Mar 26, 2015

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1 Chapter 7 Atomic Structure Slide 2 2 Light n Made up of electromagnetic radiation n Waves of electric and magnetic fields at right angles to each other. Slide 3 3 Parts of a wave Wavelength Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second Slide 4 4 Frequency = Frequency = Slide 5 5 Kinds of EM waves n There are many different and different and n Radio waves, microwaves, x rays and gamma rays are all examples n Light is only the part our eyes can detect Gamma Rays Radio waves Slide 6 6 The speed of light n in a vacuum is 2.998 x 10 8 m/s n = c c = c = n What is the wavelength of light with a frequency 5.89 x 10 5 Hz? n What is the frequency of blue light with a wavelength of 484 nm? Slide 7 7 In 1900 n Matter and energy were seen as different from each other in fundamental ways n Matter was particles n Energy could come in waves, with any frequency. n Max Planck found that the cooling of hot objects couldnt be explained by viewing energy as a wave. Slide 8 8 Energy is Quantized Planck found E came in chunks with size h Planck found E came in chunks with size h E = nh E = nh n where n is an integer. n and h is Plancks constant n h = 6.626 x 10 -34 J s these packets of h are called quantum these packets of h are called quantum Slide 9 9 EinsteinEinstein is next Einstein n Said electromagnetic radiation is quantized in particles called photons Each photon has energy = h = hc/ Each photon has energy = h = hc/ n Combine this with E = mc 2 n you get the apparent mass of a photon m = h / ( c) m = h / ( c) Slide 10 10 Which is it? n Is energy a wave like light, or a particle? n Yes n Concept is called the Wave -Particle duality. n What about the other way, is matter a wave? n Yes Slide 11 11 Matter as a wave Using the velocity v instead of the frequency we get Using the velocity v instead of the frequency we get De Broglies equation = h/mv De Broglies equation = h/mv n can calculate the wavelength of an object Slide 12 12 Examples n The laser light of a CD is 7.80 x 10 2 m. What is the frequency of this light? n What is the energy of a photon of this light? n What is the apparent mass of a photon of this light? n What is the energy of a mole of these photons? Slide 13 13 What is the wavelength? n of an electron with a mass of 9.11 x 10 -31 kg traveling at 1.0 x 10 7 m/s? n Of a softball with a mass of 0.10 kg moving at 125 mi/hr? Slide 14 14 How do they know? n When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effect n because the waves interfere with each other. Slide 15 15 A wave moves toward a slit. Slide 16 16 Comes out as a curve Slide 17 17 with two holes Slide 18 18 with two holes Two Curves Slide 19 19 Two Curves with two holes Interfere with each other Slide 20 20 Two Curves with two holes Interfere with each other crests add up Slide 21 21 Several waves Slide 22 22 Several waves Several Curves Slide 23 23 Several waves Interference Pattern Several Curves Slide 24 24 What will an electron do? n It has mass, so it is matter. n A particle can only go through one hole n A wave goes through both holes n Light shows interference patterns interference patterns interference patterns Slide 25 Electron gun Electron as Particle Slide 26 Electron gun Electron as wave Slide 27 Which did it do? It made the diffraction pattern The electron is a wave Led to Schrdingers equation Slide 28 28 What will an electron do? n An electron does go though both, and makes an interference pattern. n It behaves like a wave. n Other matter has wavelengths too short to notice. Image Slide 29 29 Spectrum n The range of frequencies present in light. n White light has a continuous spectrum. n All the colors are possible. n A rainbow. Slide 30 30 Hydrogen spectrum n Emission spectrum because these are the colors it gives off or emits n Called a line spectrum. n There are just a few discrete lines showing 410 nm 434 nm 486 nm 656 nm Spectrum Slide 31 31 What this means n Only certain energies are allowed for the hydrogen atom. n Can only give off certain energies. Use E = h = hc / Use E = h = hc / n Energy in the atom is quantized Slide 32 32 Niels Bohr n Developed the quantum model of the hydrogen atom. n He said the atom was like a solar system n The electrons were attracted to the nucleus because of opposite charges. n Didnt fall in to the nucleus because it was moving around Slide 33 33 The Bohr Ring Atom n He didnt know why but only certain energies were allowed. n He called these allowed energies energy levels. n Putting energy into the atom moved the electron away from the nucleus n From ground state to excited state. n When it returns to ground state it gives off light of a certain energy Slide 34 34 The Bohr Ring Atom n = 3 n = 4 n = 2 n = 1 Slide 35 35 The Bohr Model n n is the energy level n for each energy level the energy is n Z is the nuclear charge, which is +1 for hydrogen. n E = -2.178 x 10 -18 J (Z 2 / n 2 ) n n = 1 is called the ground state when the electron is removed, n = when the electron is removed, n = n E = 0 Slide 36 36 We are worried about the change n When the electron moves from one energy level to another. E = E final - E initial E = E final - E initial E = -2.178 x 10 -18 J Z 2 (1/ n f 2 - 1/ n i 2 ) E = -2.178 x 10 -18 J Z 2 (1/ n f 2 - 1/ n i 2 ) Slide 37 37 Examples n Calculate the energy need to move an electron from its to the third energy level. n Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. n Calculate the energy released when an electron moves from n= 5 to n=3 in a He +1 ion Slide 38 38 When is it true? n Only for hydrogen atoms and other monoelectronic species. n Why the negative sign? n To increase the energy of the electron you make it further to the nucleus. n the maximum energy an electron can have is zero, at an infinite distance. Slide 39 39 The Bohr Model n Doesnt work n only works for hydrogen atoms n electrons dont move in circles n the quantization of energy is right, but not because they are circling like planets. Slide 40 40 The Quantum Mechanical Model n A totally new approach n De Broglie said matter could be like a wave. n De Broglie said they were like standing waves. n The vibrations of a stringed instrument Slide 41 41 Slide 42 42 Whats possible? n You can only have a standing wave if you have complete waves. n There are only certain allowed waves. n In the atom there are certain allowed waves called electrons. n 1925 Erwin Schroedinger described the wave function of the electron n Much math, but what is important are the solutions Slide 43 43 Schrdingers Equation n The wave function is a F(x, y, z) n Actually F(r,,) n Solutions to the equation are called orbitals. n These are not Bohr orbits. n Each solution is tied to a certain energy n These are the energy levels AnimationAnimationAnimation Slide 44 44 There is a limit to what we can know n We cant know how the electron is moving or how it gets from one energy level to another. n The Heisenberg Uncertainty Principle n There is a limit to how well we can know both the position and the momentum of an object. Slide 45 45 Mathematically x (mv) > h/4 x (mv) > h/4 x is the uncertainty in the position x is the uncertainty in the position (mv) is the uncertainty in the momentum. (mv) is the uncertainty in the momentum. the minimum uncertainty is h/4 the minimum uncertainty is h/4 Slide 46 46 Examples n What is the uncertainty in the position of an electron. mass 9.31 x 10 - 31 kg with an uncertainty in the speed of 0.100 m/s n What is the uncertainty in the position of a baseball, mass 0.145 kg with an uncertainty in the speed of 0.100 m/s Slide 47 47 What does the wave Function mean? n nothing. n it is not possible to visually map it. n The square of the function is the probability of finding an electron near a particular spot. n best way to visualize it is by mapping the places where the electron is likely to be found. Slide 48 48 Probability Distance from nucleus Slide 49 49 Sum of all Probabilities Distance from nucleus Slide 50 50 Defining the size n The nodal surface. n The size that encloses 90% to the total electron probability. n NOT at a certain distance, but a most likely distance. n For the first solution it is a a sphere. Slide 51 51 Quantum Numbers n There are many solutions to Schrdingers equation n Each solution can be described with quantum numbers that describe some aspect of the solution. n Principal quantum number (n) size and energy of an orbital n Has integer values >0 Slide 52 52 Quantum numbers Angular momentum quantum number l Angular momentum quantum number l n shape of the orbital n integer values from 0 to n-1 l = 0 is called s l = 0 is called s l = 1 is called p l = 1 is called p l =2 is called d l =2 is called d l =3 is called f l =3 is called f l =4 is called g l =4 is called g Slide 53 53 S orbitals Slide 54 54 P orbitals Slide 55 55 P Orbitals Slide 56 56 D orbitals Slide 57 57 F orbitals Slide 58 58 F orbitals Slide 59 59 Quantum numbers Magnetic quantum number (m l ) Magnetic quantum number (m l ) integer values between - l and + l tells direction in each shape Electron spin quantum number (m s ) Electron spin quantum number (m s ) Can have 2 values either +1/2 or -1/2 Slide 60 60 1. A 2. B 3. C 4. A 5. B 6. A 7. B 8. A 9. A Slide 61 61 Polyelectronic Atoms n More than one electron n three energy contributions n The kinetic energy of moving electrons n The potential energy of the attraction between the nucleus and the electrons. n The potential energy from repulsion of electrons Slide 62 62 Polyelectronic atoms n Cant solve Schrdingers equation exactly n Difficulty is repulsion of other electrons. n Solution is to treat each electron as if it were effected by the net field of charge from the attraction of the nucleus and the repulsion of the electrons. n Effective nuclea

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