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Quantum Mechanics Chapters 4 & 5 1 WAY WAY BACK IN TIME... Greek philosopher Democritus (460370 BCE.) substances that comprised nature – empty space – tiny particles “atoms” 2 Democritus different kinds of atoms existed not able to be broken down by ordinary means 3 Aristotle More popular a contemporary of Democritus matter was a continuous substance which he called "hyle“ this idea was accepted without support for nearly two thousand years. 4 pseudo- science explained natural phenomena in philosophical ways – without experimentation – without logic maggots come from rotting meat frogs cause warts 5 Isaac Newton, Robert Boyle and John Dalton Questioned natural occurrences conducted experiments – controlled variables made observations collected data data and observations used to support hypotheses 6 John Dalton matter is particulate in nature atoms of a single element are identical atoms of different elements are different from each other Dalton's hypothesis explained the observations first modern atomic theory 7 J.J. Thomson Are atoms really the smallest particles? Cathode ray tubes Rays originated at the cathode (negative electrode) and traveled toward the anode (positive electrode). Produced rays composed of negatively charged subatomic particles – he called particles electrons (e-). – mathematically calculated the electron's mass to 8 charge ratio Oil Drop Experiment Robert Millikan determined the charge of a single electron (-1) Oil Drop Experiment 9 Thomson Atom Plum Pudding Model Electrons 10 Atomic Research Ernest Rutherford – Niels Bohr – Hans Geiger – Ernest Marsden Experiment to study structure of atom – Gold Foil Experiment 11 Gold Foil Experiment Ernest Rutherford positively charged helium nuclei (alpha () particles) propelled at high speed toward a thin sheet (tissue paper-like) of gold foil surrounded by a fluorescent screen 12 Experimental Results: 1. Most of particles pass straight through foil 2. Some particles are slightly deflected 3. A few particles (1 per 8000) are deflected greatly. Nearly bounce back to origin. 13 Conclusions based on experimental data: 1. The atom is mostly space. 2. Mild deflection was caused by repulsion of similar electrostatic charge. Therefore, the atom has a positive region. 'Protons“ 3. The positive core is very small (1 x 10-12 of total atomic volume) and contains most of the atom's mass. 'Nucleus' 14 Rutherford Atom 15 The Atom is mostly empty space….. 16 Eugene Goldstein showed that protons created rays in a cathode ray tube just as the electrons had done traveled in the opposite direction. (anode to cathode) concluded that a proton is equal but opposite in charge to the electron, or 1+, and approximately 1836 times more massive 17 Thomson's observation Atoms that are – chemically identical can have variable mass 18 James Chadwick credited with the discovery of the neutral subatomic particle - the neutron Walter Bothe obtained initial evidence nearly two years before Chadwick's experiments Neutrons have a mass nearly identical to that of the proton, but no electrical charge. 19 Explanation lies with the neutrons Isotopes – Atoms of the same element containing different numbers of neutrons. Nuclide – a particular isotope Each isotope acts the same in chemical reaction Each nuclide will produce a product of different mass. 20 Hydrogen isotopes Proton + Protium 1 proton, 1 electron Neutron Deuterium 1 proton, 1 electron, 1 neutron Electron - Tritium 1 proton, 1 electron, 2 neutrons 21 TO SUMMARIZE... The atom is the smallest particle of matter that cannot be chemically subdivided. Composed of two regions and three primary subatomic particles. – Nucleus very small positively charged dense. – Protons – Neutrons Electron Cloud – Electrons orbit the nucleus. Small point-like negative charges 22 IN PERFECT BALANCE The atom is electrically neutral contain equal number of: – protons (positive charges) and – electrons (negative charges). 23 Remind you of anything? 24 Niels Bohr 1913 Introduced ‘Planetary Model’ 25 Planetary Model Gravity and Inertia 26 Solar System Attractive force: Atom – Gravity – Pulls planet toward sun + / - charges – + nucleus pulls – electrons toward it Repulsive force: – Inertia – Pushes planet in a straight line away from sun Attractive force: Repulsive force: 27 It Ought to Go SPLAT! “A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.” Some basic principles of synchrotron radiation. (document prepared by Antonio Juarez-Reyes, AMLM group, 2001) Electrons – constant orbit Energy drain and the atom goes SPLAT! 28 Electromagnetic Radiation 29 Electromagnetic Radiation c = 3.0 X 108 m/s Wavelength = λ Frequency = f (υ) 30 Electromagnetic Radiation Louis de Broglie Dual Nature of Light Wave Nature – Travels through space in waves – Travels at speed of light (c) Particle Nature – Interacts with matter as a particle – Quanta (unit of energy) transferred to matter in packets of light 31 (photons) 32 Electromagnetic Radiation Light → 33 Electromagnetic Radiation Light → Excited atomic state 34 Electromagnetic Radiation e- jumps to Higher Energy level Light → Excited atomic state 35 Electromagnetic Radiation e- jumps to Higher Energy level e- jumps to Lower Energy level Light → Excited atomic →→→→→→ state 36 Electromagnetic Radiation e- jumps to Higher Energy level e- jumps to Lower Energy level Light → Excited atomic →→→→→→ state 37 Electromagnetic Radiation e- jumps to Higher Energy level Light →Excited atomic state e- jumps to Lower Energy level →→→→→→ Atom in Ground State photon released 38 Electromagnetic Radiation e- jumps to Higher Energy level e- jumps to Lower Energy level Light →Excited atomic state →→→→→→ Atom in Ground State photon released Bright-line Spectrum 39 Electromagnetic Radiation Speed of wave Energy of photon E=hf c=fλ solving for frequency c=f λ c= λ ch= E= solving for frequency E=f h E h Eλ ch λ 40 Electromagnetic Radiation Irwin Schrodinger Developed the ‘Wave Equation’ to support de Broglie’s idea of the dual nature of light 41 Quantum Leap Bohr’s Planetary Model is used to explain the spectral lines produced by atoms. Quantum leap animation 42 Quantum Leap The color of light indicates its wavelength A particular wavelength has a definite frequency A particular wavelength has a definite amount of energy 43 Riding the Wave (Equation) The Wave Equation – confirmed Bohr’s theory of quantized energy levels. Treating electrons as waves, explains why the tiny negative electrons are not drawn into the more massive and positive nucleus 44 Riding the Wave “A charged particle constrained to move in curved path … radiates energy according to Maxwell equations.” Some basic principles of synchrotron radiation. (document prepared by Antonio Juarez-Reyes, AMLM group, 2001) As the e- approach the nucleus, their wavelengths become shorter. E = ch λ 45 Solar System Attractive force: Atom – Gravity – Pulls planet toward sun Repulsive force: – Inertia – Pushes planet in a straight line away from sun Attractive force: + / - charges – + nucleus pulls – electrons toward it Repulsive force: – Energy produced form the shorter λ pushes the e- away from the nucleus 46 QUANTUM MECHANICS Electrons do not obey the laws of classical or Newtonian physics A new science to describe the laws of small particles was established 47 LOOK! IT ISN'T THERE! Uncertainty principle Not possible to locate an electron's exact position Position and momentum cannot be determined at the same time to determine one you effect a change in the other Electrons - only "seen” when they jump from a higher to lower energy level. once electron is "seen," its direction and Werner Heisenberg speed are different from what they were prior to observation. Determining position changes its momentum. 48 Applies to electron when it is considered a particle WAVE REVIEWS! Irwin Schrodinger Wave equation – helps locate probable regions of electron population if considered it to be like a wave. – general paths of the electrons around the nucleus can be determined 49 50 MAP IT OUT! Electrons may be described by a set of four quantum numbers which serve as 3-D for electron location. 51 D.C. Map Activity Find – Union Station – Nat’l Air & Space Museum – Watergate Complex – Capitol – Ford’s Theater – White House – Lincoln Memorial – Kennedy Center A-B 5+ C-D 4 A-B C B B C B 0 5 3-4 2 1 0 52 The Quantum Numbers principle quantum number (n) – n = 1, 2, 3... – Distance of electron from nucleus. – Electrons exist ONLY in the energy levels. – No electrons have energies to exist between energy levels [nodes]. angular momentum (azimuthal) quantum number (l) – l = s, p, d, f – Shape of paths, subshells, sublevels, magnetic quantum number (m) – m = 1, 3, 5, 7 – Spatial orientation to x, y, z axes spin quantum number (s) – s = clockwise, counterclockwise – Electron spin 53 FIRST PRINCIPLE of QUANTUM MECHANICS Only specific energy levels are possible for electrons. The principle quantum number that corresponds to the energy levels begins with 1, 2, 3, etc. beginning with the level closest to the nucleus – – – – K energy level is 1 L energy level is 2 M energy level is 3 N energy level is 4, etc. 54 SECOND PRINCIPLE of QUANTUM MECHANICS The maximum number of electrons that can occupy and energy level is given by the equation 2(n)2 = maximum number of e– n is the principle quantum number of the energy level. – Principle quantum number is 2, the electron maximum is 2(2)2 = 8 – Principle quantum number is 3, the electron maximum is 2(3)2 = 18 55 DIVIDE and CONQUER! energy levels are actually several closely bound bands of energy Each of the bands represents a sub level The number of sublevels is the same as the principle quantum number It is represented by the angular momentum numbers – s, p, d, and f. 56 K energy level – principle quantum number is 1. – 1 sub level, s L energy level – principle quantum number is 2. – 2 sublevels, s, p M energy level – principle quantum number is 3. – 3 sublevels, s, p, d N energy level – principle quantum number is 4 – 4 sublevels s, p, d, f. The energy within a level varies. Lowest Energy Highest Energy s >>> p >>> d >>> f 57 Sublevels have characteristic shapes s 58 p 59 d 60 f 61 Magnetic Quantum Number 1, 3, 5, 7 represents the number of different paths (orbits) that the electron can take in relationship to the three axes of space 62 Wolfgang Pauli electron spectra affected by magnetic fields indicated that the electrons could be spinning in two different directions within the orbital – clockwise – counterclockwise 63 Pauli Exclusion Principle Spinning in one direction causes a magnetic field that is attracted to the north pole of a magnet Spinning in the opposite direction causes it to be attracted to a south pole If two electrons occupy the same orbital then they must spin in opposite directions If they did not they would repel each other as two like magnetic poles repel each other. 64 North Pole South Pole 65 Energy Levels are Subdivided ENERGY LEVELS s SUBLEVEL p SUB SHELL d f ORBITALS 1 1 2 3 1 2 3 4 5 1 2 3 4 5 6 7 ELECTRON PAIRS 1 2 1 21 21 2 1 2 1 21 2 1 21 2 1 21 21 21 21 21 212 66 Hierarchy no two electrons in same atom can have same set of four quantum numbers. What is the maximum number of quantum numbers that can be shared by two electrons? 3 67 Summary Chart ENERGY LEVEL PRINCIPLE QUANTUM NO. SUBLEVELS ORBITAL PER SUBLEVEL ORBITAL PER LEVEL ELECTRONS PER SUBLEVEL ELECTRONS PER LEVEL K 1 s 1 1 2 2 L 2 s p 1 3 4 2 6 8 M 3 s p d 1 3 5 9 2 6 10 18 N 4 s p d f 1 3 5 7 16 2 6 10 14 32 68 I'D RATHER STAY SINGLE most stable state of an atom - ground state actual arrangement of the electrons in atom referred to as the electron configuration 69 Hund's Rule electrons arrange themselves in such a way as to MAXIMIZE THE NUMBER OF UNPAIRED ELECTRONS in a sub level Only after one electron occupies each of the sublevel’s orbitals do the electrons begin to pair up and share the same orbital e- spin oppositely when in same orbital 70 OUTERMOST Energy Level Nucleus K Energy Level 2nd from the OUTERMOST Energy Level NEXT to the OUTERMOST Energy Level 71 POSTULATES of QUANTUM MECHANICS 1. 2. 3. 4. 5. The K energy level is the most tightly bound in any atom. The outermost energy level NEVER has more than 8 electrons. The next to the outermost level NEVER has more than 18 electrons. IF the next to the outermost level does not contain its maximum number of electrons (18 e-), THEN the outermost energy level can hold no more than 2 electrons. IF the second from the outermost energy level does not contain its maximum amount of electrons (2n2), THEN the next to the outermost energy level can hold no more than 9 electrons. 72 The Aufbau Principle Experimental data indicates that sublevels within the energy levels sometimes overlap the sublevels of other energy levels electrons fill the subshells of the lowest energies first Since overlapping occurs, a means of remembering the order of sub level energies is helpful 73 Aufbau Diagram (from German Aufbauprinzip, “building-up principle”) Electrons enter atom in this order Electons are removed from atom in the reverse order Last in first out. 74 ORBITAL NOTATION Example: Oxygen 8 protons, 8 electrons, 8 neutrons Notice the application of Hund's Rule, where unpaired electrons are maximized. 75 ELECTRON CONFIGURATION NOTATION compare this method to the orbital notation. 1s2 2s2 2p4 76 ELECTRON DOT NOTATION shows only the electrons in the outer energy level (valence electrons) the e- that are involved in chemical reactions illustrates the electrons that bond with other atoms outer (valence) energy level can hold no more than eight electrons (2nd postulate of quantum mechanics) 77 78 Oxygen 8 protons, 8 electrons chemical symbol is written in the center of the notation right of the symbol represents the s orbital top, left and bottom represent each of the three orbitals in the p sub level, respectively. 79