lecture16 (11-6-2006) Ch 8

lecture16 (11-6-2006) Ch 8 - Chemistry 2A-c F2006...

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1 Chemistry 2A Chemistry 2A -c F2006 c F2006 (Ch8 (Ch8 -49)145 49)145 Bohr's Model of the Hydrogen Atom This model is limited to hydrogen and hydrogen like atoms (atoms with one electon). n = 1, 2, 3, 4… Shell K, L, M, N… Quantim Mechanics or Wave Mechanics Wave Equation (1929) Erwin Schrödinger Schrödinger Equation: H Ψ( n, l, m l ) = E Ψ( n, l, m l ) H = Hamiltonian (mathematical operator) Ψ( n, l , m l ) = wave function, where (n, l , m l ) is a set of 3 quantum #s. Probability of finding an e -1 in the atom: ⏐Ψ( n, l , m l ) 2 E((n, l , m l ) = Eigen-energy (depends on 3 quantum #s) Radial Angular e -
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2 Chemistry 2A Chemistry 2A -c F2006 c F2006 (Ch8 (Ch8 -50)146 50)146 Atomic wavefunctions are governed by 4 Quantum numbers (n, l , m l , m s ) n = principal quantum number: n = 1, 2, 3, . . . , integer Main energy level. A maximum of 2(n) 2 electrons. l = azimuthal or orbital angular momentum quantum number: l = 0, 1, 2, 3, 4, …, n-1 sub-shell: s p d f g,… Characterize orbital shapes. Allowed values are (0 to n-1) m l = magnetic quantum number: Allowed values: - l , - l+ 1, …, 0, …, l -1, l There are 2 l +1 values Orientation of orbitals in space m s = electron spin quantum number Allowed values: m s =+1/2 ( α , spin up) and m s =-1/2 ( β , spin down)
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3 Chemistry 2A Chemistry 2A -c F2006 c F2006 (Ch8 (Ch8 -51)147 51)147 Electron Spin: This is relativistic in nature (no classical analog) . Intrinsic spin – intrinsic magnetic dipole Stern-Gerlich experiment (1921) : Ag atom beam is split into two beams by inhomogeneous magnetic field Uncertainty Principle (Heisenberg, 1927) Wave nature of electron – cannot be precisely located – track cannot be drawn for electrons in atoms Inherent uncertainties in knowing the combination of a particle’s (position and momentum) or (energy and time): ( x)( p) h/2 π or ( E)( t) h/2 π
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lecture16 (11-6-2006) Ch 8 - Chemistry 2A-c F2006...

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