L08S10_Review+CHEM+1A,+Lectures+1+to+7,+02-05-10

L08S10_Review+CHEM+1A,+Lectures+1+to+7,+02-05-10 - Chem 1A,...

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Unformatted text preview: Chem 1A, L8 REVIEW Lecture Seven Topics • Quantum numbers describe the energy, shape, and spatial orientation of electronic orbital in an atom • The angular momentum quantum number “L” can also stand for s, p, d, f, etc. orbitals • Orbitals can have radial and/or angular nodes, i.e.; spatial locations where the wave function intensity goes through zero. © 2008 Nitsche, UCB L8-1 H -Atom, One-Electron Ions Onen=1 l = 0 (s) (s ml = 0 n=2 l = 0 (s) (s ml = 0 Radial Node n=2 ml = -1, +1 l = 1 (p) (p ml = 0 z - 2px Angular Node z 2py + z y x + 2pz z 1s + z 2s + - + y x - y y x y L9-5 x x © 2008 Nitsche, UCB n = 3 l = 0, 1, 2 © A.Pines,M.Kubinec UCB 3s, 3p, 3d Orbitals L8-2 L9-6 © A.Pines,M.Kubinec UCB Quantum Numbers Q.N. n : Principal values orbital property Total nodes =n-1 Energy Shape n: 1, 2, 3 . . . ℓ: 0 (s), 1 (p), 2 (d), n-1 (s), (p), (d), ℓ : Angular Momentum mℓ : Magnetic mℓ: -ℓ, -(ℓ-1),..,0,..,(ℓ-1), ℓ © 2008 Nitsche, UCB Angular nodes = ℓ Orientation L8-3 © H. Nitsche UCB 1 Chem 1A, L8 REVIEW © 2008 Nitsche, UCB L8-4 Th Three representations of the hydrogen 1s, 2s, and 3s electron © 2008 Nitsche, UCB L8-5 ChemQuiz 7.1 Which has the most radial nodes? y x x z y + - -+ z A) 4f © 2008 Nitsche, UCB B) 3d C) 4s L8-6 © H. Nitsche UCB 2 Chem 1A, L8 REVIEW Th Three representations of the hydrogen 1s, 2s, and 3s electron © 2008 Nitsche, UCB L8-8 Representation of the 3d orbitals © 2008 Nitsche, UCB L8-9 Representation of the 4f orbitals in terms of their boundary surfaces. © 2008 Nitsche, UCB L8-10 © H. Nitsche UCB 3 Chem 1A, L8 REVIEW Lecture One Topics • Chemical reaction always occur in stoichiometric ratios • Converting between numbers of moles and numbers of atoms • Atomic masses are weighted averages of the masses of the natural isotopes of an element © 2008 Nitsche, UCB L8-11 Summary 2H2 Energy Reactants + Chemical Reactions O2 2H2O High Road (barrier) Products Reaction Coordinate © 2001 UC Regents L1-4 Relative Atomic and Molecular Mass H 1.01 12C 2H2 + O2 2H2O Al 26.98 P 30.97 Fe 55.85 Pb 207.2 H2 2.02 O2 32.00 H2O 18.02 CO2 44.01 12.00 C 12.01 O 16.00 2 molecules + 1 molecule 2 moles + 1 mole 2 grams + 16 grams 2 molecules 2 moles 18 grams Chemical Reactions 2H2 Energy Reactants Products Reaction Coordinate © 2008 Nitsche, UCB + O2 2H2O Transition State High Road (barrier) L8-13 © H. Nitsche UCB 4 Chem 1A, L8 REVIEW Stoichiometry Relationships between quantities of matter that participate in chemical reactions. Macroscopic Bulk matter NA Microscopic Atoms, Molecules Avogadro’s Number: NA = 6.022 x 1023 6.022 12 12C= one Mole NA atoms in 12.00 g Molar Mass (g/mol) © 2008 Nitsche, UCB L8-14 is assigned exactly 12 atomic mass units (amu or u) • Masses of all other atoms are given relative to this standard • Atomic masses are averages of isotopic masses • Relation between amu and grams (6.022 x 1023 atoms) (12amu/atom) = 12 g 6.022 x 1023 amu = 1 g 1 amu = 1.661 x 10-24 g = 1.661 x 10-27 kg © 2008 Nitsche, UCB • 12C Atomic Mass and Mass Units L8-15 Lecture Lecture Two Topics • The structure and size of the nucleus and the atom • Obtaining empirical formula from experimental data (mass spectrometry) • Calculating a molecular formula from an empirical formula and molar mass © 2008 Nitsche, UCB L8-16 © H. Nitsche UCB 5 Chem 1A, L8 REVIEW Mass Spectrometer Ionization - N Magnet Mass Spectrum Sample Acceleration S 1 H 2H 2, 1H 12C 16 O 13C 16O 2 1H 16O 18O 2 , 16O18O 12C16O 2 1H2H 3He , 13C16O 2 0 10 20 30 18O 2 40 50 L2-5 © 2000 A.Pines M.Kubinec UCB Relative Atomic and Molecular Mass H 1.01 12C Empirical and Molecular Formula Methane Ethylene CH 4 CH2 CH4 C2H8 C3H12 CH2 C2H4 C3H6 CH C2H2 C3H3 L8-17 L2-10 Al 26.98 P 30.97 Fe 55.85 Pb 207.2 H2 2.02 O2 32.00 H2O 18.02 CO2 44.01 L2-5 12.00 C 12.01 O 16.00 © 2000 A.Pines M.Kubinec UCB Acetylene CH © 2000 A.Pines M.Kubinec UCB © 2008 Nitsche, UCB (Nucleus + Electron Shells) -Z +Z Z electrons Atomic Structure A Z e - X A: Atomic Mass Z: Atomic Number Atomic Symbol A = Z (Protons) + N (Neutrons) © 2008 Nitsche, UCB L8-18 Mass Spectrometer Ionization - N Magnet Mass Spectrum Sample Acceleration S 1H 2H 2, 1H 12C 16 O 13C 16O 1H 16O 18O 2 , 2 12C16O 2 1H2H 3He , 16O18O 13C16O 2 0 10 © 2008 Nitsche, UCB 20 30 mass units 18O 2 40 50 L8-19 © H. Nitsche UCB 6 Chem 1A, L8 REVIEW ChemQuiz© 2.1 An equimolar mixture of oxygen atomic isotopes forms oxygen molecules. Which is molecules. the correct O2 spectrum? O O 16 O 16 O 18 18 OO 18 16 16 O O 18 O O 16 18 1) 32 34 36 2) 32 34 36 3) 32 34 36 © 2008 Nitsche, UCB L8-20 Empirical and Molecular Formula Methane Ethylene CH4 CH2 CH4 C2H8 C3H12 CH2 C2H4 C3H6 CH C2H2 C3H3 L8-22 Acetylene CH © 2008 Nitsche, UCB Lecture Three Topics • Radiation/light can behave as a wave • Visible light is only a small part of the the spectrum of electromagnetic radiation • Monochromatic light waves cause an interference pattern • Matter can absorb and emit radiation/light © 2008 Nitsche, UCB L8-23 © H. Nitsche UCB 7 Chem 1A, L8 REVIEW Light as a Wave Diffraction and Interference :wavelength A A+B B Intensity ~ Probability Distribution Summary c Electromagnetic Radiation :frequency c :speed = c 700 400 = 400 nm = 700 nm © A.Pines,M.Kubinec,UCB c= 3.0 x 108 m/s 3.0 L6-4 © A.Pines,M.Kubinec,UCB L6-6 Electromagnetic Spectrum 400 500 Visible γ-rays x-rays UV IR MW Radio, NMR, MRI Absorption and Continuous Emission 600 700 nm 10-16 10-12 10-8 © A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L6-5 Line © 2008 Nitsche, UCB © A.Pines,M.Kubinec,UCB L8-24 L6-10 Light as a Wave Electromagnetic Radiation c :wavelength :frequency c :speed = c = 400 nm = 700 nm © 2008 Nitsche, UCB c= 3.0 3.0 x 108 m/s L8-25 Diffraction and Interference Intensity A+B ~ Probability Distribution © 2008 Nitsche, UCB L8-26 © H. Nitsche UCB 8 Chem 1A, L8 REVIEW Absorption and Continuous Emission Line © 2008 Nitsche, UCB L8-27 Lecture Four Topics • Light can also behave as a particle • The de Broglie relation unifies this dualism dualism between light as a wave and a particle (photon) • Light of a specific minimum wavelength can ionize atoms in metals (Photo Effect) © 2008 Nitsche, UCB L8-28 Electromagnetic Spectrum Light Intensity The Particle Nature of Light The Summary 400 500 Visible γ-rays x-rays UV IR 600 700 nm MW Radio, NMR, MRI 10-16 10-12 10-8 © A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L7-4 Ephoton = h ©2002 A.Pines,M.Kubinec, UC L8-6 Photoelectric Effect The Particle Nature of Light The Light-Wave / Particle LightDuality Wave (length) I II eΦ Ekin Particle (Momentum) c Wave h = p Duality p=mc Particle p= h Ephoton = h © A.Pines,M.Kubinec,UCB Ekin= h - Φ = h - ho L7-2 © 2008 Nitsche, UCB © A.Pines,M.Kubinec,UCB L8-29 L7-6 © H. Nitsche UCB 9 Chem 1A, L8 REVIEW Wave / Particle Duality Wave (length) Particle (Momentum) Light c Wave h = p © 2008 Nitsche, UCB p Particle Duality p= h L8-30 Photoelectric Effect The Particle Nature of Light e- Ekin Φ I o II Ephoton = h © 2008 Nitsche, UCB Ekin= hν - Φ = h - ho L8-31 Lecture Five Topics • Electrons, which we know to be particles, can also behave as waves – they too can form an interference pattern • The de Broglie relation also unifies the particle and wave character of electrons • Electron in atoms behave like standing waves- their energy is quantized • The magnitude of the de Broglie wavelength tells us if we are dealing with a quantum particles L8-32 © 2008 Nitsche, UCB © H. Nitsche UCB 10 Chem 1A, L8 REVIEW Electromagnetic Spectrum Light Intensity The Particle Nature of Light The Summary 400 500 Visible γ-rays x-rays UV IR 600 700 nm MW Radio, NMR, MRI 10-16 10-12 10-8 A.Pines,M.Kubinec,UCB 10-4 100 104 108 m L7-4 Ephoton = h ©2002 A.Pines,M.Kubinec, UC L8-6 Photoelectric Effect The Particle Nature of Light The Light-Wave / Particle LightDuality Wave (length) I II eΦ Ekin Particle (Momentum) c Wave h = p Duality p=mc Particle p= h Ephoton = h © A.Pines,M.Kubinec,UCB Ekin= h - Φ = h - ho L7-2 © 2008 Nitsche, UCB © A.Pines,M.Kubinec,UCB L8-33 L7-6 Diffraction and Interference Intensity A+B Probability Distribution ~ ~ L8-34 © 2008 Nitsche, UCB Discrete, Quantized States Standing Waves Ψ(x) E n 3 2 1 Nodes 2 1 0 L8-35 Excited States States + + + - Ground State © 2008 Nitsche, UCB + © H. Nitsche UCB 11 Chem 1A, L8 REVIEW Absorption and Emission Spectra Electronic Transtions v ΔE = hν © 2008 Nitsche, UCB L8-36 De Broglie Wavelengths Particle Photon (yellow) (yellow) e- (v ~ 105 m sec-1) 10 Na (80K, v~300 m sec-1) Baseball (170g, v~40 m sec-1) © 2008 Nitsche, UCB de Broglie (nm) ~ 600 ~6 ~ 0.06 ~ 6x10-26 L8-37 Lecture Six Topics • The uncertainty the exact position and wavelength of an atomic electron is given by the Heisenberg uncertainty relation • Solutions of the Schrödinger equation gives the energies of the quantum states of an electron • Electrons in atoms behave like standing waves- their energy is quantized • The magnitude of the de Broglie wavelength tells us if we are dealing with a quantum particles L8-38 © 2008 Nitsche, UCB © H. Nitsche UCB 12 Chem 1A, L8 REVIEW Spectra Review ΔE=h Absorption and Emission © A.Pines,M.Kubinec,UCB L8-7 Wave Functions Energy: Ψ(x) = ET Ψ(x) 8π2m dx2 d2 nπ nπ x A sin L 8π2m L h2 = ET Ψ(x) 2 Ψ(x) Ψ2(x) En 16 - h2 n=4 n=3 9 En = © 2008 Nitsche, UCB h2n2 8mL2 n=2 n=1 4 1 L8-39 L19-9 © 2004 M.Kubinec Ψ(x) = A sin 2π x known momentum () h de Broglie relation: mv = p = Uncertainty Principle Ψ2(x) = intensity or probability x uncertainty in position Ψ(x) = ΣAi sin 2π x i i uncertainty in momentum © 2008 Nitsche, UCB Δx Δp ≥ h/4π h/4 L8-40 known position x Quantum Mechanics Schrödinger equation: - h2 d2 Ψ(x) + V(x) Ψ(x) = ET Ψ(x) 8π2m dx2 Kinetic Potential Total H Ψ(x) = ET Ψ(x) © 2008 Nitsche, UCB L8-41 © H. Nitsche UCB 13 Chem 1A, L8 REVIEW Orbital Energies n : Principal Q. N. -Z 2 n2 n ∞ 3 n: 1, 2, 3 . . . Ionized E 0 -R∞ -R∞ 4 9 En = R∞ R∞ 2 = 2.18 x 10-18 J = 3.29 x1015 Hz N0R∞ = 1312 kJmol-1 © 2008 Nitsche, UCB 1 Ground -R∞ L8-42 ChemQuiz© 8.3 Was this review useful? 1) Very 2) Somewhat 3) No 4) I don’t want/need a review © 2008 Nitsche, UCB L8-43 Lecture Complete © 2008 Nitsche, UCB L8-44 © H. Nitsche UCB 14 ...
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This note was uploaded on 04/24/2010 for the course CHEM 1A taught by Professor Nitsche during the Spring '08 term at Berkeley.

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