# Chapter One (continued)

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1 Slide 1 of 39 Chapter One (continued) Many Electron Atoms and The Periodic Table

2 Slide 2 of 39 Multielectron Atoms In the hydrogen atom, all subshells of a principal shell are at the same energy level. In a multielectron atom, several electrons are attracted to the nucleus while simultaneously repelling one another. Orbital energies are lower in multielectron atoms than in the hydrogen atom. In a multielectron atom the various subshells of a principal shell are at different energy levels.

3 Slide 3 of 39 Orbital Energy Diagrams E = 2 2 n h 2 8mL E Z me 2n h Zeff me = 2 2 E = 2 2 2n h

4 Penetration Effect 3s > 3p > 3d Shielding Effect Slide 4 of 39

5 Slide 5 of 39 Slater s Rule Slater's Rule determines the shielding constant which is represented by S. To determine the effective nuclear charge use this equation: Z*=Z-S. According to Slater's rule, the electrons are grouped like: (1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p)(5d)(5f)... Electrons to the right of the electron you have chosen do not contribute because they don't shield. In the same group, each electron shields If the desired electron is in the (s,p) orbital, each electron in n-1 contribute Electrons in n-2 contribute 1.00 If the desired electron is in the (d,f) orbital, anything to the left shields completely and therefore has a value of 1.0.

6 Slide 6 of 39 Example 1: Na (Z= 11) (1s) 2 (2s,2p) 8 (3s,3p) 1 from a 3s perspective S(3s)=8 x x 1.0 = 8.8 So, Z(3s)*= = 2.2 from a 2s perspective S(2s)=7 x x 0.85 = 4.15 So, Z(3s)*= = 6.85 Example 2: Sc (Z= 21) (1s) 2 (2s,2p) 8 (3s,3p) 8 (3d) 1 (4s,4p) 2 from a 4s perspective S(4s) = 1 x (0.35) + 1 x x 1.0 = 19.2 So, Z(4s)*= = 1.8 from a 3d perspective S(3d) = 8 x x 1.0 = 18 So, Z(4s)*=21-18 = 3

7 Slide 7 of 39

8 Slide 8 of 39

9 Slide 9 of 39 Principles of atom building (the Aufbau Principle) Quantum number principle The hydrogen atom quantum numbers can be used to describe electron states in any atoms Minimum energy principle place electrons in the states which lead atom having the lowest energy Pauli exclusion principle No two electrons in the same atom may have all four quantum numbers alike (An atomic orbital can accommodate only two electrons, and these electrons must have opposing spins)

10 Slide 10 of 39 Principles of atom building (continued) Hund s rule For orbitals of half-filled or less than half-filled, electrons will go into separate orbitals of the same energy (degenerate orbitals) with parallel spins

11 Electron Configurations Electron configuration describes the distribution of electrons among the various orbitals in the atom Electron configuration is represented in two ways The s, p, d, f notation (Z = 1) H 1s 1 (Z = 2) He 1s 2 (Z = 3) Li 1s 2 2s 1 or, [He]2s 1 Mn 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 5 C 1s 2 2s 2 2p 2 or, [He]2s 2 2p 2 or An orbital diagram 3d 4s Slide 11 of 39

12 (m l ) (0) (0) (-1, 0, +1) Slide 12 of 39

13 Subshell Filling Order Slide 13 of 39

14 Slide 14 of 39 E Z = 2 4 eff me 2 2 2n h Sc Z=21 In higher numbered principal shells of a multielectron atom, some subshells of different principal shells have nearly identical energies.

15 Slide 15 of 39 Ca [Ar]4s 2 Ti [Ar]4s 2 3d 2 Ti + [Ar]4s 1 3d 2 Ti 2+ [Ar]3d 2 Fe 2+ [Ar]3d 6

16 Slide 16 of 39 Exceptions to the Aufbau Principle Elements will fill out a lower subshell to obtain a lower energy state Cr and Cu fill out their 3d shell before the 4s shell. Elements in the same family as Cr and Cu behave in a similar way.

17 Slide 17 of 39 Main Group and Transition Elements Elements in which the orbitals being filled in the aufbau process are either s or p orbitals of the outermost shell are called main group elements The first 20 elements are all main group elements In transition elements, the d subshell being filled in the aufbau process is in an inner principal shell

18 The Periodic Table Slide 18 of 39

19 Slide 19 of 39 Valence Electrons and Core Electrons The valence shell is the outermost occupied shell Valence electrons are those with the highest principal quantum number They occupy the outermost principal shell of an atom Electrons in inner shells are called core electrons Their principal quantum number are less than n In the calcium atom with the electron configuration of [Ar]4s 2, the 4s electrons are valence electrons and those in the [Ar] configuration are core electrons

20 Slide 20 of 39 Electron Configurations of Some Metal Ions [Ar]3d 10 [Kr]4d 10 [Xe]5d 10 Inert Pair Effect (6s 2 )

21 Slide 21 of 39 Periodic Atomic Properties of The Elements The distance between the nuclei of two atom is the atomic radius The covalent radius is one-half the distance between the nuclei of two identical atoms joined into a molecule The metallic radius is half the distance between the nuclei of adjacent atoms in a solid metal Atomic radii increase from top to bottom within a group of the periodic table and decrease from left to right in a period of the periodic table

22 Covalent Radius of Iodine Slide 22 of 39

23 Slide 23 of 39

24 Slide 24 of 39

25 Atomic Radii of the Elements Slide 25 of 39

26 Slide 26 of 39 Ionic Radii The ionic radius of each ion is the portion of the distance between the nuclei occupied by that ion Cations are smaller than the atoms from which they are formed; The nucleus attracts the remaining electrons more strongly Anions are larger than the atoms from which they are formed;the greater number of electrons repel more strongly Isoelectronic defines elements that all have the same number of electrons For a series of isoelectronic species with the same electron configuration, the great the nuclear charge, the smaller the species

27 The Ionic Radii of Mg 2+ and O 2- Slide 27 of 39

28 Slide 28 of 39

29 Effective nuclear charges are similar Slide 29 of 39 Representative Atomic and Ionic Radii

30 Slide 30 of 39 Ionization Energy Ionization energy is the energy required to remove an electron from a ground state atom in the gaseous state A(g) fi A + (g) + e - DH > 0, IE = DH The quantity of energy is usually expressed in terms of a mole of atoms With the continual removal of electrons, ionization energy greatly increases Removing a core electron takes impressively more energy than removing a valence electron

31 Selected Ionization Energies IE(2p) < IE(2s) IE of half-filled orbitals is higher because it has less e - -e - repulsion 1 ev = kj/mol Slide 31 of 39

32 First Ionization Energies Slide 32 of 39

33 Slide 33 of 39 Boron (B), electron configuration 1s 2 2s 2 2p 1 B(g) fi B + (g) + e - IE(1) = 801 kj/mol B + (g) fi B 2+ (g) + e - IE(2) = 2,427 kj/mol B 2+ (g) fi B 3+ (g) + e - IE(3) = 3,660 kj/mol B 3+ (g) fi B 4+ (g) + e - IE(4) = 25,025 kj/mol B 4+ (g) fi B 5+ (g) + e - IE(5) = 32,822 kj/mol Valence electrons Core electrons

34 Slide 34 of 39 Electron Affinity Electron affinity is the energy change that occurs when an electron is added to a gaseous atom A(g) + e - fi A - (g) generally DH < 0, EA = - DH Electron affinities are generally expressed as positive, although the process is exothermic Electron affinity increases to the right and up the periodic table

35 Slide 35 of 39 Selected Electron Affinities 1 ev = kj/mol

36 Electronegativity Electronegativity (EN, expressed as χ), is a measure of the ability of an atom to attract bonding electrons to itself when the atom is in a molecule. Mulliken s EN Absolute EN, χ M = (IE + EA)/2 Pauling s EN define χ (H) = 2.2 χ = χ (A) - χ (B) = [ ΑΒ (kj)/96.49] 1/2 = [ ΑΒ (kcal)/23.06] 1/2 ΑΒ = D(A-B) - [D(A-A) x D(B-B)] 1/2 Bond dissociation energy of A-B Slide 36 of 39

37 Pauling s Electronegativities 2.2 χ P = 1.35 χ M½ Slide 37 of 39

38 Slide 38 of 39 Polarizability ( )- the ability of electron distribution to be distorted by an electric field

39 Polarizability ( ) Hardness (η) Absolute hardness, η = (IE EA) /2 Y Y + + e Y + e Y - H 1 = IE H 2 = -EA 2Y Y + + Y - H 1 + H 2 = IE EA Y ½ (Y + + Y - ) ½ ( H 1 + H 2 ) = (IE EA)/2 = η e.g. η(li) = (IE EA) /2 = (520-60)/2 =230 kj/mol η(cs) = (376-46)/2 =165 kj/mol => Li is harder than Cs, or Cs is softer than Li. Slide 39 of 39

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