L35 - Atomic Emission Lecture 35 Electron Clouds: Quantum...

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Unformatted text preview: Atomic Emission Lecture 35 Electron Clouds: Quantum model Na Key Idea: The distances of electrons from the nucleus are described in terms of probability. Sr Ba Ca Emission and absorption spectra Ultraviolet absorption spectrum for hydrogen ionization Absorbance 0.75 Ry 0.89 Ry 0.94 Ry 0.96 Ry 0.97 Ry 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Light Energy (Ry) Ry = 2.18 x 10-18 J/atom Astronomers use spectroscopy to identify the elements present in stars http://casswww.ucsd.edu/public/tutorial/Stars.html Visible: 0.15Ry - 0.22Ry Ultraviolet: 0.22Ry - 73Ry Energy and radius of the electron in H depend on "n" Observable: light energy 0 -0.06Ry -0.11Ry -0.25Ry Energy n=4 n=3 n=2 Energy levels of hydrogen atom (not to scale) !E = -Ry (1/nf2 - 1/ni2) Model of the H atom: En = Ry (1/n2) r = ao n 2 n = principal quantum # Ry = 2.18 x 10-18 J/atom ao = 0.053 nm or 0.53 visible infrared -0.06Ry -0.11Ry -0.25Ry -1.00Ry n=1 Why are the energies negative? How much energy is needed to remove the electron? -1.00Ry ultraviolet -1.00Ry = 2.18 x 10-18 J/atom = 1312 kJ/mol Bohr model of hydrogen atom and H emission spectrum wavelength 434 nm frequency 6.9 x 1014 Hz energy 0.46 x 10-18 J/atom energy 0.21Ry color violet 486 nm 6.2 x 1014 Hz 0.41 x 10-18 J/atom 0.19Ry blue-green 657 nm 4.6 x 1014 Hz 0.31 x 10-18 J/atom 0.14Ry red The potential energy landscape of H atom: the Bohr model Energy ni=5 ni=4 ni=3 nf=2 E = h" = h c # Only the first three orbits are shown. En = ! Z2 Ry n2 ! 1 1 " #E = Z 2 Ry % 2 $ 2 & , ni > n f = 1, 2, 3... %n & ' f ni ( Energy levels of hydrogen-like atoms H 0 -0.06Ry -0.11Ry -0.25Ry -1.00Ry Energy n=4 n=3 n=2 n=1 Energy 0 Energy levels of hydrogen-like atoms Model for hydrogen-like atoms: He+ -0.24Ry -0.44Ry -1.00Ry n=4 n=3 n=2 En = Ry (Z2) (1/n2) r = aon2/Z Z = nuclear charge ChemQuestions: Draw a shell model of H and He+. Predict the ionization energy of Li2+. -4.00Ry n=1 Emission and absorption spectra of low pressure Hg vapor Wave diffraction is a signature behavior of light. Hg atomic emission spectrum Light source Hg atomic absorption spectrum 400 500 600 700 nm What about electrons? Electron beam Electron gun Issues with the shell model of the atom: - If only works reasonably well for H-like atoms - For other atoms, there are more lines than predicted. - Why can a bound electron only have certain energies? - What is the significance of the number "n"? ? Just as light can behave as particles (photons), particles (electrons) behave as waves! Wave like diffraction pattern Traveling waves and standing waves L de Broglie: electron wavelength, # = h/mev != 2L ; n = 1, 2, 3, ... n Properties of standing waves L n=1 n=2 n=3 n=4 # of nodes 0 1 2 3 Electron in an atom behaves as a circular standing wave. The energy is higher for: larger n larger # of nodes larger " smaller # Unlike the vibrating guitar string, the electron wave persists forever. Since the electron behaves as a wave, or rather is a wave, it is not correct to think of it as orbiting the nucleus. nodes Wave Mechanics had to be developed to replace the classical Newtonian mechanics. Description of an electron in an atom is given by a wave function, $(x, y, z). In addition to n, the principle quantum number, Two more quantum numbers appear: l and m While $ is just a mathematic description of the electron wave, $2 gives the probability density of finding the electron in a vicinity of a particular point in space. Probability density [1/m3] is the probability divided by the volume of space of interest. $ gives the amplitude of the electron standing wave. $ can take positive and negative values. $ shows nodes where electron wave has amplitude of 0. $1s2 of the electron in H atom in its ground state, n = 1. Note the radial symmetry of $1s2 To obtain the probability of finding an electron at a particular distance from the nucleus, we compute 4%r2$2, the probability distribution function. ao Wrap-up points The energy of light emitted and absorbed can be related to the energies of the electrons. For hydrogen-like atoms, the energy and radius of the electron depend on "n" and Z. Just as light can behave as particles (photons), particles (electrons) behave as waves. Spheres marking 90% probability of finding an electron. ao is Bohr radius of 0.529 or 0.0529 nm Quantum mechanics provides the best description of the energy and radius of an electron in terms of probability. ...
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