5.111 Lecture Summary #7 Wednesday, September 17, 2014
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1 5.111 Lecture Summary #7 Wednesday, September 17, 2014 Readings for today: Section 1.12 Orbital Energies (of many-electron atoms), Section 1.13 The Building-Up Principle. (Same sections in 5 th and 4 th ed.) Read for Lecture #8: Section 1.14 Electronic Structure and the Periodic Table, Section 1.15, 1.16, 1.17, 1.18, and The Periodicity of Atomic Properties. (Same sections in 5 th and 4 th ed.) Topics: Multi-Electron Atoms I. Wavefunctions and Binding Energies for Multi-electron Atoms II. Electron Configurations I. WAVEFUNCTIONS AND BINDING ENERGIES FOR MULTIELECTRON ATOMS The Schrödinger equation correctly describes the electronic structure for all atoms. Multi-electron orbitals are similar in shape and have the same nodal structure as corresponding hydrogen one-electron orbitals. However, there are important differences in thinking about multi-electron binding energies! All orbitals in a multi-electron atom are lower in energy ( ) than the corresponding orbital in a hydrogen atom. The lower energy results in multi-electron atoms results from a higher Z--- a stronger pull from the nucleus. 1
2 The principal quantum number, n, is no longer the sole determining factor for the orbital energies of multi-electron atoms. Binding energy now depends on and. For -electron atoms For -electron atoms Where Z eff is the effective charge experienced by the electron in the n,l state. Z eff the same as Z for the nucleus. Z eff differs from Z because of. SHIELDING and Z eff To illustrate the effect of shielding, consider the two extreme shielding situations possible for the He atom (Z = 2). Extreme CASE A for He: Extreme shielding Electron #2 Electron #1 Z= 2 He nucleus (charge = ) Electron #2 maximally shields electron #1 from the (+) charge of the He nucleus Electron #1 experiences a force on average of Z eff =, not Z eff = +2e. The energy of electron #1 is that of an electron in an H (1-electron) atom. 2
3 Extreme CASE B for He: No shielding Electron #1 Electron #2 Z= 2 He nucleus (charge = +2e) Electron #2 doesn t participate in shielding electron #1 from the He nucleus Electron #1 experiences a force on average of Z eff =. The energy of electron #1 is that of an electron in a (1-electron) ion. Extreme case A: Z eff = 1, IE He = 2.18 x J Extreme case B: Z eff = 2, IE He = 8.72 x J Experimentally determined IE He = 3.94 x J shielding shielding So the reality is somewhere between total shielding and no shielding. We can calculate the Z eff from the experimentally determined IE: For an IE He of 3.94 x J, Z eff = between ( shielding) and ( shielding). 3
4 Why is E2s < (more negative than) E2p and E3s < E3p < E3d? For a given n state (shell), electrons in orbitals with lower values of l to the nucleus (even though r mp decreases with increasing l!). closer This means (for the same n): s-electrons are less shielded than p electrons. Thus E 2s E 2p p-electrons are less shielded than d- electrons. Thus E 3p E 3d Thus in a multi-electron atom, effects of penetration and shielding give rise to the order of energies of orbitals in a given shell of s < p < d < f. II. ELECTRON CONFIGURATIONS Electron configuration describes the electronic structure of an atom by specifying which orbitals are occupied. This notation is very useful, since electron structure dictates the chemical properties and reactivity of a given atom. How do we determine the electron configuration of an atom? AUFBAU PRINCIPLE Fill energy states (which depend on and ) one electron at a time, starting with the lowest energy state and following: 1) The Pauli Exclusion Principle 2) Hund s rule: when electrons are added to states of the same E, a single electron enters each state before a second electron enters any state. Spins remain prior to adding a second electron to any state. Let s try this for O (Z = 8). Electron configuration: (specifying m l ): You need only provide m l notation if specifically asked. 4
5 Electron configurations can be simplified by considering core versus valence electrons. Core electrons: electrons in inner shells making up a noble gas configuration. Valence electrons: electrons in the outer most shell. Valence electrons are the exciting ones. In general, only the valence electrons participate in chemical reactions. * Exceptions to the Aufbau principle: filled ( ) and half-filled ( ) d-orbitals have lower energy than simple theory predicts. Fifth Period: Rb to Xe. Mo and Ag are counterpart anomalies to Cr and Cu in 4 th period. Additional anomalies and other effects are difficult to predict. Mnemonic for electron configuration: diagonals Using this chart, we can write out the correct order of orbitals with increasing energy from left to right: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p 5
6 The periodic table can use be used for writing electron configurations Periodic Table of the Elements, by 2012rc, Wikimedia Commons. License CC-BY. ELECTRON CONFIGURATIONS OF IONS Electron configurations of ions are NOT ALWAYS the same as neutrals!!! Once a d orbital is filled, the orbital energy drops to below the corresponding s orbital. Consider Ti vs. Ti 2+ Ti [Ar]4s 2 3d 2 (standard notation) but, Ti [Ar] 3d 2 4s 2 (based on energy levels) thus, Ti 2+ [Ar] (electrons lost are from 4s) 6
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