7 1 Chapter 7 The Quantum Mechanical Model of the Atom Electromagnetic Radiation amplitude E h c continuous spectrum line spectrum Fundamental equations You must know the relative ordering of the various regions of the electromagnetic spectrum E 7 2 What is the wavelength range of visible light Example What is the wavelength of a radio signal operating at a frequency of 90 1 MHz Example What is the energy of this radio signal expressed in kJ mol Properties of Waves Refraction Interference Constructive Interference Destructive Interference 7 3 Diffraction Two slit Interference Evidence for the Particle Nature of Light The Photoelectric Effect and Atomic Spectra Classical Mechanics 1 The Photoelectric Effect The classical electromagnetic theory explanation of the photoelectric effect Classical theory would predict A dim light should result in 7 4 Two observations that did not fit with classical mechanics Presence of a frequency Example Na s 0 6 7 x 1014Hz blue light but red light 4 0 x 1014Hz Absence of a lag Einstein proposed that a beam of light behaves as if it were composed of a string of small or called The energy of a photon depends only on and not on The intensity of light corresponds to A rough analogy ping pong balls thrown at a window The main conclusions 1 In addition to behaving as light also behaves as 2 Energy is meaning it exists only in Continuous vs Quantized 2 Atomic Spectra Observation The light given off by excited H atoms is not a spectrum but rather a spectrum One explanation Bohr s Model of Hydrogen 7 5 En where En n E E Example Calculate the wavelength of light emitted absorbed when a hydrogen electron makes a transition from the n state to the n state Show the energy diagram for a hydrogen atom E The Main Point Energy is Quantum Mechanics says that the amount of energy that can be transferred is That is energy can only be transferred in discrete units of size The smallest packet of energy is called a An individual packet or particle of electromagnetic radiation is called a 7 6 Wave like Properties of Matter So up to this point science was indicating that light which is has characteristics de Broglie proposed that if energy is then perhaps matter is Since Ephoton and E Einstein s relativistic equation substitute solve for This indicates that a photon with wavelength exhibits a sometimes called the For a particle traveling at velocity v de Broglie equation 6 Example What is the characteristic wavelength associated with an electron moving at a velocity of 5 97 x 10 m s 31 Given mass of an electron is 9 11 x 10 kg Example What is the characteristic wavelength associated with a baseball thrown 95 mi hr Given mass of a baseball 5 0 oz and 16 oz 0 4536 kg and 1 mi 1 609 km Quantum Mechanics and the Heisenberg Uncertainty Principle Niels Bohr initially suggested that electrons exist in Quantum Mechanics treats electrons differently Quantum Mechanics says that an electron has both and properties The Heisenberg uncertainty principle says it is impossible to know both the and the of a particle simultaneously 7 7 Mathematically Thus we cannot assign for electrons and the most we can hope to know is the of finding an electron in a given region of space Since an electron has wave like properties quantum mechanics is also called QM is a of an electron Schr dinger s equation where What is the physical meaning of So when Schr dinger s equation is solved for the lowest energy electron in hydrogen you get a Shapes of Orbitals 7 8 Quantum Numbers Quantum mechanics uses quantum numbers to describe the allowable states of an electron in an atom Four quantum numbers completely describe the state of an electron in an atom n l ml and ms Important If you understand electron configurations then you can understand quantum numbers Electron configurations are just a simpler way of communicating much of the information that we get from quantum numbers You need to know four things about quantum numbers the letter designation the name what that quantum number describes and the possible values of that quantum number letter designation name what the quantum number describes possible values