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Lacey_Che131_F2010_Lect-24p

Lacey_Che131_F2010_Lect-24p - Lec Lec-22-23 Electron...

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Lec-22-23: Electron configurations Lec 22 23: Electron configurations Roy A. Lacey, Stony Brook University; Che 131, Spring 2011 1 Matter waves De Broglie - Electron is a standing wave in the H 2 n L λ = atom Here Here The state of the electron must be described by a quantum Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 2 number, n.

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Electron waves ` The description of the behavior of particles as waves is called wave mechanics or quantum mechanics mechanics. ` The mathematical description of an electron wave is called the wave equation. ` Wave functions, ψ , are mathematical descriptions of the motion of electron waves as they vary with location and with time. Quantum mechanics allows us to predict the probabilities of where we can find an electron. Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 3 Electron waves Heisenberg’s uncertainty principle You cannot accurately determine the position and You cannot accurately determine the position and momentum of an electron at the same time. 4 x px m u π Δ ⋅Δ ≡ Δ ⋅ Δ What is the uncertainty in the position of an electron moving near to a nucleus with a speed of 8x10 7 m/s if the uncertainty u=1.0% 34 2 2 31 7 1 1 6.626 10 J s hk g ms x −− ×⋅ Δ≥ = ( )( ) -11 4 49 .109 10 0.01 8 10 = 7.24 10 mu J kg ms m Δ ×× × × Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 4 5.29177×10 11 m Bohr radius
Solutions to the wave equation Solutions are characterized by quantum numbers ` The principle quantum number, n , is a positive integer that indicates the shell and relative size of orbital(s) orbital(s). ` The angular momentum quantum number, l , is an integer from zero to n-1. It defines the shape of the orbital and subshell. V a l u e o f l 01234 Letter identifier s p df g ` The magnetic quantum number, m l , is an integer with a value from -l to +l. It defines the orientation of an orbital in the space around the nucleus of an atom orbital in the space around the nucleus of an atom. ` The spin magnetic quantum number, m s , is to account for the two possible spin orientations. The values for m are +1/2 and 1/2 Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 5 m s are +1/2 and -1/2. Quantum numbers n lm l # orbitals Quantum numbers are related to each other 1 0 0 1 20 0 1 1 -10+1 3 -1,0,+1 30 0 1 1 -1,0,+1 3 2 -2.-1,0,+1,+2 5 40 0 1 1 -1,0,+1 3 2 -2.-1,0,+1,+2 5 Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 6 3 -3,-2.-1,0,+1,+2,+3 7

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Quantum numbers Quantum numbers are related to each other Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 7 Spin quantum number Here The spin quantum number has two values Roy A. Lacey, Stony Brook University; Che 131, Fall 2010 8
Quantum numbers

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Lacey_Che131_F2010_Lect-24p - Lec Lec-22-23 Electron...

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