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Chemistry: A Molecular Approach, 2nd Ed. Nivaldo Tro Chapter 7 The Quantum– Mechanical Model of the Atom Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 2 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 3 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 4 Copyright 2011 Pearson Education, Inc. 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 108 m/s in a vacuum = the speed of light, c Tro: Chemistry: A Molecular Approach, 2/e 5 Copyright 2011 Pearson Education, Inc. Electromagnetic Radiation Tro: Chemistry: A Molecular Approach, 2/e 6 Copyright 2011 Pearson Education, Inc. Speed of Energy Transmission Tro: Chemistry: A Molecular Approach, 2/e 7 Copyright 2011 Pearson Education, Inc. 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 (l) is a measure of the distance covered by the wave the distance from one crest to the next, or trough to trough Tro: Chemistry: A Molecular Approach, 2/e 8 Copyright 2011 Pearson Education, Inc. Wave Characteristics Tro: Chemistry: A Molecular Approach, 2/e 9 Copyright 2011 Pearson Education, Inc. Characterizing Waves • The frequency (n) 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 Tro: Chemistry: A Molecular Approach, 2/e 10 Copyright 2011 Pearson Education, Inc. The Relationship Between Wavelength and Frequency • For waves traveling at the same speed, the shorter the wavelength, the more frequently they pass c ln Tro: Chemistry: A Molecular Approach, 2/e •λ = Wavelength. Units of meters. •ν = frequency. Units of hertz (Hz) or 1/sec. 11 Copyright 2011 Pearson Education, Inc. Calculate the wavelength of red light in units of nanometers with a frequency of 4.62 x 1014 s−1 Given: n = 4.62 x 1014 s−1 Find: l, (nm) (Given: 1m = 1 x10-9nm) Conceptual Plan: n (s−1) l (m) l (nm) Relationships: l∙n = c, 1 nm = 10−9 m Solve: Check: the unit is correct, the wavelength is appropriate for red light Tro: Chemistry: A Molecular Approach, 2/e 12 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 13 Copyright 2011 Pearson Education, Inc. Amplitude & Wavelength Tro: Chemistry: A Molecular Approach, 2/e 14 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 15 Copyright 2011 Pearson Education, Inc. Energy and Frequency relationship E hn • 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. Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Example: • A photon of light has a frequency of 1.1 x 1010 Hz. What is the energy of this photon? Tro: Chemistry: A Molecular Approach, 2/e Copyright 2011 Pearson Education, Inc. Electromagnetic Spectrum Tro: Chemistry: A Molecular Approach, 2/e 18 Copyright 2011 Pearson Education, Inc. Continuous Spectrum Tro: Chemistry: A Molecular Approach, 2/e 19 Copyright 2011 Pearson Education, Inc. Thermal Imaging using Infrared Light Tro: Chemistry: A Molecular Approach, 2/e 20 Copyright 2011 Pearson Education, Inc. Sunburns Caused by High-Energy UV Radiation Tro: Chemistry: A Molecular Approach, 2/e 21 Copyright 2011 Pearson Education, Inc. Using High-Energy Radiation to Kill Cancer Cells Tro: Chemistry: A Molecular Approach, 2/e 22 Copyright 2011 Pearson Education, Inc. Practice – Order the following types of electromagnetic radiation: microwaves, gamma rays, green light, red light, ultraviolet light • By wavelength (short to long) gamma < UV < green < red < microwaves • By frequency (low to high) microwaves < red < green < UV < gamma • By energy (least to most) microwaves < red < green < UV < gamma Tro: Chemistry: A Molecular Approach, 2/e 23 Copyright 2011 Pearson Education, Inc. Ejected Electrons • One photon at the threshold frequency gives the electron just enough energy for it to escape the atom binding energy, f • 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 = Ephoton – Ebinding KE = hn − f Tro: Chemistry: A Molecular Approach, 2/e 24 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 25 Copyright 2011 Pearson Education, Inc. Exciting Gas Atoms to Emit Light with Electrical Energy Tro: Chemistry: A Molecular Approach, 2/e 26 Copyright 2011 Pearson Education, Inc. Identifying Elements with Flame Tests Na K Tro: Chemistry: A Molecular Approach, 2/e Li 27 Ba Copyright 2011 Pearson Education, Inc. Emission Spectra Tro: Chemistry: A Molecular Approach, 2/e 28 Copyright 2011 Pearson Education, Inc. Examples of Spectra Tro: Chemistry: A Molecular Approach, 2/e 29 Copyright 2011 Pearson Education, Inc. Emission vs. Absorption Spectra Spectra of Mercury Tro: Chemistry: A Molecular Approach, 2/e 30 Copyright 2011 Pearson Education, Inc. Solutions to the Wave Function, Y • 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, ml Magnetic spin quantum number, ms PAULI EXCLUSION PRINCIPLE: No two electrons can have the same four quantum numbers. Tro: Chemistry: A Molecular Approach, 2/e 31 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 32 Copyright 2011 Pearson Education, Inc. Principal Energy Levels in Hydrogen Tro: Chemistry: A Molecular Approach, 2/e 33 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 34 Copyright 2011 Pearson Education, Inc. l = 0, the s orbital Tro: Chemistry: A Molecular Approach, 2/e 35 Copyright 2011 Pearson Education, Inc. p orbitals Tro: Chemistry: A Molecular Approach, 2/e 36 Copyright 2011 Pearson Education, Inc. d orbitals Tro: Chemistry: A Molecular Approach, 2/e 37 Copyright 2011 Pearson Education, Inc. f orbitals Tro: Chemistry: A Molecular Approach, 2/e 38 Copyright 2011 Pearson Education, Inc. Magnetic Quantum Number, ml • 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 ml are −2, −1, 0, +1, +2; which means there are five orbitals with l = 2 Tro: Chemistry: A Molecular Approach, 2/e 39 Copyright 2011 Pearson Education, Inc. Magnetic Spin Quantum Number, ms • Designates the spin of the electron; clockwise or counterclockwise • The value can only be +1/2 or -1/2 Tro: Chemistry: A Molecular Approach, 2/e 40 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 41 Copyright 2011 Pearson Education, Inc. 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 Tro: Chemistry: A Molecular Approach, 2/e 42 Copyright 2011 Pearson Education, Inc.