1. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 1 Chemistry FIFTH EDITION by Steven S. Zumdahl University of Illinois

2. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 2 Chemistry FIFTH EDITION Chapter 7 Atomic Structure and Periodicity

3. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 3 Section 7.5 (READ!!!) Quantum Mechanical Model of the Atom Totally different approach was needed. Three physicists: Heisenberg, de Broglie, & Schrodinger. Emphasizes the wave properties of an electron. Electron bound to the nucleus similar to a standing wave.

4. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 Figure 7.9 The Standing Waves Caused by the Vibration of a Guitar String Fastened at Both Ends Standing Waves  Waves not Traveling down the length of the string. Waves have nodes.

5. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 5 For the Electron in a Hydrogen Atom Electron bound to the nucleus. Similar situation of only certain allowable “Electron Waves.” Modeled by Schrödinger

6. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Figure 7.10 The Hydrogen Electron Visualized as a Standing Wave Around the Nucleus Limitations on allowed wavelength due to NODES. Node at each end. Therefore, wavelength must be a whole number of Half wavelengths.

7. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 7 Quantum Mechanics Based on the wave properties of the atom  = wave function = mathematical operator E = total energy of the atom A specific wave function is often called an orbital.

8. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 When eq’n is anaylzed, there are many solutions. Each sol’n is a wave function, , characterized by a particular value of E and is often called an orbital. Orbitals describe volumes of space where the electron is likely to be found. Orbitals are not orbits/not detailed pathways.

9. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 9 Heisenberg Uncertainty Principle For a particle so small such as an electron, the uncertainties become so significant that we can not know the exact motion of the electron as it moves around the nucleus. The quantum mechanical wave function provides us with the greatest probability of finding an electron near a particular point in space.

10. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 Heisenberg Uncertainty Principle x = position mv = momentum h = Planck’s constant The more accurately we know a particle’s position, the less accurately we can know its momentum.

11. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Probability Distribution 4 square of the wave function (Ψ 2 ) 4 probability of finding an electron at a given position 4

12. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12 Figure 7.11 Probability Distribution for the 1s Wave Function Intensity in color indicates the probability value near a given pt. in space.

13. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 Solution of Schrodinger Equation for the Hydrogen Atom Atomic Orbitals: space that encloses 90% of the total electron probability. Wave function for an electron in the Hydrogen atom. Each electron described by 4 different quantum numbers.

14. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 Homework Do Exercises 49, 51, 53, & 55.

15. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 Section 7.6 Quantum Numbers (QN) Four different quantum numbers. Three (n, l, m l ) specify the wave function that gives the probability of finding the electron at various pts. in space. Fourth (m s ) specifies the electron”spin”.

16. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 16 Quantum Numbers (QN) 1.Principal QN (n = 1, 2, 3,...) - related to size and energy of the orbital. - Shell Number - larger n, then higher energy

17. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 2. Angular Momentum Quantum Number (l = 0 to n  1) - relates to shape of the orbital. - Subshell l = 0 s subshell l = 1p subshell l = 2 d subshell l = 3f subshell

18. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 3. Magnetic Quantum Number (m l = l to  l) - relates to orientation of the orbital in space relative to other orbitals.

19. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 4. Electron Spin Quantum Number (m s = + 1 / 2,  1 / 2 ) - relates to the spin states of the electrons.

20. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 Section 7.7 Orbital Shapes & Energies Read Summary on page 296.

21. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 Figure 7.13 Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals Node – Area of Zero Probability.

22. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22 Figure 7.14 The Boundary Surface Representations of All Three 2p Orbitals No 1p orbital. In 2p, two lobes separated by a node at the nucleus. Labeled according to orientation.

23. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 23 Figure 7.15 A Cross Section of the Electron Probability Distribution for a 3p Orbital 3p -- Similar but more complex & larger.

24. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 24 Figure 7.16 The Boundary Surfaces of All of the 3d Orbitals No 1d or 2d orbitals. Five 3d orbital

25. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 25 Figure 7.17 Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

26. Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 Figure 7.18 Orbital Energy Levels for the Hydrogen Atom Orbitals with same n values are degenerate, i.e., same energy. Hydrogen’s single electron can occupy any of its atomic orbitals. What is the ground state or lowest energy state for Hydrogen?