Chap 6B - Chem 210 Chapter 6B / WANG Chapter 6.4 through...

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Unformatted text preview: Chem 210 Chapter 6B / WANG Chapter 6.4 through 6.5 Electronic Electronic Structure of Atoms Diffraction patterns of x-rays (“waves” of “light”) (“waves” and and electrons (“particles” of “matter”). (“particles” 6.1 Wave Nature of Light 6.2 Quantized Energy & Photons 6.3 Bohr’s Atomic Model 6.4 Wave Behavior of Matter 6.4 6.5 Quantum Mechanics and Atomic Orbital Online practice goal: achieve >90% in Chap 6. goal: homework 5 and Quiz 5 EOC (end-of-chapter problems) (end-of6.14, 6.16, 6.36, 6.44, 6.54, 6.64, 6.68, 6.74 (textbook page 253-255) 253- due due date – Wed. Sept. 23rd Matter Waves The idea of particle-wave duality of light was articlelight boldly extended to matter, such as electrons, matter by de Broglie, who proposed the existence of de “matter waves”, for which he received the 1929 Nobel Prize in physics. de Broglie’s equation: λ = h mv • mv (momentum): particle property • λ: w ave property • h: Planck’s constant Experimental proof of Matter Waves Matter Diffraction pattern of electron beams. As visible light allows visible allows our eyes to detect objects by diffraction patterns at the edges, electron electron micrographs reveal objects on the cellular cellular and atomic levels, levels, as the λ values of electron beams are 100 100 5000 times smaller than smaller than visible light. Fall 2009 UM-SJTU JI Electron micrograph of cotton fibers. x-ray diffraction of aluminum foil electron diffraction of aluminum foil Electrons behave as if they are “waves”! Matter Waves Wavelength (λ) of a particle depends on of its its mass (m) and velocity (v). Question: Calculate the wavelength of an electron with mass of 9.0×10-31 kg traveling at a velocity of 6.7×106 m/s. Question: Calculate the wavelength of a ball with mass of 0.20 kg traveling at a velocity of 25 m/s. Matter Waves Why is it that we do not notice the wave characteristics of matter in general? • wavelength is too small (~10-34 m) • frequency is too high (~ 1042 Hz) • Similar reason why we can’t “see” x-ray xwhich has… wavelength ~10-10 m Frequency ~ 1018 Hz Page 1 Chem 210 Chapter 6B / WANG Heisenberg’s Uncertainty Principle λ = h /mu The de Broglie Wavelengths of Several Objects Substance Mass (g) slow electron Speed (m/s) 9x10-28 λ (m) 7x10-4 1.0 fast electron 9x10-28 5.9x106 1x10-10 alpha particle 6.6x10-24 1.5x107 7x10-15 1.0 0.01 7x10-29 142 25.0 2x10-34 one-gram mass baseball Earth 6.0x1027 3.0x104 4x10-63 Heisenberg’s Uncertainty Principle Uncertainty • On the mass scale of atomic particles, we cannot determine exactly the exactly position, direction of motion, and speed simultaneously simultaneously. • The product of the uncertainty in the uncertainty position position (∆ x) and that of the momentum momentum (∆p) are greater or equal to h/2π. greater h/2 ∆x ⋅∆p ≥ h 2π Schrödinger’s Schrödinger’s equation Schrödinger (1926) incorporated the idea of particleparticle-wave duality of an electron in the H atom by proposing a differential equation for which he received the Nobel Prize in Nobel 1933. Fall 2009 UM-SJTU JI Based on the dual nature of matter, Heisenberg formulated his uncertainty principle. At age 32, he received the 1933 Nobel Prize in physics for this work. Heisenberg’s principle states that particle - wave duality fundamentally limits how precisely we can know both the location and the momentum of any matter. The uncertainty becomes proportionally important only when we study matters at the subatomic level. Quantum Mechanical Model of the Atom Heisenberg’s and de Broglie’s work led to the replacement of Bohr’s planetary atomic Bohr’s model by the Quantum Mechanical (QM) Quantum model, precise • in which the precise location of an electron is uncertain when its uncertain momentum momentum (or kinetic energy) is known kinetic for certain. impossible • And, it is impossible for an electron to move in well-defined orbits about the wellnucleus. Schrödinger’s wave equation • Each particle is represented by a wave function, particle momentum Ψ , with precisely determined momentum, but position momentum totally uncertain position. The momentum corresponds to the allowed energy level of allowed electrons. • Ψ 2 represents the probability of finding the probability electron at a certain location. – a specific distribution of electron density in space with characteristic shape and volume. Page 2 Chem 210 Chapter 6B / WANG Ψ2 of an s orbital Ψ2 = region in space where an electron is most likely found. S orbital shows electron electron density occurs in a spherical spherical distribution around the nucleus. Ψ2 of Atomic Orbitals in the QM Model Orbitals Ψ 2 of p orbitals Ψ2 = region in space where an electron is most likely found. Ψ 2 of d orbitals Higher density occurs closer closer to the nucleus Size of Atomic Orbitals of • Orbitals vary in size or the volume occupied in space. • QM uses the principal quantum number, n, to indicate this size. • Smallest orbital size has n = 1. • Orbital becomes larger as n increases to 2, 3, 4, etc. • All orbitals w ith the same n same value is called an electron electron shell. Shape of Atomic Orbitals of Atomic • Designated by the angular momentum quantum number, l. • Each value of l corresponds to a letter: all designate certain shapes. – s (l = 0), spherical shape – p (l = 1), dumbbell shape – d (l = 2), two shapes, one is like a clover. – f (l = 3), – g (l = 4), – h (l = 5), etc. Fall 2009 UM-SJTU JI 1s 2s 3s All are spherical, though size increases with spherical, quantum number, n. p sub-shells are dumbbell shaped; they orient differently in the 3-D space. Ways to represent one of the 2p orbitals. Three 2p orbitals shown together. Page 3 Chem 210 Chapter 6B / WANG One of the seven possible 4f orbitals. 3d orbitals. orbitals. five 3d orbitals shown together. Shape of Atomic Orbitals: of Atomic (continued) (continued) • Orbitals of the same l are called a sub-shell. same subelectron • Each electron shell has different number of subsub-shells. – Shell n = 1: one sub-shell sub1s – Shell n = 2: two sub-shells 2s & 2p sub– Shell n = 3: three sub-shells 3s, 3p, 3d sub– Shell n = 4: four sub-shells 4s, 4p, 4d, 4f sub– Etc. Possible sub-shells from shell n = 1 to n = 7 subshell Each higher shell has one more variety of subsub-shells. 7s larger 6s size 5s 7p 7d 7f 7g 7h 6p 6d 6f 6g 6h 5p 5d 5f 5g 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Orientation of Atomic Orbitals Atomic •Orbital has specific orientations in space, orientations each designated by the magnetic quantum magnetic number, m. Possible m values depend on the l values value (shape). For example, (shape). •p orbitals (l = 1) has 1) 3 possible m values = (-1, 0, +1) possible values +1) 2px, 2py 2pz each is perpendicular to others. 2p others. Fall 2009 UM-SJTU JI 7i shape variations Orientation of Atomic Orbitals (continued) Atomic d orbitals (l = 2) has 5 possible m values possible values (-2, -1, 0, +1, +2) dxy, dyz and dzx each sits on a plane perpendicular to others. dx2-y2 sits on the x & y x2axes. dz2 is on the z axis & has is a ring on the xy plane. –Depending on how x, y, z axes are defined, the above d orbital designations are orbital each linked to a specific m value: (-2, -1, 0, +1, +2). Page 4 Chem 210 Chapter 6B / WANG Question: How many orientations are possible for the s orbital based on its quantum numbers, l and m? Explain. The f Orbitals Question: Tell how many orientations are possible for f orbitals. Explain your answer. ml: -3, -2, -1, The Hierarchy of Quantum Numbers for Atomic Orbitals Name, Symbol Allowed Values (Property) Principal, n Positive (size, energy) integer (1, 2, 3, ...) Angular momentum, l 0 to n-1 (shape) Magnetic, ml -l,…,0,…,+l (orientation) Quantum Numbers 1 2 0 0 0 3 1 0 0 1 2 0 -1 0 +1 -1 0 +1 -2 -1 0 +1 +2 Since each atomic orbital can be occupied by 2 electrons …. electrons A 4th quantum number is needed to label each electron: Spin quantum number. Spin ms = -½ or +½ Denoting the direction of direction of electron electron spin. Example: (1,0,0, +½) and (1,0,0, -½) identify the two electrons in the Helium atom at ground state. Fall 2009 UM-SJTU JI 0, +1, +2, +3 Capacity of Atomic Orbitals Atomic Each orbital has 2e capacity. Examples: • 2s 2e capacity • 2p total capacity of 6e from 2px, 2py, 2pz • 3 orbitals, each can hold 2 electrons. • 3d total capacity of 10 e from 5 orbitals. How many electrons can occupy 4f? Explain. • 4f has 7 possible orientations (orbitals), each can hold 2e total of 14 electrons! Summary Summary of Quantum Numbers Principal quantum number: n = 1, 2, 3, … Value denotes an electron shell electron azimuthal quantum number: l = 0 to n-1 nValue denotes an electron subshell electron subshell Magnetic quantum number: ml = -l to +l Value denotes the orientation of an electron orientation of subshell Spin quantum number: ms = -½ or +½ Each value denotes the direction of electron direction of spin spin Page 5 Chem 210 Chapter 6B / WANG QM model of the atom Question: Compare and contrast these terms used to describe electronic structure: orbit versus orbital. Quantum Numbers and Atom Orbitals Question: Give the set of 3 quantum numbers for the: (a)3s orbital: Similarities: Electrons are located outside nucleus quantized energy level Larger size, greater energy Differences: Orbital - QM model a wave function Ψ Ψ2 ~ electron density Ψ2 has different shapes & orientations Fall 2009 UM-SJTU JI (b) 4px orbital: orbit – Bohr’s model a circular path. electron path. all circular Page 6 ...
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This note was uploaded on 07/30/2011 for the course CHEM 210 taught by Professor Zhang during the Spring '09 term at Shanghai Jiao Tong University.

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