Prentice Hall © 2003Chapter 6 Chapter 6 Electronic Structure of Atoms CHEMISTRY The Central Science 9th Edition

Prentice Hall © 2003Chapter 6 Electromagnetic Radiation carries energy through space Speed of EMR through a vacuum: 3.00x10 8 m/s wavelike characteristics: wavelength,  distance from crest to crest) amplitude, A (height) frequency, (# of cycles which pass a point in 1 second) 6.1: The Wave Nature of Light

Prentice Hall © 2003Chapter 6 The wave nature is due to periodic oscillations of the intensities of electronic and magnetic forces associated with the radiation The # of times the cork bobs up and down is the frequency

Frequency and wavelength are inversely related Text, P. 200

Prentice Hall © 2003Chapter 6 The speed of a wave, c, is given by its frequency multiplied by its wavelength: For light, speed = c (that is 3.00 x 10 8 m/s)

Prentice Hall © 2003Chapter 6 Modern atomic theory arose out of studies of the interaction of radiation with matter Example: the visible spectrum

The Electromagnetic Spectrum, P. 201 (or Hz)

Prentice Hall © 2003Chapter 6 Text, P. 201

Prentice Hall © 2003Chapter 6 Sample Problem #19

The Nature of Energy The wave nature of light does not explain how an object can glow when its temperature increases.

Prentice Hall © 2003Chapter 6 Problems with wave theory: –Emission of light from hot objects “black body radiation”: stove burner, light bulb filament –The photoelectric effect –Emission spectra 6.2: Quantized Energy and Photons

Prentice Hall © 2003Chapter 6 Planck: energy can only be absorbed or released from atoms in certain amounts called quanta The relationship between energy and frequency is where h is Planck’s constant (6.626  J-s)

Prentice Hall © 2003Chapter 6 Quantization Analogy: Consider walking up a ramp versus walking up stairs: For the ramp, there is a continuous change in height Movement up stairs is a quantized change in height

Prentice Hall © 2003Chapter 6 The Photoelectric Effect Evidence for the particle nature of light -- “quantization” Light shines on the surface of a metal: electrons are ejected from the metal threshold frequency must be reached Below this, no electrons are ejected Above this, the # of electrons ejected depends on the intensity of the light

Text, P. 217

Prentice Hall © 2003Chapter 6 Einstein assumed that light traveled in energy packets called photons The energy of one photon: Energy and frequency are directly proportional Therefore radiant energy must be quantized!

Prentice Hall © 2003Chapter 6 Flame Tests: Pretty colors!

Prentice Hall © 2003Chapter 6 Sample Problems # 25, 29, 31

Prentice Hall © 2003Chapter 6 Line Spectra Radiation that spans an array of different wavelengths: continuous White light through a prism: continuous spectrum of colors Spectra tube emits light unique to the element in it Looking at it through a prism, only lines of a few wavelengths are seen Black regions correspond to wavelengths that are absent 6.3: Line Spectra and the Bohr Model

Continuous Visible Spectrum, P. 206

Prentice Hall © 2003Chapter 6

Prentice Hall © 2003Chapter 6 Bohr Model Rutherford model of the atom: electrons orbited the nucleus like planets around the sun Physics: a charged particle moving in a circular path should lose energy Therefore the atom should be unstable

Prentice Hall © 2003Chapter 6 3 Postulates for Bohr’s theory: 1.Electrons move in orbits that have defined energies 2.An electron in an orbit has a specific energy 3.Energy is only emitted or absorbed by an electron as it changes from one allowed energy state to another (E=hν)

Prentice Hall © 2003Chapter 6 Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra Bohr showed that where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else)

Prentice Hall © 2003Chapter 6 The first orbit in the Bohr model has n = 1, is closest to the nucleus, and has the lowest energy (ground state) The furthest orbit in the Bohr model has n close to infinity

Prentice Hall © 2003Chapter 6 Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hν) The amount of energy absorbed or emitted on movement between states is given by Sample Problems # 33 and 39

Prentice Hall © 2003Chapter 6 Line Spectra, P. 207 The Balmer series for Hydrogen (n f = 2, which is in the visible region) The Rydberg Equation (P. 206) allows for the calculation of wavelengths for all the spectral lines n = energy level n f values for other regions of the EMS: Lyman (UV): n f = 1 Paschen (IR): n f = 3 Brackett (IR): n f = 4 Pfund (IR): n f = 5 Note the units

Figure 6.14, P. 208 Using the Rydberg Equation, the existence of spectral lines can be attributed to the quantized jumps of electrons between energy levels (therefore justifying Bohr’s model of the atom) Balmer Series Energy Level Diagram Lyman Series Paschen Series Sample Problems # 41 and 43

Prentice Hall © 2003Chapter 6 The Electromagnetic Spectrum, P. 215 (or Hz)

Prentice Hall © 2003Chapter 6 Limitations of the Bohr Model It can only explain the line spectrum of hydrogen adequately Electrons are not completely described as small particles It doesn’t account for the wave properties of electrons DEMOS!

Prentice Hall © 2003Chapter 6 Using Einstein’s and Planck’s equations, de Broglie showed: The momentum, mv, is a particle property, but is a wave property Sample Exercise 6.5, P :The Wave Behavior of Matter VelocityMass

Prentice Hall © 2003Chapter 6 The Uncertainty Principle Heisenberg’s Uncertainty Principle: we cannot simultaneously define the position and momentum (= mv) of an electron. At best we can describe the position and velocity of an electron by a PROBABILITY DISTRIBUTION,

Moving Electron Photon Before Electron velocity changes Photon wavelength changes After

Prentice Hall © 2003Chapter 6 Erwin Schrödinger proposed an equation that contains both wave and particle termswave and particle terms Solving the equation leads to wave functions (shape of the electronic orbital) 6.5: Quantum Mechanics and Atomic Orbitals Schrödinger's cat

Prentice Hall © 2003Chapter 6 The electron density distribution in the ground state of the hydrogen atom Text, P. 227

Prentice Hall © 2003Chapter 6 Orbitals and Quantum Numbers If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. We call wave functions orbitals (regions of highly probable electron location). Schrödinger’s equation requires 3 quantum numbers: 1.Principal Quantum Number, n This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. Orbitals and Quantum Numbers If we solve the Schrödinger equation, we get wave functions and energies for the wave functions We call wave functions orbitals (regions of highly probable electron location) Schrödinger’s equation requires 3 quantum numbers: 1.Principal Quantum Number, n This is the same as Bohr’s n As n becomes larger, the atom becomes larger and the electron is further from the nucleus

Prentice Hall © 2003Chapter 6 2. Azimuthal Quantum Number, l This quantum number depends on the value of n The values of l begin at 0 and increase to (n - 1) We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3) Usually we refer to the s, p, d and f-orbitals (the shape of the orbital) (AKA “subsidiary quantum number”) 3. Magnetic Quantum Number, m l This quantum number depends on l The magnetic quantum number has integral values between -l and +l Magnetic quantum numbers give the 3D orientation of each orbital

Prentice Hall © 2003Chapter 6 “Aufbau Diagram”: electrons fill low energy orbitals first Figure 6.18, P. 229 As n increases, note that the spacing between energy levels becomes smaller

Prentice Hall © 2003Chapter 6 Sample Problems # 55, 57, 61,

Prentice Hall © 2003Chapter 6 The s-Orbitals All s-orbitals are spherical As n increases, the s-orbitals get larger 6.6: Representations of Orbitals

Prentice Hall © 2003Chapter 6 the s orbitals Text, P. 232

Prentice Hall © 2003Chapter 6 The p-Orbitals There are three p-orbitals p x, p y, and p z The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system The letters correspond to allowed values of m l of -1, 0, and +1 The orbitals are dumbbell shaped As n increases, the p-orbitals get larger

Prentice Hall © 2003Chapter 6 the p orbitals Text, P. 233

Prentice Hall © 2003Chapter 6 The d and f-Orbitals There are five d and seven f-orbitals FYI for the d-orbitals: Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes Four of the d-orbitals have four lobes each One d-orbital has two lobes and a collar Text, P

the d orbitals Text, P. 234

Prentice Hall © 2003Chapter 6 the f orbitals (not in text)

Prentice Hall © 2003Chapter 6

P orbitals Prentice Hall © 2003Chapter 6

d orbitals d orbitals Prentice Hall © 2003Chapter 6

Prentice Hall © 2003Chapter 6

Prentice Hall © 2003Chapter 6

S, P and D orbitals

Prentice Hall © 2003Chapter 6 (-l to +l) Max = (n-1) l  letter (n 2 ) (# of orientations) Text, P. 229

Prentice Hall © 2003Chapter 6 Orbitals and Their Energies Orbitals of the same energy are said to be degenerate For n  2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other Therefore, the Aufbau diagram looks slightly different for many-electron systems 6.7: Many-Electron Atoms

BOHR Text, P. 229 MODERN Text, P. 235

Electron Spin and the Pauli Exclusion Principle Since electron spin is also quantized, we define m s = spin quantum # =  ½ Text, P. 235

n ---> shell1, 2, 3, 4,... l ---> subshell0, 1, 2,... n - 1 m l ---> orbital -l l m s ---> electron spin+1/2 and -1/2 n ---> shell1, 2, 3, 4,... l ---> subshell0, 1, 2,... n - 1 m l ---> orbital -l l m s ---> electron spin+1/2 and -1/2 QUANTUMNUMBERSQUANTUMNUMBERS

Prentice Hall © 2003Chapter 6 :Pauli’s Exclusion Principle: no two electrons can have the same set of 4 quantum numbers Therefore, two electrons in the same orbital must have opposite spins Electron capacity of sublevel = 4l + 2 Electron capacity of energy level = 2n 2

Prentice Hall © 2003Chapter 6 Sample Problems # 67, 71 and configurations for hydrogen through oxygen

Prentice Hall © 2003Chapter 6 Hund’s Rule Electron configurations tell us in which orbitals the electrons for an element are located Three rules are applied: Aufbau Principle Pauli’s Exclusion Principle Hund’s Rule: for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron 6.8: Electron Configurations

Prentice Hall © 2003Chapter 6 Aufbau Diagram

Prentice Hall © 2003Chapter 6 Types of electron configurations Electron configuration notation: energy level, subshell, # of electrons per orbital Orbital diagram: each m l value is represented by a line, electrons are also shown Noble gas configuration: “condensed configuration” [Proceeding noble gas] electron configuration notation for outer shell electrons Inner shell e -

Orbital Diagrams Each box in the diagram represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the relative spin of the electron.

Periodic Patterns Shorthand Configuration  Core e - : Go up one row and over to the Noble Gas.  Valence e - : On the next row, fill in the # of e - in each sublevel.

[Ar]4s 2 3d 10 4p 2 Periodic Patterns Example - Germanium

Prentice Hall © 2003Chapter 6 The periodic table can be used as a guide for electron configurations The period number is the value of n 6.9: Electron Configurations and the Periodic Table

# of columns is related to the number of electrons that can fit in the subshells Regular trends Text, P. 225

 Full energy level  Full sublevel (s, p, d, f)  Half-full sublevel Stability

Irregularities: half filled and completely filled subshells are stable Text, P. 245

Electron Configuration Exceptions Copper EXPECT :[Ar] 4s 2 3d 9 ACTUALLY :[Ar] 4s 1 3d 10 Copper gains stability with a full d-sublevel. Stability

Electron Configuration Exceptions Chromium EXPECT :[Ar] 4s 2 3d 4 ACTUALLY :[Ar] 4s 1 3d 5 Chromium gains stability with a half-full d- sublevel. Stability

Stability Ion Formation  Atoms gain or lose electrons to become more stable.  Isoelectronic with the Noble Gases.

O 2- 10e - [He] 2s 2 2p 6 Stability Ion Electron Configuration  Write the e - config for the closest Noble Gas  EX: Oxygen ion  O 2-  Ne

Prentice Hall © 2003Chapter 6 Sample Problems # 75, 79, 77 and 79 elements.htmlhttp:// elements.html

Prentice Hall © 2003Chapter 6 End of Chapter 6