Lecture8-9

U o we saw this in helium u at some point this

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Unformatted text preview: d singly o  Energy par2cle 46 Atoms 47 The Pauli Exclusion Principle u༇  The four quantum numbers discussed so far can be used to describe all the electronic states of an atom regardless of the number of electrons in its structure u༇  The Exclusion Principle states that no two electrons in an atom can ever be in the same quantum state o  Therefore, no two electrons in the same atom can have the same set of quantum numbers o  The energy levels fill up from the lowest E The spin sta2s2cs makes the MaOer par2cles like the electron and proton, and the Energy par2cles like the photon. Atomic Spectra are Rich in Informa2on If we measure the energy of a Hydrogen atom, the only possible answers we can get are one of the En. Similarly if we measure the z component of angular momentum, the mj only possible values we can get are 2 If we measure total angular momentum squared we can get j ( j + 1)49 Clicker: Angular Momentum u༇  A Hydrogen atom is in the 3p state (n=3, l=1). If a measurement of L2, the square of the angular momentum vector is made, what are the possible outcomes? A.  B.  C.  D.  E.  0 or 0 or 2 2 anything less than 50 Clicker: Angular Momentum u༇  A Hydrogen atom is in the 3d state (n=3, l=2). If a measurement of Lz, the z component of angular momentum is made, what are the possible outcomes? A.  B.  C.  D.  E.  - 2, - 1, 0, 1, 2 - 1, 0, 1 2 2 - 2 , - 1 , 0 , 1 , 2 51 Hydrogenic States in Mul2- electron Atoms u༇ It will prove to be very useful to understand atoms in terms of the states that we have studied for Hydrogen, with Z increased. u༇ Consider Helium (Z=2, 2e) as a simple case of the problem. p Ze p Ze e H= 2 1 2m 2 − 4πε 0 r1 + 2 2 2 − 2 m 4πε 0 r2 H = H1 + H 2 + V (| r1 − r2 |) 2 + 4πε 0 | r1 − r2 | o  We use solu2ons of the problem without V and treat V as a (large) correc2on o  H1 and H2 are the same (iden2cal electrons) 52 Spin States for 2 Electrons u༇  There is one spin state of two electrons that is an2symmetric under interchange. o  lets call it the singlet u༇  There are three spin states of two electrons that are symmetric under interchange. o  lets call them the triplet u༇  Remember symmetric...
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