092810 Lecture 2

092810 Lecture 2 - Welcome to:! Chemistry 120A! Lecture 2!...

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Unformatted text preview: Welcome to:! Chemistry 120A! Lecture 2! Atomic Properties, Periodic Trends and Bonding Types! Prof. Joshua Figueroa ! The Electronic Structure of Hydrogen
 States of the Electron in an Atom! The spin quantum number arises from rela3vis3c effects that are not included in the Schrödinger equa3on. An electron in an orbital is fully described by the four quantum numbers: n, l, ml and ms The electron spin does not affect the spa3al probability density of the electron, but it doubles the number of quantum states with energy En: 2n2 Ground state of H atom: 1s (n = 1, l = 0, ml = 0, ms = + ½ or –½) Therefore, two degenerate states. 1st excited states of H atom: 2s (n = 2, l = 0, ml = 0, ms = +/ ­ ½) or 2p (n = 2, l = 1, ml =  ­1,0,1, ms = +/ ­ ½) Therefore, eight degenerate states. Multi-Electron Atoms! How can we construct the periodic table based on quantum numbers? 1.  Solve the wave equa3on exactly for the H atom. 2.  Use the exact orbitals for the H atom as a star3ng approxima3on for the many electron atom; treat a mul3 ­electron state as a sum of single electron states (Hartree orbital approxima3on). 3.  Quantum numbers obtained for H atom can be used to describe the many ­electron atom. What is the Orbital Approximation for a Many-Electron Atom?! The electron density of an isolated many-electron atom is ~ the sum of the electron densities of each of the individual electrons. The electrons in an orbital are described by the same four quantum numbers as the H atom: (n, l, ml, ms) but the energies of the orbits depend on both n and l. •  Orbital energies in a given n become lower (more nega3ve) with increasing Z •  Orbital energies are related to the type of orbital; the orbitals with different values of l within a shell are not degenerate (as in H atom) What is the Effect of Other Electrons? Effec3ve Nuclear Charge, Zeff •  Shielding is responsible for the different energies of electrons with the same value of n and different values of l: the inner electrons (those with greater penetra3on) screen or shield the outer electrons from the full Coulombic effect of the nucleus, increasing the energy of the orbital in which the electron is found What is the Effect of Other Electrons? Effec3ve Nuclear Charge, Zeff • Shielding is responsible for the different energies of electrons with the same value of n and different values of l: the inner electrons (those with greater penetra3on) screen or shield the outer electrons from the full Coulombic effect of the nucleus, increasing the energy of the orbital in which the electron is found •  Zeff = net effec3ve posi3ve charge aXrac3ng an electron. Zeff = Z – Zcore_electrons In general, Zeff < Z   Penetration of the subshells: s > p > d > f   Zeff(ns) > Zeff(np) > Zeff(nd) > Zeff(nf) to a first approximation   E(ns) < E(np) < E(nd) RH = Rydberg Constant (mass of proton) Orbital Energies! Relative Orbital Energies for the 
 Multi-Electron Atom! For atoms with Z < 20 4s is lower energy (more negative) than 3d. For Z >20 the reverse is true. 3s < 3p <3d 2s < 2p Similar valence shell configura3ons result in similar proper3es: Radii of isoelectronic atoms, anions, and ca3ons Ioniza3on energies Electron affini3es •  Elements in the same group have the same number of valence electrons and therefore exhibit similar chemical proper3es •  The ground ­state electron configura3on of the elements (and therefore, the proper3es that depend on it) vary periodically with atomic number 10 Values of Zeff for Atoms! Across a period, electrons join the same valence shell (n is constant). Electrons in the same shell are not effective in shielding the charge of the nucleus (shielding is constant for same value of n). Rule: Zeff increases going across a period of the Table. 11 12 There is a correlation between Zeff for the valence electrons and atomic radius of each element. 13 14 From the Bohr model: rn = (n2/Zeff)a0 “average” radius of an orbital For the same value of n (across a period): r ∝ 1/Zeff –  Zeff increases across a period –  Each successive electron is added to the same shell (constant shielding), resulting in an increased attraction of nucleus to electrons –  Atomic radius decreases across a period For different values of n (down a group): r ∝ n2/Zeff –  Relative Zeff increases (slightly) down a group –  Electrons are added to a shell of higher n, a greater distance from the nucleus (lower penetration). –  Atomic radius increases down a group 15 16 17 18 From the Bohr model: En =  ­(Zeff2/n2)RH energy of electron in orbital n rn = (n2/Zeff)a0 “average” radius of an orbital The energy needed to remove an electron from the outermost occupied shell depends on both Eeff and reff. Eeff increases and reff decreases (both increase IE) as one goes across a period. Excep3ons are due to special stability of subshells. Eeff decreases and reff increases (both decrease IE) as one goes down a group. Conclusions from experimental IE values: An abrupt change in IE in going along a period or group of the periodic table indicates a change in the valence electron shell or subshell. 19 20 21 22 23 24 In most heteronuclear covalent bonds, the nucleus of one atom attracts e- more strongly than the nucleus of the other atom. This creates an electric dipole moment, µ (Greek mu), whereby one nucleus has a partial (+) charge and the other a partial (–) charge. Partial charges are indicated by superscript δ+ or δ- (Greek delta); The cross-base arrow points to the negative partial charge A measure of the ability or tendency of an atom to attract electrons from another atom to which it is bound is termed electronegativity, χ (Greek “chi”). This unitless property is related to the ionization energy and electron affinity, which provide an indication of how readily an atom may want attract or release electron density in a bond. When comparing two elements, that with the higher χ value will attract e- more strongly in the bond (it has the greater pulling power). Linus Pauling advanced an electronegativity scale which is based on the dissociation energies, D (in eV), of the homonuclear (A-A, B-B) and heteronuclear (A-B) bonds. He defined the difference in electronegativities of two elements A and B as: χA − χB = 0.102 D( A − B ) − 0.5( D( A − A ) + D( B − B ) ) Pauling argued that the excess bond energy is a result of the ionic component of the bond caused by partial charges on atoms A and B. € Electronegativities (unitless averages) computed with this method are based on fluorine having an arbitrarily set value of 4.00 (today χF = 3.98). The relative values for all other elements are positive < 3.98. Many other electronegativity scales exist, but a simple and intuitive relationship was devised by Robert Mulliken: 1 χ = ( IE1 + EA1 ) 2 € χ Since ionization energies are much greater than electron affinities, electronegativities correlate reasonably well with IEs. That is, the higher IE1, the greater the value of χ for an element. On the Mulliken Scale, Ne is the most ! Electronegative (but it forms no bonds!)! χ Increases with Increasing Zeff (or) χ Decreases with Increased Shielding For Different Periods, Orbital Energies Decrease with Increasing Z! For Different Periods, Orbital Energies Decrease with Increasing Z! For Different Periods, Orbital Energies Decrease with Increasing Z! χ Increases with Increasing Zeff (or) χ Increases with Increasing Zeff (or) For Different Periods, Orbital Energies Decrease with Increasing Z! z x y 2px 2px z x y 2px ΔE! 2px More carbon character! z x y 2px 2px More oxygen character! ...
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This note was uploaded on 08/15/2011 for the course CHEM 114B taught by Professor Wang during the Spring '09 term at UCSD.

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