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Quantum Theory & Electron clouds

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The Great The Great Niels Bohr (1885 - 1962)

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Niels Bohr (Danish) tried to explain the spectrum of hydrogen atoms. Energy is transferred in photon units (quanta), therefore specific amounts of energy are absorbed or emitted Because the energy of an electron is quantized (discreet), there are only certain energy levels (orbits) for electrons Therefore, this e-m radiation can behave as waves or particles = Wave-Particle Duality Theory When an electron gains a certain amount of energy (absorbs a certain number of photons) it becomes excited and moves to a higher energy level The Hydrogen Atom and Quantum Theory

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…produces all of the colors in a continuous spectrum Spectroscopic analysis of the visible spectrum…

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…produces a “bright line” spectrum Spectroscopic analysis of the hydrogen spectrum…

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This produces bands of light with definite wavelengths. Electron transitions involve jumps of definite amounts of energy.

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Bohr Model Energy Levels

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Schrodinger Wave Equation probability Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger

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Heisenberg Uncertainty Principle You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! “One cannot simultaneously determine both the position and momentum of an electron.” Werner Heisenberg

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Heisenberg Uncertainty Principle : shows that we can only predict or estimate the position and momentum of the electron Because we record position by measuring radiant energy from a particle, we can never know the exact position and the exact momentum of an electron!!! Electrons are so small and so easily affected by energy (of any form) that "lighting up" an electron to see it causes it to change momentum (position and/or direction)

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The de Broglie Hypothesis Location __Probability__ Friend's house15% Shopping10% McDonald's15% Home in bed30% Cruising15% Work15% Working in Chem Lab 0% Basic Premise of Quantum Mechanics = small particles in small regions of space (e - ) do NOT behave like large visible objects. Therefore… we cannot tell exactly where an e - is at any given time or how it got there. We CAN predict the position of the e - Hypothetical example for comparison: If I want to find you on a Saturday afternoon… Probable places for finding electrons = ORBITALS

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QUANTUM THEORY: shows how the electron determines an atom's behavior and properties 4 Quantum Numbers must be used to describe the position of the electrons in an atom n, l, m, s are the "numbers" Each electron has a different set (just like each locker out in the hall has a different combination)

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Identifies the major energy levels that electrons can occupy Shows the distance from the nucleus Numbered 1,2,3,4,5,6,7,8 (any integer from 1-∞ Equation: 2n 2 - shows how many electrons can be in each energy level (e.g. level 3: 2(3) 2 = 18 e-'s) Principle Quantum Number - n

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Angular momentum Quantum Number - l Identifies the shape of the sublevels of the main energy levels s, p, d, f - used to identify the shape = "sphere, peanut, double peanut, flower" 1 st energy level has 1 subshell (s) 2 nd energy level has 2 subshells (s,p) 3 rd energy level has 3 subshells (s,p,d) 4 th energy level has 4 subshells (s,p,d,f) At higher energies, these orbitals overlap l can be from 0 to n-1 s=0 p=1 d=2 f=3

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Shapes of the Charge Clouds s for "Sphere": simplest shape, or shape of the simplest atoms like hydrogen and helium Electrons don't interfere with, or block, each other from the pull of the nucleus - ball shape Each energy level has an "s" orbital at the lowest energy within that level

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p for "Peanut": more complex shape that occurs at energy levels 2 and above Shapes of the Charge Clouds

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d for "Double Peanut": complex shape occurring at energy levels 3 and above The arrangement of these orbitals allows for "s" and "p" orbitals to fit closer to the middle/nucleus Shapes of the Charge Clouds

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f for "Flower": 7 bizarre-shaped orbitals for electrons of very large atoms electrons filling these orbitals are weakly attached to the atom because they are so far away from the pull of the nucleus Shapes of the Charge Clouds

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Is indicated by the orientation of these orbitals in each dimension. Magnetic Quantum Number m "p" orbitals line up on the x, y, z, axes in space "d" and "f" orbitals can line up on the axes as well as in between them Equation: there are n 2 orbitals (of various shapes) per energy level e.g. level 3 has 3 2 = 9 orbitals (one s, 3 p's, 5 d's) m can be from – l to + l

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s subshell can have only one orientation (orbital) m can be 0 only, meaning 1 possible orientation in space

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p subshell can have 3 different orientations (orbitals) m can be -1, 0, +1, meaning 3 possible orientations in space

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d subshell can have 5 different orientations (orbitals) m can be -2, -1, 0, +1, +2 meaning 5 possible orientations in space

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f subshell can have 7 different orientations (orbitals) m can be -3, -2, -1, 0, +1, +2, +3 meaning 7 possible orientations in space

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Spin Quantum Number (s): indicates the clockwise or counterclockwise spin of the electron Designated by -1/2 or +1/2 Needed because NO 2 ELECTRONS CAN HAVE THE SAME SET OF QUANTUM NUMBERS! Sometimes called left-handed or right- handed spin

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No two electrons in an atom have the same set of 4 quantum numbers! Therefore, only 2 electrons can fit in any one orbital This works because spinning electrons act like tiny electromagnets and magnetically attract each other when they have opposite spin Pauli Exclusion Principle

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Electrons fill the lowest energy levels first (always) As principle quantum number increases, spacing between the shells decreases Therefore, the third subshell and beyond start to overlap energy levels Aufbau Principle

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Hund's Rule = electrons entering a subshell containing more than one orbital will spread out over the available orbitals with their spins in the same direction until all orbitals have one electron in them

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Three ways to describe the electron structure of atoms in the ground state: orbital notation, electron configuration notation, electron dot notation Order of Fill for sublevels

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This is how many orbitals the p-subshell has. 1. 1 2. 2 3. 3 4. 5 5. 7

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How many electrons can be in the 3 rd level (n=3) 1. 2 2. 3 3. 10 4. 18 5. 36

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This quantum number indicates the shape of the orbital. 1. Angular momentum quantum number 2. Magnetic quantum number 3. Principle quantum number 4. Shape quantum number 5. Spin quantum number

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This is subshell shown below. 1. n 2. m 3. s 4. p 5. d 6. f

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This says that electrons entering a subshell will spread out over the available orbitals 1. Aufau principle 2. Hund’s rule 3. Heisenberg uncertainty principle 4. Pauli exclusion principle 5. De Broglie hypothesis

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