chem lecture 6

chem lecture 6 - Let's Recap The Evolution of Quantum...

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Chemistry 6A Let’s Recap: The Evolution of Quantum Mechanics • Planck Equation E = h ν : Based on the photoelectric effect, E K of an electron is independent of intensity and proportional to frequency. • Bohr’s quantization of angular momentum for one-electron atoms: Yields allowed orbits and energy levels (states), and accounts for transitions between allowed states (defined by n). • Wave mechanics: Consider an electron as a wave. The wavefunction, ψ , describes the motion (location) of the electron, and is known as an atomic orbital . Ψ 2 is related to the probability of finding an electron. The solutions to the Schrödinger equation are the energies and wavefunctions of the allowed states. An electron in an orbital is characterized by four quantum numbers . 1
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Chemistry 6A Key Ideas and Nobel Prizes in Physics! "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta" 1918: Max Karl Ernst Ludwig Planck , Germany 1922: Niels Henrik David Bohr , Denmark "for his services in the investigation of the structure of atoms and of the radiation emanating from them" 1921: Albert Einstein , Germany and Switzerland "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" 2
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Chemistry 6A Key Ideas and Nobel Prizes in Physics! 1932: Werner Karl Heisenberg , Germany "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen" 1929 : Louis-Victor Pierre Raymond de Broglie , France "for his discovery of the wave nature of electrons" 1933: Erwin Schrödinger , Germany (1/2 of the prize) “for the discovery of new productive forms of atomic theory" And more! 3
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Chemistry 6A What is the total number of orbitals in principal shell 4? (a) 4 (b) 8 (c) 10 (d) 12 (e) 16 4
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Chemistry 6A A 4 th Quantum Number: Spin QN, m s Spin is a fundamental property of the electron, like its charge and mass An electron has two spin states, represented by and or α and β . The spin quantum number, m s , distinguishes the two spin states: m s = + ½ (spin up, ), or - ½ (spin down, ) An electron, because of its spin, generates a magnetic field (see arrows). Two electrons with opposing spins have opposing magnetic fields that cancel, leaving no net magnetic field for the pair. 5
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Chemistry 6A A beam of H atoms in the 1s state is split into two beams when passed through a non-uniform magnetic field. There must be two states of H which have a different energy in a magnetic field. 6
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Chemistry 6A The Electronic Structure of Hydrogren States of the Electron in an Atom The spin quantum number arises from relativistic effects that are not included in the Schrödinger equation. An electron in an orbital is fully described by the four quantum numbers : n, l , m l and m s The electron spin does not affect the spatial probability density of the electron, but it doubles the number of quantum states with energy E n : 2 n 2 Ground state of H atom: 1s (n = 1, l = 0, m l = 0, m s = + ½ or – ½ ) Therefore, two degenerate states.
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This note was uploaded on 08/07/2009 for the course CHEM 6A taught by Professor Pomeroy during the Spring '08 term at UCSD.

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chem lecture 6 - Let's Recap The Evolution of Quantum...

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