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322.3 CHEM ATOMIC AND MOLECULAR STRUCTURE I This week we shall examine in greater detail how the Schrodinger atom explains the fine lines in atomic spectra and how the Schrodinger model treats multi-electron atoms. Fine lines involve two types of transitions: transitions from p and d orbitals, and doublets produced by the interaction of electron spin (spin angular momentum, S) with the angular spin (orbital angular momentum, L) creating a total angular momentum, J, of the electron. Photons have angular momentum; thus an electron transition must be accompanied by a change in angular momentum (the law of conservation of momentum) as well as a change in principle quantum number (energy depends on n). These requirements are called SELECTION RULES (TRANSPARENCY - Selection Rules). Since the selection rules allow for transitions from any principle quantum number, transitions such as 2p 3d or 3p 5s are permitted. The transitions represented by the Grotrian diagram of lithium (TRANSPARENCY - Energy Level Diagram of the Li Atom) illustrate the application of these selection rules to atomic spectra for multi-electron atoms. Example 3.1 Since electrons have spin, a clockwise-spinning electron that is promoted to a p orbital could end up either clockwise-spinning or anticlockwise-spinning. This spin angular momentum couples with the orbital momentum to create two transitions: When the spin and orbital angular momenta are parallel, the total angular momentum is their sum; when the two angular momenta are opposed, the total angular momentum is their difference. Spectroscopists (physicists and chemists who specialize in spectroscopy) invented a shorthand for conveying the possible outcomes of spin-orbit coupling, called term symbols. Term symbols show the S, L, and J values at a glance (TRANSPARENCY - Term Symbols and Atomic Spectra). Example 3.2 Example 3.3 Although the Schrodinger model provides a way to proceed to atoms more complex than hydrogen, it must be understood that the Schrodinger equation can be solved exactly only for hydrogen. Electronic configurations for all other atoms are only approximate. To generate electronic configurations for multi-electron atoms, electrons are put into hydrogen-like orbitals in accordance with three principles: 1) the Buildingup Principle (fill the lowest energy levels first), 2) the Pauli principle (no more than two electrons in an orbital), and 3) Hund's rule (maximize the number of electrons in separate orbitals). The effect of Hund's rule is that many have atoms unpaired electrons and have a weak attraction to a magnetic field called paramagnetism (TRANSPARENCY - Guoy Balance for Measuring Paramagnetism) Example 3.4: Example 3.5 Periodic properties of atoms depend on the tightness with which they hold their electrons. The fact that the properties are periodic points to the importance of the outer or valence configuration in predicting binding. But what about the exceptions: Why does size decrease across a row? Why does 4s fill before 3d? Why is the ionization potential of boron less than that of beryllium? Why is the ground state electron configuration of Cu [K]4s13d10 rather than [K] 4s23d10? The answer to all of these is the effect of the filled inner orbitals which decrease the nuclear charge as felt by the outermost electrons. Thus an electron far from the nucleus is "shielded" by the presence of the many electrons between it and the nuclear center wheras an electron close to the nucleus is "shielded" by only a few electrons. Shielding explains why size decreases; nuclear charge is increasing but the electrons are entering orbitals of the same radial energy so they feel the nuclear charge more. 4s fills before 3d because the s orbitals are less shielded (have a greater electron density near to the nucleus) than the p orbitals and both s and p orbitals penetrate more than d orbitals. In a multi-electron atom each inner electron shields the outer electrons from the nucleus. Thus orbitals that can penetrate more experience a more favorable electrostatic potential and their orbitals energies are lowered from what they are in a single electron atom (TRANSPARENCY - Radial Distributions). Thus ns orbitals always fill before np orbitals. And, because d orbitals lie even farther from the nucleus, ns orbitals fill up even before (n-1)d orbitals. As a result 4s is at a lower energy level than 3d and fills first and K falls under Na in the periodic table as predicted by the empirical evidence. In fact, it requires the presence of only seven electrons to distort the orbitals enough to reduce the energy of the 4s orbital below that of 3d (TRANSPARENCY - Orbital Energies as a Function of Atomic Number). Several chemists have developed scales to calculate Zeff, this "effective nuclear charge". An easy to use set of rules to evaluate Zeff for electrons in different orbitals has been developed by Slater. Example 3.6 The fact that the hydrogenic orbitals permit such adjustment for charge is a great strength of the Schrodinger approach Example 3.7

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