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

Section 11.1 Rutherford’s Atom Return to TOC Copyright © Cengage Learning. All rights reserved 2 Nuclear Model of the Atom The atom has a small dense nucleus which  is positively charged.  contains protons (+1 charge).  contains neutrons (no charge). The remainder of the atom  is mostly empty space.  contains electrons (–1 charge).

Section 11.1 Rutherford’s Atom Return to TOC Copyright © Cengage Learning. All rights reserved 3 The nuclear charge (n+) is balanced by the presence of n electrons moving in some way around the nucleus. What are the electrons doing? How are the electrons arranged and how do they move?

Section 11.2 Electromagnetic Radiation Return to TOC Copyright © Cengage Learning. All rights reserved 4 One of the ways that energy travels through space is by LIGHT (huge amount of photons). How do these various types of electromagnetic radiation differ from one another?

Properties of Waves Wavelength ( ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. 7.1 Electromagnetic radiation Frequency ( ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c

x = c = c/ = 3.00 x 10 8 m/s / 500 x m What is the frequency of light with wavelength of 500nm? = 6.00 x s Practice problem of chap7:Q1

Section 11.2 Electromagnetic Radiation Return to TOC Copyright © Cengage Learning. All rights reserved 7 Characteristics Frequency ( ) – number of waves (cycles) per second that pass a given point in space Speed (c) – speed of light (3.00×10 8 m/s) So, different wavelengths of electromagnetic radiation carry different amount energy. E = h  = hc/  (h is Plank constant)

E = h x E = 6.63 x (J s) x 3.00 x 10 8 (m/s) / x (m) E = 1.29 x J E = h x c /  7.2 When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is nm. Energy of light: E = h  h x c /  Planck’s constant (h)  h = 6.63 x Js

Light is emitted as e - moves from one energy level to a lower energy level Bohr’s Model of the Atom (1913) E n = -R H ( ) 1 n2n2 n (principal quantum number) = 1,2,3,… R H (Rydberg constant) = 2.18 x J 7.3

E photon =  E = E f - E i E f = -R H ( ) 1 n2n2 f E i = -R H ( ) 1 n2n2 i i f  E = R H ( ) 1 n2n2 1 n2n2 n f = 1 n i = 2 n f = 1 n i = 3 n f = 2 n i = Transition between energy states if n i > n f, then emission occurs = h x

E photon = 2.18 x J x (1/25 - 1/9) E photon =  E = x J = 6.63 x (Js) x 3.00 x 10 8 (m/s)/1.55 x J = 1280 nm Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. E photon = h x c /  = h x c / E photon i f  E = R H ( ) 1 n2n2 1 n2n2 E photon = 7.3

Section 11.4 The Energy Levels of Hydrogen Return to TOC Copyright © Cengage Learning. All rights reserved 12 Atomic states  Excited state – atom with excess energy(NOT STABLE)  Ground state – atom in the lowest possible state When an H atom absorbs energy from an outside source it enters an excited state.

Section 11.4 The Energy Levels of Hydrogen Return to TOC Copyright © Cengage Learning. All rights reserved 13 Energy Level Diagram Energy in the photon corresponds to the energy used by the atom to get to the excited state.

Section 11.4 The Energy Levels of Hydrogen Return to TOC Copyright © Cengage Learning. All rights reserved 14 When an electric current is passed through a glass tube that contains hydrogen gas at low pressure the tube gives off blue light. When this light is passed through a prism. Only Four narrow bands of bright light are observed against a black background. Only certain types of photons are produced when H atoms release energy. Why?

Section 11.4 The Energy Levels of Hydrogen Return to TOC Copyright © Cengage Learning. All rights reserved 15 Quantized Energy Levels Since only certain energy changes occur the H atom must contain discrete energy levels.

Section 11.4 The Energy Levels of Hydrogen Return to TOC Copyright © Cengage Learning. All rights reserved 16 Quantized Energy Levels The energy levels of all atoms are quantized.

Section 11.7 The Hydrogen Orbitals Return to TOC Copyright © Cengage Learning. All rights reserved 17 Hydrogen Energy Levels Hydrogen has discrete energy levels.  Called principal energy levels  Labeled with whole numbers

Section 11.7 The Hydrogen Orbitals Return to TOC Copyright © Cengage Learning. All rights reserved 18 Energy Levels Each principal energy level is divided into sublevels.  Labeled with numbers and letters  Indicate the shape of the orbital  Orbital: Potential space for an electron. 1s 2s 3s 4s 2p 3p 4p 3d 4d4f

Electron Orbitals s orbital-1-spherical. The letter s means a spherical orbital. p orbitals--3-with different Orientation The letter p means a two–lobed orbital. The x, y, or z subscript on a p orbital label tells along which of the coordinate axes the two lobes lie. Orbitals grow larger with increasing n. Orientation of the 3 orbitals in a p subshell. l = 0 (s orbitals) l = 1 (p orbitals) l (angular momentum quantum number)

d Orbitals l = 2 (d orbitals)

f orbitals—7 with different Orientation

Electron Subshells The s, p, d & f subshells can hold specific numbers of electrons: s subshells (1 orbital) hold 2 electrons p subshells (3 orbitals) hold 6 electrons d subshells (5 orbitals) hold 10 electrons f subshells (7 orbitals) hold 14 electrons

Section 11.8 The Wave Mechanical Model: Further Development Return to TOC Copyright © Cengage Learning. All rights reserved 23 Principal Components of the Wave Mechanical Model of the Atom 1.Atoms have a series of energy levels called principal energy levels (n = 1, 2, 3, etc.). 2.The energy of the level increases as the value of n increases. 3.Each principal energy level contains one or more types of orbitals, called sublevels. 4.The number of sublevels present in a given principal energy level equals n.

Section 11.8 The Wave Mechanical Model: Further Development Return to TOC Copyright © Cengage Learning. All rights reserved 24 5.The n value is always used to label the orbitals of a given principal level and is followed by a letter that indicates the type (shape) of the orbital (1s, 3p, etc.). 6.An orbital can be empty or it can contain one or two electrons, but never more than two. If two electrons occupy the same orbital, they must have opposite spins. (Pauli Exclusion Principle) 7.The shape of an orbital does not indicate the details of electron movement. It indicates the probability distribution for an electron residing in that orbital.

Quantum Mechanical Description of the distribution of electrons in the atom: 4 quantum numbers: n (principal quantum number) l (angular momentum quantum number) m l (magnetic quantum number) m s (spin quantum number) Allowed values: n = 1,2,3 …,n l = 0,1,2,…,(n-1) m l = (-l, …, 0. …+l) m s = +1/2, -1/2

 = fn(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 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation 7.6

l = 0 (s orbitals) l = 1 (p orbitals) 7.6

l = 2 (d orbitals) 7.6

 = fn(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 7.6

m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2 7.6

 = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½ 7.6 Two possible spinning motions of an electron result in two different magnetic fields.

Schrodinger Wave Equation  = fn(n, l, m l, m s ) Shell (energy level) – electrons with the same value of n Subshell (sublevel) – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l 7.6

Which of the following sets of quantum numbers in an atom is acceptable? (a)(1, 0, +½, +½) (b) (3, 2, -2, -½) (c) (3, 3, 0, -½). (d) (4, 2, +3, +½) (e) (3, 0, +1, +½) Group practice problem of chap7:Q6 Allowed values: n = 1,2,3 …,n l = 0,1,2,…,(n-1) m l = (-l, …, 0. …+l) m s = +1/2, -1/2

Energy diagram 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 = s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

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 7.8

Electron Configurations Periods 1, 2, and 3 Three rules: 1.Electrons fill orbitals starting with lowest n and moving upwards (Aufbau principle: Fill up electrons in lowest energy orbitals ) 2. No more than two electrons can be placed in each orbital. No two electrons can fill one orbital with the same spin (Pauli exclusion principle: no two electrons in an atom can have the same four quantum numbers.) 3. For degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule: The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins ) Period 4 and Beyond the d orbitals begin to fill

1s 2 2s 2 2p 4 How to Write Electron Configurations the electron configuration for an oxygen atom would be written as… Principle #Letters represent subshells within shell(shapes of orbitals) Number of electrons in a given subshell 1s 2 2s 2 2p42p4 1s2 2s2 2p41s2 2s2 2p4 How about its orbital diagram? The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons in a particular set of degenerate (same energy) orbitals.

RIGHT General Rules for Writing Orbital Diagrams (Easy explanation of Hund’s rule) “Empty Bus Seat Rule” –Within a sublevel, place one e - per orbital before pairing them. So if you were putting electrons in a 2p sublevel, and all you had left was 4 electrons…

“Fill up” electrons in lowest energy orbitals (Aufbau principle) H 1 electron H 1s 1 He 2 electronsHe 1s 2 Li 3 electronsLi 1s 2 2s 1 Be 4 electronsBe 1s 2 2s 2 B 5 electronsB 1s 2 2s 2 2p 1 7.9

C 6 electrons The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C 1s 2 2s 2 2p 2 N 7 electronsN 1s 2 2s 2 2p 3 O 8 electronsO 1s 2 2s 2 2p 4 F 9 electronsF 1s 2 2s 2 2p 5 Ne 10 electronsNe 1s 2 2s 2 2p 6 7.7

Orbital diagrams Mn (25e - ): 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 5 1s2s3s4s3d2p3p Suppose you were asked to write the orbital diagram for manganese… The electron configuration is given by: The orbital diagram would be written…

What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s = 12 electrons 7.8 Abbreviated as [Ne]3s 2 core electronsvalence electrons electrons in the outermost (highest) principal energy level of an atom inner electrons [Ne]: 1s 2 2s 2 2p 6

What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p = 17 electrons Abbreviated as [Ne]3s 2 3p 5 [Ne]: 1s 2 2s 2 2p 6

Section 11.9 Electron Arrangements in the First Eighteen Atoms on the Periodic Table Return to TOC Copyright © Cengage Learning. All rights reserved 46 The electron configurations in the sublevel last occupied for the first eighteen elements.  The elements in the same group on the periodic table have the same valence electron configuration.  Elements with the same valence electron arrangement show very similar chemical behavior.

8.2 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

General rules for assigning electrons to atomic orbitals 1.Each shell or principle level of quantum number n contains n subshells. E.g. if n=2, there are two subshells (two values of l) of angular momentum quantum number. 2.Each subshell of quantum number l contains (2l+1) orbitals. E.g. if l=1, there are 3 p orbitals. 3.No more than two electrons can be placed in each orbital. 4.A quick way to determine the maximum number of electrons that an atom can have in principle level n is to use the formula of 2n 2.

Outermost subshell being filled with electrons 7.8

Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p 7.8 (not drawn into a magnetic field)(attracted by a magnetic field)

How many unpaired electrons are present in Al,N,Si,S? Unpaired electrons Al: 1s 2 2s 2 2p 6 3s 2 3p 11 N: 1s 2 2s 2 2p 33 Si: 1s 2 2s 2 2p 6 3s 2 3p 22 S: 1s 2 2s 2 2p 6 3s 2 3p 42 Practice problems of chap7:Q8,9