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p31318notes10.pdf - 1 P313 Notes 10 Electron Configurations...

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1 P313 Notes 10 Electron Configurations Addition, or “coupling”, of Angular Momenta Electron Configurations The energy of an electron depends mostly upon the principal quantum number n , and to a lesser extent on the other quantum numbers. All electrons with n = 1 are said to be in the K -shell. (The notation comes from X-ray spectroscopy). These are the electrons with the lowest-lying energy. To remove a K- shell electron from an atom requires a lot of energy. All electrons with n = 2 are said to be in the L -shell. All electrons with n = 3 are said to be in the M -shell. All electrons with n = 4 are said to be in the N -shell. etc. A electron is specified by four quantum numbers: n , l , m l , m x . ( m j l n , , , will also do, but for the present discussion we are going to use n , l , m l , m x .) No two electrons can have the same set of these four quantum numbers. This is Pauli’s Exclusion Principle . If you think of an eigenfunction (or rather of ψψ *) as representing a charge distribution, a charge distribution is uniquely determined by the four quantum numbers, and there cannot be two different eigenfunctions with the same set of quantum numbers. In a more sophisticated alternative interpretation, which you will meet in courses on Statistical Mechanics and Quantum Mechanics, you will understand that the Exclusion Principle is a consequence of the indistinguishability of electrons. Furthermore, the principle applies only to particles with integral-plus-one-half spin. Such particles are known collectively as fermions , of which electrons, protons and neutrons are examples. Photons and pions have integral spin, and are known collectively as bosons . For a given n , there are n possible values of l , namely . 1 ,... 3 , 2 , 1 , 0 - = n l Such electrons are referred to as s, p. d, f ... electrons. For a given l , there are 1 2 + l values of m l , namely l l l l l m l , 1 , .... , 0 .... , 2 , 1 , - + - + - - = For a given n that’s 2 1 0 ) 1 2 ( n l n l = + - = combinations so far. But for each of these n 2 combinations, there are two possible values of s m , namely .
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