Chapter 9: Electrons in Atoms Chemistry 140 Fall 2002 General Chemistry Principles and Modern Applications Petrucci • Harwood • Herring 8th Edition Chapter 9: Electrons in Atoms Philip Dutton University of Windsor, Canada N9B 3P4 Prentice-Hall © 2002 (modified 2003 by Dr. Paul Root and 2005 by Dr. David Tramontozzi) When we look at electron in atoms we begin to look into a field of chemistry / physics known as quantum theory. It is used to explain what is going on at the molecular and atomic level. Prentice-Hall © 2002 General Chemistry: Chapter 9

Unofficial Midterm Marks Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Contents 9-1 Electromagnetic Radiation 9-2 Atomic Spectra 9-3 Quantum Theory 9-4 The Bohr Atom 9-5 Two Ideas Leading to a New Quantum Mechanics 9-6 Wave Mechanics 9-7 Quantum Numbers and Electron Orbitals Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Contents 9-8 Quantum Numbers 9-9 Interpreting and Representing Orbitals of the Hydrogen Atom 9-9 Electron Spin 9-10 Multi-electron Atoms 9-11 Electron Configurations 9-12 Electron Configurations and the Periodic Table Focus on Helium-Neon Lasers Prentice-Hall © 2002 General Chemistry: Chapter 9

9-1 Electromagnetic Radiation Chemistry 140 Fall 2002 9-1 Electromagnetic Radiation Electric and magnetic fields propagate as waves through empty space or through a medium. A wave transmits energy. This chapter looks at atomic structure, by looking at the interactions between electromagnetic radiation and atomic structure, but to do this we first look at interactions of electromagnetic radiation and matter. To do any of this we must first understand what is electromagnetic radiation. A wave is a disturbance that transmit energy through a medium. Small boat as a wave passes by knows the boat moved up with the wave and drops down after the wave passes. A more tangible approach to look at waves is to use a rope: fixing a rope at one end and oscillating the other, creates waves that pass along a rope. amplitude – height of the wave above the line it starts from wavelength – distance from peak to peak, designated by the letter lambda wavelength Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Chemistry 140 Fall 2002 EM Radiation Low  Low frequency, high wavelength Along with wavelength another important characteristic of a wave is the frequency Frequency (v) is a measure of velocity, or how fast the front wave is travelling High  High frequency, low wavelength Prentice-Hall © 2002 General Chemistry: Chapter 9

Frequency, Wavelength and Velocity Chemistry 140 Fall 2002 Frequency, Wavelength and Velocity Frequency () in Hertz—Hz or s-1. Wavelength (λ) in meters—m. cm m nm Å pm (10-2 m) (10-6 m) (10-9 m) (10-10 m) (10-12 m) Velocity (c) = 2.997925 × 108 m s-1. constant velocity c = λ λ = c/ = c/λ The relationship between wavelength. Frequency and speed of light. Is shown……. Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Example 9-1 Most of the light from a sodium vapour lamp has a wavelength of 589nm. What is the frequency of this radiation? 1 x 10-9m 1 nm = 5.89 x 10-7m λ = 589 nm x c = 2.998 x 108m/s v = l c 2.998 x 108 m/s = = 5.09 x 1014 s-1 = 5.09 x 1014 Hz 5.89 x 10 -7 m Prentice-Hall © 2002 General Chemistry: Chapter 9

Electromagnetic Spectrum Chemistry 140 Fall 2002 Electromagnetic Spectrum Diagram shows the wide range of possible wavelengths and frequencies for some common types of electromagnetic radiation. Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 ROYGBIV Red Orange Yellow 700 nm 450 nm Green Blue Indigo Violet Prentice-Hall ©2002 General Chemistry: Chapter 9 Slide 8 Prentice-Hall © 2002 General Chemistry: Chapter 9

Constructive and Destructive Interference Constructive Interference Destructive Interference Prentice-Hall © 2002 General Chemistry: Chapter 9

Examples of Interference Chemistry 140 Fall 2002 Examples of Interference As waves collide / interfere with each other constructive interference occurs In cd’s sunlight containing all wavelengths hits a cd that have groves that reflect light. Depending on the angle of the CD, the reflected light interferes either constructively or destructively. Changing the angle of the CD to the light source changes the rainbow. Prentice-Hall © 2002 General Chemistry: Chapter 9

Waves of differing λ differ in speeds in other media. Chemistry 140 Fall 2002 Refraction of Light The speed of light in any medium other that a vacuum is slower, as a consequence light is refracted When a beam of white light is passed through a transparent medium, the wavelengths of light are refracted differently and are dispersed into its components Speed of light slows in any media other than a vacuum therefore, light gets refracted. Waves of differing λ differ in speeds in other media. Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Chemistry 140 Fall 2002 9-2 Atomic Spectra H2(g) He(g) Li Na K Hydrogen Helium Lithium Sodium Potassium Characteristic of wavelenght in each element Each element has its own distinctive line spectrum-akin to a fingerprint!! Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Chemistry 140 Fall 2002 Atomic Spectra Also called a discontinuous spectrum Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Chemistry 140 Fall 2002 9-3 Quantum Theory Blackbody Radiation: Max Planck, 1900: Energy, like matter, is discontinuous. Heated bodies emit light – stove elements = red, light bulb = white Blackbody Radiation I  λ Classical theory predicts continuous increase of intensity with wavelength. 1900, Max Planck made the revolutionary proposal that ENERGY, LIKE MATTER, IS DISCONTINUOUS. Introduces the concept of QUANTA of energy. h = 6.62607 x 10-34 J s. E = h h = 6.62607 x 10-34 J s Prentice-Hall © 2002 General Chemistry: Chapter 9

The Photoelectric Effect Chemistry 140 Fall 2002 The Photoelectric Effect Light striking the surface of certain metals causes ejection of electrons.  > o - threshold frequency e- α I - # e- emitted depends on intensity ek a  - kinetic energy of emitted e- depends on frequency of light Discovery that light striking an object results in the ejection of electrons. Electromagnetic radiation has particle like qualities light has particle like qualities called photons. Prentice-Hall © 2002 General Chemistry: Chapter 9

The Photoelectric Effect Chemistry 140 Fall 2002 The Photoelectric Effect Phonton strikes a bound eletron which absorbges the energy, if binding energy (known as the work function) is less than photon energy, the e- is ejected. Stopping voltage of photoelectrons as a function of frequency of incident radiation. Threshold frequency found by extrapolation. Prentice-Hall © 2002 General Chemistry: Chapter 9

The Photoelectric Effect Chemistry 140 Fall 2002 The Photoelectric Effect At the stopping voltage the kinetic energy of the ejected electron has been converted to potential. 1 mu2 = eVs 2 At frequencies greater than o: M, u , e = mass, speed, charge Vs = stopping voltage Vo = thresh hold frequency Vs = k ( - o) Prentice-Hall © 2002 General Chemistry: Chapter 9

The Photoelectric Effect eVo Ek = eVs Eo = ho o = h eVo, and therefore o, are characteristic of the metal. Conservation of energy requires that: 1 Ephoton = Ek + Ebinding h = mu2 + eVo 2 1 Ek = Ephoton - Ebinding eVs = mu2 = h - eVo 2 Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Chemistry 140 Fall 2002 9-4 The Bohr Atom En = -RH n2 RH = 2.179  10-18 J Electrons move in circular orbits about the nucleus. Motion described by classical physics. Fixed set of stationary states (allowed orbits). Governed by angular momentum: nh/2π, n=1, 2, 3…. Energy packets (quanta) are absorbed or emitted when electrons change stationary states. The integral values are allowed are called quantum numbers. rn = n2a0 = 0.53Å (53 pm) Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Example 9-3 Is it likely that there is an energy level for the hydrogen atom En = -1.00 x 10-20 J ? En = -RH / n2 n2 = -RH / En n2 = -2.179 x 10-18 J / -1.00 x 10-20 J = 217.9 n = 14.79 ….. because n is not an integer, this is not an allowed energy level for hydrogen ….. Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Energy-Level Diagram ΔE = Ef – Ei = -RH nf2 ni2 – = RH ( ni2 1 nf2 – ) = h = hc/λ Prentice-Hall © 2002 General Chemistry: Chapter 9

Example 9-4 λ = 434.1 nm 1 1 1 1 DE = E5 – E2 = RH ( ) – = RH ( ) – Determine the wavelength of the Balmer series of hydrogen corresponding to the transition from n = 5 to n = 2 1 1 1 1 DE = E5 – E2 = RH ( ) – = RH ( ) – ni2 nf2 52 22 the negative sign indicates that energy is emitted = -4.576 x 10-19 J E = hv and v = c / l then E = hc / l λ = (6.626 x 10-34 J s photon-1)(2.998 x 108 m s-1) 4.576 x 10-19 J = 434.1 nm Prentice-Hall © 2002 General Chemistry: Chapter 9

Ionization Energy of Hydrogen 1 1 ΔE = RH ( – ) = h ni2 nf2 As nf goes to infinity for hydrogen starting in the ground state: h = RH ( ni2 1 ) = RH This also works for hydrogen-like species such as He+ and Li2+. En = -Z2 RH Where Z = atomic number n2 Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Example 9-5 Determine the kinetic energy of the electron ionized from a Li2+ ion from its ground state, using a photon frequency of 5.000 x 1016 s-1. En = -Z2RH / n2 En = [-(32)(2.179 x 10-18J) / 12 ] = -1.961 x 10-17 J (energy required to remove electrons creating Li2+) E = hv = (6.626 x 10-34 J s photon-1)(5.000 x 1016 s-1) = 3.313 x 10-17 J photon-1 (energy carried by the photon) Prentice-Hall © 2002 General Chemistry: Chapter 9

General Chemistry: Chapter 9 Example 9-5 The ionization energy (the energy required to remove the electron) is Ei = -E1 = 1.961 x 10-17J. The extra energy from the photon is converted into kinetic energy Kinetic energy = 3.313 x 10-17 J – 1.961 x 10-17 J = 1.352 x 10-17 J Prentice-Hall © 2002 General Chemistry: Chapter 9

HAVE A GOOD HALLOWE’EN WEEKEND (DON’T FORGET TO TURN YOUR CLOCKS BACK AND ENJOY THAT EXTRA HOUR OF SLEEP ON SUNDAY!!) Prentice-Hall © 2002 General Chemistry: Chapter 9