Quantum Model of the Atom Ch 4 Electrons

Quantum Model of the Atom Ch. 4 - Electrons in Atoms Electron Configuration & Orbitals 1 s 22 p 63 s 23 p 64 s 23 d 104 p 65 s 24 d 105 p 66 s 24 f 145 d 106 p 6…

Quantum Model of the Atom Ch. 4 - Electrons in Atoms Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Electrons as Waves Louis de Broglie ~1924 • Louis de Broglie (1924) – Applied wave-particle theory to electrons – electrons exhibit wave properties QUANTIZED WAVELENGTHS Fundamental mode 200 Second Harmonic or First Overtone 200 150 150 100 100 50 50 50 0 - 50 -100 -150 -200 0 50 100 150 200 Standing Wave 200 0 50 100 150 200 0 Adapted from work by Christy Johannesson www. nisd. net/communicationsarts/pages/chem 50 100 150 200

Electrons as Waves QUANTIZED WAVELENGTHS Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Electrons as Waves Evidence: DIFFRACTION PATTERNS VISIBLE LIGHT Davis, Frey, Sarquis, Modern Chemistry 2006, page 105 ELECTRONS Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Quantum Mechanics • Heisenberg Uncertainty Principle – Impossible to know both the velocity and position of an electron at the same time g Microscope Electron Werner Heisenberg ~1926

Quantum Mechanics • Schrödinger Wave Equation (1926) Erwin Schrodinger ~1926 – finite # of solutions quantized energy levels – defines probability of finding an electron Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Quantum Mechanics • Orbital (“electron cloud”) – Region in space where there is 90% probability of finding an electron 90% probability of finding the electron Electron Probability vs. Distance Electron Probability (%) 40 30 20 10 0 0 50 100 150 Distance from the Nucleus (pm) Orbital Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem 200 250

Quantum Numbers • Four Quantum Numbers: – Specify the “address” of each electron in an atom UPPER LEVEL Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Quantum Numbers Principal Quantum Number ( n ) Angular Momentum Quantum # ( l ) Magnetic Quantum Number ( ml ) Spin Quantum Number ( ms )

Relative Sizes 1 s and 2 s 1 s Zumdahl, De. Coste, World of Chemistry 2002, page 334 2 s

Quantum Numbers 1. Principal Quantum Number ( n ) – Energy level 1 s – Size of the orbital – n 2 = # of orbitals in the energy level Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem 2 s 3 s

Quantum Numbers y y z x px y z x pz py

p-Orbitals px Zumdahl, De. Coste, World of Chemistry 2002, page 335 pz py

Quantum Numbers 2. Angular Momentum Quantum # ( l ) – Energy sublevel – Shape of the orbital s p d Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem f

Quantum Numbers • Orbitals combine to form a spherical shape. 2 s 2 px 2 py 2 pz Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Quantum Numbers Principal level n=1 Sublevel s Orbital n=2 s p px py pz n=3 s p px py pz d dxy dxz • n = # of sublevels per level • n 2 = # of orbitals per level • Sublevel sets: 1 s, 3 p, 5 d, 7 f Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem dyz dz 2 dx 2 - y 2

Maximum Capacities of Subshells and Principal Shells n 1 2 l 0 0 1 2 3 Subshell designation s s p d f Orbitals in subshell 1 1 3 5 7 Subshell capacity 2 2 6 10 14 Principal shell capacity 2 8 Hill, Petrucci, General Chemistry An Integrated Approach 1999, page 320 3 18 4 . . . n 32 . . . 2 n 2

Quantum Numbers 3. Magnetic Quantum Number ( ml ) – Orientation of orbital – Specifies the exact orbital within each sublevel Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

d-orbitals Zumdahl, De. Coste, World of Chemistry 2002, page 336

Shapes of s, p, and d-Orbitals

Atomic Orbitals

s, p, and d-orbitals A s orbitals: Hold 2 electrons (outer orbitals of Groups 1 and 2) Kelter, Carr, Scott, , Chemistry: A World of Choices 1999, page 82 B p orbitals: Each of 3 pairs of lobes holds 2 electrons = 6 electrons (outer orbitals of Groups 13 to 18) C d orbitals: Each of 5 sets of lobes holds 2 electrons = 10 electrons (found in elements with atomic no. of 21 and higher)

Principal Energy Levels 1 and 2

Quantum Numbers 4. Spin Quantum Number ( ms ) – Electron spin +½ or -½ – An orbital can hold 2 electrons that spin in opposite directions. Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Quantum Numbers • Pauli Exclusion Principle – No two electrons in an atom can have the same 4 quantum numbers. – Each electron has a unique “address”: 1. Principal # 2. Ang. Mom. # 3. Magnetic # 4. Spin # energy level sublevel (s, p, d, f) orbital electron Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Feeling overwhelmed? Read Section 4 -2! Chemis try "Teacher, may I be excused? My brain is full. " Courtesy Christy Johannesson www. nisd. net/communicationsarts/pages/chem

Electron Orbitals: Electron orbitals Equivalent Electron shells (a) 1 s orbital 1999, Addison, Wesley, Longman, Inc. (b) 2 s and 2 p orbitals c) Neon Ne-10: 1 s, 2 s and 2 p

What sort of covalent bonds are seen here? H H O O (b) O 2 (a) H 2 H H O H H C H H (c) H 2 O H H (d) CH 4 H