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Lecture September 19 Goal for today: finish Chapter 7 (almost) Sec. 7.6 with Chap.8 Packet of light is also a “particle” called a photon Energy of a photon of light E = hν OR E = hc/λ h = 6.626 x 10-34 J-s Planck’s constant CHEM131 - Fall 11 - September 19 1 The Hydrogen Atom and the Bohr Model 1H atom is a proton surrounded by an electron n=1 An over simplified model but very instructive Three distinct orbits n=2 n=3 Quantized CHEM131 - Fall 11 - September 19 2 Rydberg Formula n=2 En = -Rhc/n2 Rhc = 2.179 x 10-18 J/atom E2 = -[(2.18 x 10-18)/22] J/atom =-0.545 x 10-18 J/atom ΔE = Efinal - Einitial = (-2.18 x 10-18) - (-0.545 x 10-18) =-1.64 x 10-18 J/atom ✮energy emitted - photons n=1 E1 = -2.18 x 10-18 J/atom See Fig. 7.21 CHEM131 - Fall 11 - September 19 3 Energy Wavelength h = 6.626 x 10 J-s E = hν = hc/λ c =2.998 x 10 m/s OR λ = hc/E -34 8 What wavelength of light is ΔE = 1.63 x 10-18 J/atom? (n=2 ➞ n=1) λ = (6.626 x 10-34 J●s)(2.998x108 m/s)/(1.63 x 10-18 J/atom =1.22 x 10-7 m OR 122 nm (Fig 7.12) Not visible - ultraviolet (uv) region Comment: the per atom is the same as a single photon. E/mol = 1.63 x 10-18 J/atom x (6.022 x 1023 atoms/mol) = 982 kJ/mol CHEM131 - Fall 11 - September 19 4 Emission and Absorption Spectra ΔE = -Rhc (1/nf2 - 1/ni2) ΔE negative = emission ΔE positive = absorption nf = ∞ n1 =2 Balmer - visible ionize the atom complete removal of the electron CHEM131 - Fall 11 - September 19 5 Electromagnetic Spectrum See Fig. 7.5 CHEM131 - Fall 11 - September 19 6 Example What wavelength of light is needed to completely ionize hydrogen that is initially excited to the n=3 energy level? ΔE = -Rhc [(1/∞) - 1/32)] = -2.179 x 10-18(-1/9) = 2.421 x 10-19 J Absorption positive!! ΔE = E photon = hν = hc/λ λ = [(6.626 x 10-34 J-s)(2.998 x108 m/s)]/ (2.421 x 10-19 J) Wavelength cannot Ans: 820.5 nm be negative!! CHEM131 - Fall 11 - September 19 7 Introduction to Quantum Mechanics Two important scientific advances that shaped the way we view electronic structure Particles (electrons) can have wave-like properties de Broglie wavelength λ = h/mv Electron E(n=1) = 2.18 x 10-18 J ☞ λ = 330 pm me= 9.11x10-31kg Size of a Bohr n=1 radius = 53 pm CHEM131 - Fall 11 - September 19 8 More on Quantum Mechanics AND Uncertainty Principle - cannot know both the energy (momentum) and the position of a particle - an electron Talk about it in terms of probability and WAVE FUNCTIONS Schrodinger Equation HΨ = EΨ Ψ is called the wave function that describes the spatial of the electron in the atom CHEM131 - Fall 11 - September 19 9 Quiz of the Day What is the energy of the photon that is absorbed when the hydrogen atom initially in its ground state (n=1) is excited to the n=5 state? ΔE = -Rhc [(1/52) - 1/12)] = -2.179 x 10-18(0.04-1) = 2.092 x 10-18 J CHEM131 - Fall 11 - September 19 10