energy levels are uniquely determined by the single integer n Quantum Numbers that Define the Radial and Angular Solutions to the Schr dinger Equation Determine physical interpretation of those integer n l m quantum numbers Determine spatial shapes of Rn m l magnetic quantum number orbits orientation m s spin state spin direction n principal quantum number energy level size l azimuthal angular momentum quantum number shape Geometry and Spatial Characteristics of the Three Dimensional Waves of the Hydrogen Atom 1s orbital spherical 1s orbital zero radial nodes 2s orbital one radial node 3p orbital one radial node one angular node 3d orbital 2 angular nodes zero radial nodes Physical Interpretation of the Schr dinger Wavefunction Electron density position plays into the chemical behavior of the atoms of different elements and in the structure of chemical bonding Radial Distribution Function probability that an electron is found a certain distance from the nucleus wavefunction2