1. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Chapter 7 The Quantum– Mechanical Model of the Atom Chemistry: A Molecular Approach, 2nd Ed. Nivaldo Tro

2. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e The Beginnings of Quantum Mechanics Quantum mechanics forms the foundation of chemistry – explaining the periodic table and the behavior of the elements in chemical bonding – as well as providing the practical basis for lasers, computers, and countless other applications 2 Tro: Chemistry: A Molecular Approach, 2/e

3. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e The Behavior of the Very Small Electrons are incredibly small a single speck of dust has more electrons than the number of people who have ever lived on earth Electron behavior determines much of the behavior of atoms 3 Tro: Chemistry: A Molecular Approach, 2/e

4. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e A Theory that Explains Electron Behavior The quantum-mechanical model explains the manner in which electrons exist and behave in atoms It helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons why some elements are metals and others are nonmetals why some elements gain one electron when forming an anion, whereas others gain two why some elements are very reactive while others are practically inert and other periodic patterns we see in the properties of the elements 4 Tro: Chemistry: A Molecular Approach, 2/e

5. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e The Nature of Light: Its Wave Nature Light is a form of electromagnetic radiation composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field  an electric field is a region where an electrically charged particle experiences a force  a magnetic field is a region where a magnetized particle experiences a force All electromagnetic waves move through space at the same, constant speed 3.00 x 10 8 m/s in a vacuum = the speed of light, c 5 Tro: Chemistry: A Molecular Approach, 2/e

6. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Electromagnetic Radiation 6 Tro: Chemistry: A Molecular Approach, 2/e

7. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Speed of Energy Transmission 7 Tro: Chemistry: A Molecular Approach, 2/e

8. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Characterizing Waves The amplitude is the height of the wave the distance from node to crest  or node to trough the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light The wavelength ( ) is a measure of the distance covered by the wave the distance from one crest to the next, or trough to trough 8 Tro: Chemistry: A Molecular Approach, 2/e

9. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Wave Characteristics 9 Tro: Chemistry: A Molecular Approach, 2/e

10. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Characterizing Waves The frequency ( ) is the number of waves that pass a point in a given period of time the number of waves = number of cycles units are hertz (Hz) or cycles/s = s −1  1 Hz = 1 s −1 The total energy is proportional to the amplitude of the waves and the frequency the larger the amplitude, the more force it has the more frequently the waves strike, the more total force there is 10 Tro: Chemistry: A Molecular Approach, 2/e

11. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e The Relationship Between Wavelength and Frequency For waves traveling at the same speed, the shorter the wavelength, the more frequently they pass 11 Tro: Chemistry: A Molecular Approach, 2/e λ = Wavelength. Units of meters. ν = frequency. Units of hertz (Hz) or 1/sec.

12. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Calculate the wavelength of red light in units of nanometers with a frequency of 4.62 x 10 14 s −1 the unit is correct, the wavelength is appropriate for red light Check: Solve: ∙ = c, 1 nm = 10 −9 m Conceptual Plan: Relationships: = 4.62 x 10 14 s −1, (nm) (Given: 1m = 1 x10 -9 nm) Given: Find: (s −1 )  (m) (nm) 12 Tro: Chemistry: A Molecular Approach, 2/e

13. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Color The color of light is determined by its wavelength or frequency White light is a mixture of all the colors of visible light a spectrum RedOrangeYellowGreenBlueViolet 13 Tro: Chemistry: A Molecular Approach, 2/e

14. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Amplitude & Wavelength 14 Tro: Chemistry: A Molecular Approach, 2/e

15. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e The Electromagnetic Spectrum Visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum Shorter wavelength (high-frequency) light has higher energy radiowave light has the lowest energy gamma ray light has the highest energy High-energy electromagnetic radiation can potentially damage biological molecules ionizing radiation 15 Tro: Chemistry: A Molecular Approach, 2/e

16. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Energy and Frequency relationship E= energy. Units of J h= Planck’s constant (6.626x10 -34 J. s). This number does not change. v= frequency. Units of Hz or 1/sec.

17. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Example: A photon of light has a frequency of 1.1 x 10 10 Hz. What is the energy of this photon?

18. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Electromagnetic Spectrum 18 Tro: Chemistry: A Molecular Approach, 2/e

19. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Continuous Spectrum 19 Tro: Chemistry: A Molecular Approach, 2/e

20. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Thermal Imaging using Infrared Light 20 Tro: Chemistry: A Molecular Approach, 2/e

21. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Sunburns Caused by High-Energy UV Radiation 21 Tro: Chemistry: A Molecular Approach, 2/e

22. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Using High-Energy Radiation to Kill Cancer Cells 22 Tro: Chemistry: A Molecular Approach, 2/e

23. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Practice – Order the following types of electromagnetic radiation: microwaves, gamma rays, green light, red light, ultraviolet light By wavelength (short to long) By frequency (low to high) By energy (least to most) gamma < UV < green < red < microwaves microwaves < red < green < UV < gamma 23 Tro: Chemistry: A Molecular Approach, 2/e

24. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Ejected Electrons One photon at the threshold frequency gives the electron just enough energy for it to escape the atom binding energy,  When irradiated with a shorter wavelength photon, the electron absorbs more energy than is necessary to escape This excess energy becomes kinetic energy of the ejected electron Kinetic Energy = E photon – E binding KE = h −  24 Tro: Chemistry: A Molecular Approach, 2/e

25. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Spectra When atoms or molecules absorb energy, that energy is often released as light energy fireworks, neon lights, etc. When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum non-continuous can be used to identify the material  flame tests 25 Tro: Chemistry: A Molecular Approach, 2/e

26. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Exciting Gas Atoms to Emit Light with Electrical Energy 26 Tro: Chemistry: A Molecular Approach, 2/e

27. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Identifying Elements with Flame Tests NaKLiBa 27 Tro: Chemistry: A Molecular Approach, 2/e

28. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Emission Spectra 28 Tro: Chemistry: A Molecular Approach, 2/e

29. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Examples of Spectra 29 Tro: Chemistry: A Molecular Approach, 2/e

30. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Emission vs. Absorption Spectra Spectra of Mercury 30 Tro: Chemistry: A Molecular Approach, 2/e

31. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Solutions to the Wave Function,  Calculations show that the size, shape, and orientation in space of an orbital are determined to be four integer terms These integers are called quantum numbers principal quantum number, n angular momentum quantum number, l magnetic quantum number, m l Magnetic spin quantum number, m s 31 Tro: Chemistry: A Molecular Approach, 2/e PAULI EXCLUSION PRINCIPLE: No two electrons can have the same four quantum numbers.

32. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Principal Quantum Number, n Characterizes the energy of the electron in a particular orbital corresponds to Bohr’s energy level n can be any integer  1 The larger the value of n, the more energy the orbital has 32 Tro: Chemistry: A Molecular Approach, 2/e

33. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Principal Energy Levels in Hydrogen 33 Tro: Chemistry: A Molecular Approach, 2/e

34. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Angular Momentum Quantum Number, l The angular momentum quantum number determines the shape of the orbital l can have integer values from 0 to (n – 1) Each value of l is called by a particular letter that designates the shape of the orbital s orbitals are spherical p orbitals are like two balloons tied at the knots d orbitals are mainly like four balloons tied at the knot f orbitals are mainly like eight balloons tied at the knot 34 Tro: Chemistry: A Molecular Approach, 2/e

35. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e l = 0, the s orbital 35 Tro: Chemistry: A Molecular Approach, 2/e

36. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e p orbitals 36 Tro: Chemistry: A Molecular Approach, 2/e

37. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e d orbitals 37 Tro: Chemistry: A Molecular Approach, 2/e

38. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e f orbitals 38 Tro: Chemistry: A Molecular Approach, 2/e

39. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Magnetic Quantum Number, m l The magnetic quantum number is an integer that specifies the orientation of the orbital the direction in space the orbital is aligned relative to the other orbitals Values are integers from −l to +l including zero gives the number of orbitals of a particular shape  when l = 2, the values of m l are −2, −1, 0, +1, +2; which means there are five orbitals with l = 2 39 Tro: Chemistry: A Molecular Approach, 2/e

40. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Magnetic Spin Quantum Number, m s Designates the spin of the electron; clockwise or counterclockwise The value can only be +1/2 or -1/2 40

41. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Quantum Mechanical Explanation of Atomic Spectra Each wavelength in the spectrum of an atom corresponds to an electron transition between orbitals When an electron is excited, it transitions from an orbital in a lower energy level to an orbital in a higher energy level When an electron relaxes, it transitions from an orbital in a higher energy level to an orbital in a lower energy level When an electron relaxes, a photon of light is released whose energy equals the energy difference between the orbitals 41 Tro: Chemistry: A Molecular Approach, 2/e

42. Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, 2/e Electron Transitions To transition to a higher energy state, the electron must gain the correct amount of energy corresponding to the difference in energy between the final and initial states Electrons in high energy states are unstable and tend to lose energy and transition to lower energy states Each line in the emission spectrum corresponds to the difference in energy between two energy states 42 Tro: Chemistry: A Molecular Approach, 2/e