1. Chapter 5/1© 2012 Pearson Education, Inc. Wavelike Properties of Matter The de Broglie equation allows the calculation of a “wavelength” of an electron or of any particle or object of mass m and velocity v. mv h = Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light. In other words, perhaps matter is wavelike as well as particlelike.

2. Chapter 5/2© 2012 Pearson Education, Inc. Wavelike Properties of Matter mv h = What is the de Broglie wavelength in meters of a small car with a mass of 1150 kg traveling at a velocity of 24.6 m/s? 24.6 s m 6.626 x 10 -34 s kg m 2 = 2.34 x 10 -38 m (1150 kg) =

3. Chapter 5/3© 2012 Pearson Education, Inc. Quantum Mechanics and the Heisenberg Uncertainty Principle In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron. In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.

4. Chapter 5/4© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers Probability of finding electron in a region of space (  2 ) Wave equation Wave function or orbital (  ) solve A wave function is characterized by three parameters called quantum numbers, n, l, m l.

5. Chapter 5/5© 2012 Pearson Education, Inc. Principal Quantum Number (n) Describes the size and energy level of the orbital Commonly called a shell Positive integer (n = 1, 2, 3, 4, …) As the value of n increases: The energy increases The average distance of the e - from the nucleus increases Wave Functions and Quantum Numbers

6. Chapter 5/6© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers Angular-Momentum Quantum Number (l) Defines the three-dimensional shape of the orbital Commonly called a subshell There are n different shapes for orbitals If n = 1 then l = 0 If n = 2 then l = 0 or 1 If n = 3 then l = 0, 1, or 2 Commonly referred to by letter (subshell notation) l = 0s (sharp) l = 1p (principal) l = 2d (diffuse) l = 3f (fundamental)

7. Chapter 5/7© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers Magnetic Quantum Number (m l ) Defines the spatial orientation of the orbital There are 2l + 1 values of m l and they can have any integral value from -l to +l If l = 0 then m l = 0 If l = 1 then m l = -1, 0, or 1 If l = 2 then m l = -2, -1, 0, 1, or 2 etc.

8. Chapter 5/8© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers

9. Chapter 5/9© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers

10. Chapter 5/10© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers Identify the possible values for each of the three quantum numbers for a 4p orbital.

11. Chapter 5/11© 2012 Pearson Education, Inc. Wave Functions and Quantum Numbers n = 4l = 1m l = -1, 0, or 1 Identify the possible values for each of the three quantum numbers for a 4p orbital.

12. Chapter 5/12© 2012 Pearson Education, Inc. The Shapes of Orbitals Node: A surface of zero probability for finding the electron

13. Chapter 5/13© 2012 Pearson Education, Inc. The Shapes of Orbitals Node: A surface of zero probability for finding the electron

14. Chapter 5/14© 2012 Pearson Education, Inc. The Shapes of Orbitals