Lecture 7 part II Chem 102 IR(2)

Lecture 7 part II Chem 102 IR(2) - Chapter 7 part II...

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Chapter 7 part II
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Quantum mechanics
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So far…. . Planck - Energy is absorbed and released from an atom in fixed amounts –QUANTA Δ E = hν Einstein- Energy as a form of light is quantized – PHOTONS dual nature of light- particles and waves E=mc 2 de Broglies – Particles don t move with a speed of light λ = h/mv Bohr - Proposed model of an atom (Hydrogen) electrons in allowed circular orbitals around nucleus. (energy level n=1,2,3) atom must absorb E for an e- to move from lower to higher level; or emit energy when e- moves from higher to lower level. (ground and excited state) hydrogen atom energy levels consistent with the hydrogen emission spectrum
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Quantum mechanical model of an atom Schrodinger E: energy This math is too complicated for us to do. We will simply look at the results. WAVE FUNCTION calculations lead to ORBITALS Ψ 2 : Orbital information
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Wave Function (Ψ): standing waves Ψ essentially describes an electron orbital in an x,y,z plane When we apply the Schrodinger equation for a given atom we get a set of Ψ’s, each with its own energy value These waves are the electrons These allow us to calculate all the possible “standing waves” around the nucleus
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The solutions are defined by a set of 3 quantum numbers: n, l and m l Describe the size, shape, and orientation in space of the orbitals on an atom Quantum numbers The solutions to the Schrodinger equation essentially give us the atomic orbitals that are available to an electron Electrons occupy 3-D space and need three coordinates to explain the orbital
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Quantum numbers n: integer value Represents the orbital energy level (shell) Potential Energy n = 1 n = 3 n = 2 n = 4 principal quantum number ( n ) describes the size of the orbital
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l: n-1,…,0 Represents the orbital shape (type of shell) Subshells come in different types: s, p, d, (f), (g) Quantum numbers angular quantum number ( l )
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m l : l, l-1,…,0,…,-l Represents the number of subshells within an orbital S orbital: 1 subshell P orbitals : 3 subshells (p x , p y , p z ) D orbitals : 5 subshells (d z2 , d x2-y2 , d xy , d xz , d yz ) (7 f orbitals, 9 g orbitals) Quantum numbers How many subshells exist for each orbital? magnetic quantum number ( m ) to describe the orientation in space of a particular orbital
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Calculate all the orbitals for the n=4 energy level !!!! Quantum numbers n=1 shell, 1 orbital 1s n=2 shell, 4 orbitals 2s, 2p n=3 shell, 9 orbitals 3s, 3p, 3d n=4 shell, 16 orbitals 4s, 4p, 4d, 4f n: principle quantum number (shell number – size and energy) Integers, 1,2,3, … l: anular momentum quantum number (orbital designation) 0, 1, …, n-1 m l : magnetic quantum number (orbital subshells) integers between l
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Quantum numbers
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For n = 5, the allowed values of l run from 0 to 4 (n – 1 = 5 – 1). Thus the subshells and their designations are l = 0 l = 1 l = 2 l = 3 l = 4 5s 5p 5d 5f 5g 8. For principal quantum level n = 5, determine the number of allowed subshells (different values of l ), and give the designation of each.
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This note was uploaded on 04/21/2011 for the course CHEM 102 taught by Professor Peterpastos during the Spring '08 term at CUNY Hunter.

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Lecture 7 part II Chem 102 IR(2) - Chapter 7 part II...

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