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Transcript

Chemistry 2000 Spring 2017 Review: The quantum mechanical model of the atom 1 Review: Quantum Mechanics (Section 6.4) http://fakescience.org 2 Review: Quantum Mechanics (Section 6.4) 3 The Schrödinger equation – the solution for the H atom o o Austrian physicist Erwin Schrödinger used de Broglie’s insight to calculate what electron waves might act like, using a branch of mathematics known as wave mechanics The result is encapsulated in a complex formula known as the Schrödinger equation: 2 2 2 8 2m 2 ( E V ) 2 2 2 x y z b o o o o o o This equation was know to belong to a special class known as an eigenvector equation: an operator acts on a function (ψ) and generates a scalar times the same function Ψ is known as the wavefunction of the electron: there are an infinite number of such wavefunctions, each of which is characterized by a precise energy En, where n is an integer from 1,2,3,4….∞. V in the equation is a constant value: the potential energy from attraction to the nucleus. The remaining terms are all fundamental constants A wave function that satisfies the Schrödinger equation is often called an orbital. Orbitals are named for the orbits of the Bohr theory, but are fundamentally different entities An orbital is a wave function An orbital is a region of space in which an electron is most likely to be found The square of the amplitude of the wavefunction, ψ2, expresses the probability of finding the electron within a given region of space, which is called the electron density. Wavefunctions do not have a precise size, since they represent a distribution of possible locations of the electron, but like most distributions, they do have a maximum value. 5 probability distribution 6 probability density Figure 6.17 7 Quantum Numbers of an Atomic Orbital 8 Shells Subshells Table 6.2 The hierarchy of quantum numbers for atomic orbitals 9 Figure 6.19 The 2p orbitals 10 Figure 6.22 Energy levels of the H atom 11 Multi-electron atoms: Electron-electron repulsion - impossible to solve exactly. ms also enters into the theory (+½ or −½). 12 The quantum mechanics of molecules: H2+ Simplest molecule Three-body problem, no exact solutions. e− 1H + 1H+ 13 Born-Oppenheimer approximation Treat nuclei as immobile Separated by distance R Orbital energy = kinetic energy + electron-nuclear attraction H nuclei 14 The Effective Potential Figure courtesy of Prof. Marc Roussel 15 The Effective Potential Figure 8.13 16