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1 Chapter 7 Part 2 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Quantum Theory and the Electronic Structure of Atoms

2 Shortcomings of Bohr’s model Did not account for the emission spectra of atoms containing more than on electron. Did not explain extra lines in the emission spectra for hydrogen when magnetic field is applied. Conflict with discovery of ‘wavelike’ properties – how can you define the location of a wave? Heisenberg Uncertainty Principle It is impossible to know simultaneously both the momentum p (defined as mass times velocity) and the position of a particle with certainty.

Schrodinger Wave Equation 3 In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e -

4 Schrodinger Wave Equation Wave function (  ) describes: 1. energy of e - with a given  2.    probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. http://www.youtube.com/watch?v=LFBrRKnJMq4

Electron Density of Helium electron density – probability that an electron will be found in a particular region of an atom atomic orbital – probability of locating an electron in space 5

6 Schrodinger Wave Equation  is a function of four numbers called quantum numbers (n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus

7 Where 90% of the e - density is found for the 1s orbital

8 quantum numbers: (n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

9 l = 0 (s orbitals) l = 1 (p orbitals)

10 l = 2 (d orbitals)

11 quantum numbers: (n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation

12 m l = -1, 0, or 1 3 orientations is space

13 m l = -2, -1, 0, 1, or 25 orientations is space

14 (n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½

15 Existence (and energy) of electron in an atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation quantum numbers: (n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

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17 Schrodinger Wave Equation quantum numbers: (n, l, m l, m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l How many electrons can an orbital hold?

18 How many 2p orbitals are there in an atom? How many electrons can be placed in the 3d subshell?

19 List the values of n, ℓ, and m ℓ for orbitals in the 4d subshell. What is the total number of orbitals associated with the principle quantum number n=3?

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Problem 6 Give the values of the quantum numbers associated with the orbitals in the 3p subshell. n = ____ ℓ = ____ m ℓ =____ 21

Problem 7 What is the total number of orbitals associated with the principle quantum number n=4. 22

23 Energy of orbitals in a single electron atom Energy only depends on principal quantum number n E n = -R H ( ) 1 n2n2 n=1 n=2 n=3

24 Energy of orbitals in a multi-electron atom Energy depends on n and l n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2

25 “Fill up” electrons in lowest energy orbitals (Aufbau principle) H

26 “Fill up” electrons in lowest energy orbitals (Aufbau principle) He

27 “Fill up” electrons in lowest energy orbitals (Aufbau principle) Li

28 “Fill up” electrons in lowest energy orbitals (Aufbau principle) Be

29 “Fill up” electrons in lowest energy orbitals (Aufbau principle) B

30 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C

31 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). N

32 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). O

33 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). F

34 The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). Ne

35 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

36 Write the four quantum numbers for an electron in a 3p orbital (6 combinations).

37 An oxygen atom has a total of eight electrons. Write the four quantum numbers for each of the electrons in the ground state..

38 Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 principal quantum number n angular momentum quantum number l number of electrons in the orbital or subshell Orbital diagram H 1s 1

39 What are the electron configurations of fluorine and chlorine?

40 What is the electron configuration of Mg? What are the possible quantum numbers for the last (outermost) electron in Cl?

41 What is the maximum number of electrons that can be present in the principle level for which n=3?

Problem 9 Calculate the total number of electrons that can be present in the principle level for which n=4 42

Problem 10 Write a complete set of quantum numbers for each of the electrons in boron. 43

44 Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

45 Outermost subshell being filled with electrons

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47 Write the ground state electron configuration for sulfur Write the ground state electron configuration for palladium which is diamagnetic

Problem 11 Write the ground state configuration for phosphorus. 48

49 ns 1 ns 2 ns 2 np 1 ns 2 np 2 ns 2 np 3 ns 2 np 4 ns 2 np 5 ns 2 np 6 d1d1 d5d5 d 10 4f 5f Ground State Electron Configurations of the Elements

Irregularities in Electron Configurations Chromium Expected: [Ar] 4s 2 3d 4 Actual: [Ar] 4s 1 3d 5 Copper Expected: [Ar] 4s 2 3d 9 Actual: [Ar] 4s 1 3d 10 Why? There is a slightly greater stability in a perfectly half-filled or fully-filled d orbital 50

51 Electron Configurations of Cations and Anions Na [Ne]3s 1 Na + [Ne] Ca [Ar]4s 2 Ca 2+ [Ar] Al [Ne]3s 2 3p 1 Al 3+ [Ne] Atoms lose valence electrons so that cation has a noble-gas outer electron configuration. H 1s 1 H - 1s 2 or [He] F 1s 2 2s 2 2p 5 F - 1s 2 2s 2 2p 6 or [Ne] O 1s 2 2s 2 2p 4 O 2- 1s 2 2s 2 2p 6 or [Ne] N 1s 2 2s 2 2p 3 N 3- 1s 2 2s 2 2p 6 or [Ne] Atoms gain valence electrons so that anion has a noble-gas outer electron configuration. Of Representative Elements

52 +1+2+3 -2-3 Cations and Anions Of Representative Elements

53 Na + : [Ne]Al 3+ : [Ne] F - : 1s 2 2s 2 2p 6 or [Ne] O 2- : 1s 2 2s 2 2p 6 or [Ne]N 3- : 1s 2 2s 2 2p 6 or [Ne] Na +, Al 3+, F -, O 2-, and N 3- are all isoelectronic with Ne What neutral atom is isoelectronic with H - ? Isoelectronic: have the same number of electrons, and hence the same ground-state electron configuration

54 Electron Configurations of Cations of Transition Metals When a cation is formed from an atom of a transition metal, electrons are always removed first from the ns orbital and then from the (n – 1)d orbitals. Fe: [Ar]4s 2 3d 6 Fe 2+ : [Ar]4s 0 3d 6 or [Ar]3d 6 Fe 3+ : [Ar]4s 0 3d 5 or [Ar]3d 5 Mn: [Ar]4s 2 3d 5 Mn 2+ : [Ar]4s 0 3d 5 or [Ar]3d 5 What are the electron configurations of Cu +2 and Cu +1 ?

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