Heisenberg's Uncertainty Principle De Broglie's Matter Wave h h △x·m△)≥ = 4π mv A model:precisely describes the energy of the electron while describing its location not precisely,but in terms of probability! Macroscopic objects h △x·m△)≥ h二 4元 mv Microscopic objects Matter at the subatomic level
Macroscopic objects Heisenberg’s Uncertainty Principle & De Broglie’s Matter Wave 4 h x m υ π ∆ ⋅ ∆ ≥ mv h λ = A model: precisely describes the energy of the electron while describing its location not precisely, but in terms of probability! Macroscopic objects , ; ------------------------- 4 v Microscopic objects x h m h m υ π λ ∆ ∆ ⋅ ≥ = → Matter at the subatomic level
6.5 Atomic Orbitals and Quantum Numbers Relationship Among Values of n,/and m,Through n =4 Possible Number Total Number Values Subshell Possible of Orbitals of Orbitals in n of/ Designation Values ofm in Subshell Shell 0 1s 2 0 25 00 1 1 1 1 1,0,-1 3 4 3 0 0 1 服 1,0,-1 3 20 2,1,0,-1,-2 9 4 4s 1 n 1 1,0,-1 23 21,0-1, -2 3 2,1,0,-1,-2,-3 357 16 5 ? ? ？
6.5 Atomic Orbitals and Quantum Numbers n 2 5 ? ? ? ? ?
6.5 Atomic Orbitals and Quantum Numbers e shell Total of Possible l e Possible m Orbitals n:positive “0ton-l” subshell "-l to +l" in an e shell: integer n2 1 0 1s 0 1 2 0, 2s 0 4 1 2p -1,0,+1 3 0, 3s 0 1, 3p -1,0,+1 -2,-1,0,+l,+2 9 2 3d 4 0, 4s 0 1, 4p -1,0,+1 23 4d -2,-1,0,+1,+2 4f-3,-2,-1,0,+L,+2,+3 16
6.5 Atomic Orbitals and Quantum Numbers e shell 12 e subshell Possible l “0 to n “0 to n-1” 0 0, 1 n: positive integer 1s 2s 2p Possible ml “-l to +l” l to +l” 00 -1, 0, +l Total # of Orbitals in an e shell: n 2 14 3 4 1 0, 1, 2 0, 1, 2, 3 2p 3s 3p 3d 4s 4p 4d 4f -1, 0, +l 0 -1, 0, +l 1, 0, +l -2, -1, 0, +l, +2 1, 0, +l, +2 0 -1, 0, +l 1, 0, +l -2, -1, 0, +l, +2 1, 0, +l, +2 -3, -2, -1, 0, +l, +2, +3 1, 0, +l, +2, +3 49 16
Question: 1)Which one(s)of the following sets of quantum number is (are) unreasonable? 则(n,4m)=(5,2,-2; b)(m,m)=(4,2,-35 cn,↓m)=(3,3,-25 d(n,gm)=(6,-2,2; 2)Which orbital does this set of quantum numbers represent:(n,l, m)=(5,2,-2)? Answer: one of five 5d orbitals in one ofthe five possible orientations dx2-y2 Depending on how the x,y,z axes are defined
Question: 1) Which one(s) of the following sets of quantum number is ( Which one(s) of the following sets of quantum number is (are) unreasonable? a) (n, l, ml ) = (5, 2, ) = (5, 2, -2); b) (n, l, m 2); b) (n, l, ml ) = (4, 2, ) = (4, 2, -3); c) (n, l, ml ) = (3, 3, ) = (3, 3, -2); d) (n, l, m 2); d) (n, l, ml ) = (6, ) = (6, -2, 2); 2) Which orbital does this set of quantum numbers represent: (n, l, ml ) = (5, 2, ) = (5, 2, -2)? Answer: Depending on how the x, y, z axes are defined one of five 5d orbitals in one of the five possible orientations
Electron Spin and the Pauli Exclusion Principle 4.Spin quantum number ms: N S Electrons actually spin around itself. 1 m,=士 2 S N Copyright2009 Pearson Prentice Hall,Inc
4. Spin quantum number ms: Electrons actually spin around itself. Electron Spin and the Pauli Exclusion Principle 1 2 m s = ± spin around itself
Electron Spin and the Pauli Exclusion Principle N N “Antiparallel' AE External X3aug N S magnetic N field s N No external "Parallel" magnetic field
Electron Spin and the Pauli Exclusion Principle
Electron Spin and the Pauli Exclusion Principle Fact:Experiment Beam of atoms Slit Beam collector Magnet plate
Electron Spin Electron Spin and the Pauli Exclusion Principle Fact: Experiment
Pauli's Exclusion Principle 4.Spin quantum number ms: 1 m, 2 Pauli's Exclusion Principle No two electrons can have the same set of 4 quantum Wolfgang Pauli numbers. Nobel Prize in Physics(1945) Each atomic orbital has capacity for 2 electrons
4. Spin quantum number ms: 1 2 m s = ± Pauli’s Exclusion Principle Pauli’s Exclusion Principle No two electrons can have the same set of 4 quantum numbers. Each atomic orbital has capacity for 2 electrons Wolfgang Pauli Nobel Prize in Physics (1945)
Pauli's Exclusion Principle No two electrons in the same atom can have the same set of four quantum numbers:n,l,m and m Question:which orbital is occupied by an electron which has the following set of quantum numbers in one atom: n1,m1m=(3,2,1,+)? N=3,l=2→d→3d Answer:one of the five 3d orbitals (such as 3d) Question:Give all possible sets of 4 reasonable quantum numbers corresponding to an electron which is located in 4px orbital of an atom.(n,1,m,m)=(?,??? One of(4,1,+L,+,(4,1,+L,-,4,1,0,+),(4,1,0,-), 4,1,-1,+,(4,1,-1,-
No two electrons in the same atom can have the same set of four quantum numbers : n, l, ml and ms Question: which orbital is occupied by an electron which has the following set of quantum numbers in one atom: (n, l, ml m s) =(3, 2, 1, +½)? Pauli’s Exclusion Principle N=3, l= 2 d 3d Question: Give all possible sets of 4 reasonable quantum numbers corresponding to an electron which is located in 4p x orbital of an atom. (n, l, ml , m s) = (?, ?, ?, ?) N=3, l= 2 d 3d Answer: one of the five 3d orbitals (such as 3dxy) One of (4, 1, +1, +½) , (4, 1, +1, One of (4, 1, +1, +½) , (4, 1, +1, -½) , (4, 1, 0, +½), (4, ½) , (4, 1, 0, +½), (4, 1, 0, -½), 1, 0, ½), (4, 1, -1, +½) , (4, 1, 1, +½) , (4, 1, -1, -½)
Electron Which room I should stay? 19K Neutron Orbital Nucleus Proton Elect Iow跳a7mJy electron(s)will live in my room?
19K Electron Orbital