Quantum mechanics provides us with an understanding of atomic structure and atomic properties Lasers are one of the most important applications of the quantummechanical properties of atoms and light Chapter Goal To understand the structure and properties of atoms Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Topics today The Electron s Spin Multielectron Atoms The Periodic Table of the Elements Excited States and Spectra Lifetimes of Excited States Stimulated Emission and Lasers Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley The electron has an inherent magnetic moment and inherent angular momentum called spin designated vector S The z component of this spin angular momentum is The quantity ms is called the spin quantum number The ms state with Sz h bar is called the spinup state and the ms state is called the spin down state Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Example For 2 m 2 1 0 1 2 correspond to three different directions of orbital motion A magnetic moment is associated with the electron current The z component of the magnetic moment appears to be quantized Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Like a compass needle a magnetic moment interacts with an external magnetic field depending on its direction Low energy when aligned with field high energy when anti aligned The total energy of a hydrogenic electron in an external magnetic field is approximately This means that spectral lines will split in a magnetic field Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley 13 6 eV B 2 n 13 6 2 eV z B n 13 6 2 eV m B B n E Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley A neutral atom moving in uniform magnetic field feels no net force only a torque resulting in spin precession In an inhomogeneous magnetic field the net force is not zero It proportional to magnetic moment along the direction of magnetic field variation An atomic beam passing through an inhomogeneous field is observed to separate into discrete beams one per quantum angular momentum state Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley The currents and magnetism of electrons in atoms generally cancel out The magnetism of an unbalanced electron should produce an odd number 2L 1 values of m of beams Observation of an even number of beams and oddities in spectral splitting motivated the idea of intrinsic electron angular momentum and magnetism The electron has two magnetic states and two values of angular momentum Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Spin up Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Spin down Pauli discovered that two complex waves are required to describe a non relativistic electron In a magnetic field these are linked and describe spin orientation polarization Paul Dirac generalized this A relativistic electron is described by four coupled complex waves two more because an electron can go backwards in time appearing as an antielectron positron That s eight waves total counting real and imaginary parts Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley When analyzing a multielectron atom each electron is treated independently of the other electrons This approach is called the independent particle approximation or IPA This approximation allows the Schr dinger equation for the atom to be broken into Z separate equations one for each electron A major consequence of the IPA is that each electron can be described by a wave function having the same four quantum numbers n l m and ms used to describe the single electron of hydrogen A major difference however is that the energy of an electron in a multielectron atom depends on both n and l Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Notice for example 2p states are higher that 2s They are further out in radius so see a nuclear charge partially screened by 1s and 2s electrons Note that the scale and details will depend on Z Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley In 1925 Pauli hypothesized that no two electrons in a quantum system can be in the same quantum state In other words no two electrons can have exactly the same set of quantum numbers n l n and ms If one electron is present in a state it excludes all others This statement which is called the Pauli exclusion principle turns out to be an extremely profound statement about the nature of matter It applies to all spin kinds of particles fermions but not to integer spin particles bosons like photons Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley Putting electrons on atom Electrons are obey exclusion principle Only one electron per quantum state unoccupied occupied Hydrogen 1 electron n 1 states one quantum state occupied Helium 2 electrons two quantum states occupied Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley n 1 states Other elements Li has 3 electrons n 2 0 m 0 1 ms 2 n 2 0 m 0 1 ms 2 n 2 1 m 0 1 ms 2 n 2 1 m 0 1 ms 2 n 2 1 m 1 1 ms 2 n 2 1 m 1 1 ms 2 n 2 1 m 1 1 ms 2 n 2 1 m 1 1 ms 2 n 2 states 8 total 1 occupied n 1 states 2 total 2 occupied one spin up one spin down n 1 n 1 0 0 m 0 m 0 Copyright Pearson Education Inc publishing as Pearson Addison Wesley ms 1 2 m2008 s 1 2 Atom Configuration H 1s1 He 1s2 Li 1s22s1 Be 1s22s2 B 1s22s22p1 Ne etc 1s shell filled n 1 shell filled noble gas 2s shell filled 1s22s22p6 2p shell filled Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley n 2 shell filled noble gas Elements are arranged in the periodic table so that atoms in the same column have similar chemical properties Quantum mechanics explains this by similar outer electron configurations If not for Pauli exclusion principle all electrons would be in the 1s state H 1s1 Li 2s1 Na 3s1 Be 2s2 Mg 3s2 B 2p1 Al 3p1 C 2p2 Si 3p2 Copyright 2008 Pearson Education Inc publishing as Pearson Addison Wesley N 2p3 P 3p3 O 2p4 S 3p4 H 1s1 F 2p5 Cl 3p5 He 1s2 Ne 2p6 Ar 3p6 Orbital electron currents and magnetism generally cancel in multi electron atoms Spin and its magnetism generally cancels Unpaired orbital currents explain diamagnetism Unpaired spin
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