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23-Chapt-6-Quantum2 The Nature of Energy • For atoms and molecules, one does not observe a continuous spectrum, as one gets from a ? white light source. • Only a line spectrum of discrete wavelengths is Electronic Structure observed. of Atoms © 2012 Pearson Education, Inc. The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell Neils Bohr Explained the emission spectrum of the hydrogen atom on basis of quantization of electron energy. Neils Bohr Explained the emission spectrum of the hydrogen atom on basis of quantization of electron energy. Emission spectrum Emitted light is separated into component frequencies when passed through a prism. 397 410 434 486 656 wavelenth in nm Hydrogen, the simplest atom, produces the simplest emission spectrum. In the late 19th century a mathematical relationship was found between the visible spectral lines of hydrogen the group of hydrogen lines in the visible range is called the Balmer series 1 1 1 = R – λ ( 22 n2 ) Rydberg 1.0968 x 107m–1 Constant Johannes Rydberg Bohr Solution the electron circles nucleus in a circular orbit imposed quantum condition on electron energy only certain “orbits” allowed energy emitted is when electron moves from higher energy state (excited state) to lower energy state the lowest electron energy state is ground state ground state of hydrogen atom n = 5 n = 4 n = 3 n = 2 n = 1 e- excited state of hydrogen atom n = 5 n = 4 n = 3 e- n = 2 n = 1 hν excited state of hydrogen atom n = 5 n = 4 n = 3 n = 2 e- n = 1 hν excited state of hydrogen atom n = 5 n = 4 n = 3 e- n = 2 n = 1 hν Emission spectrum Emitted light is separated into component frequencies when passed through a prism. 397 410 434 486 656 wavelenth in nm 1 1 1 = R – λ ( 22 n2 ) Rydberg Constant 1.0968 x 107m–1 Rewritten to solve for energy 1 1 h = E = - 2.178 x 10-18J – ν Δ ( 2 2) nf ni Where E is the energy is the released by an excited electron moving to a lower energy level Example What is the wavelength of a photon emitted during a transition from the ni = 5 state to the nf = 2 state in the hydrogen atom? 1 1 -18 – ΔE = - 2.178 x 10 J ( 2 2 ) nf ni Example What is the wavelength of a photon emitted during a transition from the ni = 5 state to the nf = 2 state in the hydrogen atom? ΔE = hν 1 1 ΔE = - 2.178 x 10-18J – c ( 22 52 ) = λ ν hc (3.00 x 108 m/s) (6.63 x 10-34Js) λ = = = 4.34 x 10-7m ΔE - 4.58 x 10-19J = 434 nm A Complex and only Partially Correct Solution Neils Bohr The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell Wave /Particle Duality If a light wave has a “particular” nature might not a particle have wave properties. The Wave Nature of Matter • Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass and wavelength was h λ = Electronic mv Structure of Atoms © 2012 Pearson Education, Inc. Louis Victor De Broglie showed that electrons have wave properties wave-particle duality h The less massive an object the λ = longer its wavelength mv Standing Waves node node 1/2 wave length n = 4 n = 4.32 hydrogen electron the circumference of a visualized as a standing particular circular wave around the orbit has to correspond nucleus to a whole number of wavelengths The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell The Uncertainty Principle Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position is known: Electronic Structure of Atoms © 2012 Pearson Education, Inc. The Uncertainty Principle h (Δx) (Δmv) ≥ 4π position momentum Electronic Structure of Atoms © 2012 Pearson Education, Inc. The Uncertainty Principle In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! Electronic Structure of Atoms © 2012 Pearson Education, Inc. The Players Erwin Schrodinger Werner Heisenberg Louis Victor De Broglie Neils Bohr Albert Einstein Max Planck James Clerk Maxwell Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • This is known as quantum mechanics. Electronic Structure of Atoms © 2012 Pearson Education, Inc. Quantum Mechanics • The wave equation is designated with a lowercase Greek psi (ψ). Electronic Structure of Atoms © 2012 Pearson Education, Inc. Quantum Mechanics • The square of the wave equation, ψ2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. Electronic Structure of Atoms © 2012 Pearson Education, Inc. Erwin Schrodinger an orbital can be thought of as the wave function of an electron (ψ) which coordinates the x ,y, and z of an electrons position in a three- dimensional space Solutions of the Schrodinger Wave Equation for a One-Electron Atom Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. Electronic Structure of Atoms © 2012 Pearson Education, Inc. Erwin Schrodinger n l ml ( 1, 0, 0 ) Ψ 2 1s Electron density Distance from the nucleus (r) Charge-Cloud Model No orbit path for electrons. Energy levels or shells are the average points on a probability plot. 38 Erwin Schrodinger the square of the Schrodinger Equation gives us the probability of finding an electron in a certain region of space Ψ 2 1s Electron density Distance from the nucleus (r) Neils Bohr Explained the emission spectrum of hydrogen atom on basis of quantization of electron energy..
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