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Chapter 4 Arrangement of Electrons in Atoms Reference to the best of my knowledge 8-14-11: Supriya Moore, Monta Vista HS, from John D. Bookstaver, St. Charles Community College, Cottleville, MO, from Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten (Prentice Hall) Planck, Bohr, Einstein, deBroglie, Heisenberg, Schrodinger • 4.1 The Development of a New Atomic Model • 4.2 The Quantum Model of the Atom • 4.3 Electron Configurations Ch. 3: Democritus, Dalton, Thomson, Millikan, Goldstein, Rutherford, Chadwick Waves • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength (). © 2009, Prentice-Hall, Inc. Waves is Greek letter lambda is Greek letter nu • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. – Wavelength: It is the distance between two consecutive peaks or troughs in a wave. – Frequency: It indicates how many waves pass a given point per second. – Speed: It indicates how fast a given peak is moving through the space. – Speed of light ,c= ,where =wave length and =frequency © 2009, Prentice-Hall, Inc. EMR Electromagnetic Radiation: Electromagnetic radiation is one of the ways in which energy travels through space. All forms of EMR compose the electromagnetic radiation spectrum, which includes sun rays, microwaves, Xrays, visible spectrum, UV rays and IR rays. • Some characteristics of EMR are: • All electromagnetic radiation moves at a constant speed of about 3.0 X 108 m/s. • All EMR exhibit wave like behavior. Waves have three primary characteristics: – Wavelength: It is the distance between two consecutive peaks or troughs in a wave. – Frequency: It indicates how many waves pass a given point per second. – Speed: It indicates how fast a given peak is moving through the space. – Speed of light ,c= ,where =wave length and =frequency Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 108 m/s. • Therefore, c = © 2009, Prentice-Hall, Inc. Refer to the following EMR spectrum. (visible spectrum Roy G. BiV) • Imagine you have invented a machine that allows you to see all types of EMR. Make a list of type of EMR you might see in your home. Wave Nature of Light • Before the concept of quantization of energy, the wave like nature of light/energy was widely accepted. • Two properties that exhibit the wave like behavior of light are interference and diffraction. Animation Diffraction: http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm Animation for Interference: http://id.mind.net/~zona/mstm/physics/waves/interference/waveInterference1/WaveIn terference1.html The Nature of Energy • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta. © 2009, Prentice-Hall, Inc. Planck’s Theory of Quantization of Energy • Planck’s theory: Before Planck’s theory, the wave model of the light was widely accepted. But it was unable to explain some phenomenon for example change in the radiation (wave length) emitted by an object with the change in temperature. h = 6.626 x 10-34 J∙s • To explain this, Planck suggested that the energy transfer or exchange is not a continuous process, but is done in small packets of energy called by him as quantum.(Word quantum means fixed amount.) So, he introduced the concept of quantization of energy. • According to Planck’s theory, E= hv, where E= energy of radiation h= Planck’s constant v= frequency of radiation Quantization of Energy: Max Plank • Where else do you see quantization in real life? Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h The Nature of Energy Another mystery in the early 20th century involved the emission spectra observed from energy emitted by atoms and molecules. © 2009, Prentice-Hall, Inc. The Nature of Energy • Einstein used this assumption to explain the photoelectric effect. • He concluded that electromagnetic radiation has a dual wave-particle nature © 2009, Prentice-Hall, Inc. Photoelectric Effect: It refers to the emission of electrons from a metal, when the light shines on the metal. For each metal the frequency of light needed to release the electrons is different. But the wave theory of light could not explain it. The photoelectric effect led scientists to think about the dual nature of light i.e. as a wave and a particle both. Animation 1: http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/Nuclear/XRayIntera ct/XRayInteract.html Animation 2: http://faculty.ucc.edu/chemistry-pankuch/Photoelectric/PE3.html Photoelectric Effect • Max Planck suggested that the hot object emits energy in small, specific amounts called quanta. • 1905, Einstein said electromagnetic radiation has a dual wave- particle nature. • A photon is a particle of emr having zero rest mass and carrying a quantum of energy • Emr is absorbed onl in whole numbers of photons, thus electrons in different metals require different minimum frequencies to exhibit the photoelectric effect http://www.shsu.edu/%7Echm_tgc/sounds/flashfiles/pee.s wf The Nature of Energy • For atoms and molecules one does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed. © 2009, Prentice-Hall, Inc. Continuous and Line Spectra (Absorption and Emission Spectrum- Line Spectra) (http://images.google.com/imgres?imgurl=http://csep10.phys.utk.edu/astr162/lect/light/spectra.gif&imgrefurl=http://csep10.phys.utk.edu/astr162/lect/light/a bsorption.html&h=240&w=450&sz=33&hl=en&start=2&tbnid=TaN57QO8MhMG4M:&tbnh=66&tbnw=124&prev=/images%3Fq%3Dabsorption%2Band%2Bemission%2Bspectr um%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN) Bohr Model Of the Hydrogen Atom • Ephoton=hv The energy levels of Hydrogen ( As explained by Bohr’s Model) : •An excited atom (excited state) can release some or all of its excess energy by emitting a photon, thus moving to a lower energy state. •The lowest possible energy state of an atom is called the ‘ground state’. •Different wavelengths of light carry different amount of energy per photon. Ex. A beam of red light has a lower energy photons than beam of blue light. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 1. Electrons in an atom can only occupy certain orbits (corresponding to certain energies). Animation : http://pokok.mysch.net/~chemistry/AL2.htm#Animation Animation: http://physics.gac.edu/~chuck/PRENHALL/Chapter%2031/AABXTEJ0.html © 2009, Prentice-Hall, Inc. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 2. Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. © 2009, Prentice-Hall, Inc. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: 3. Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h © 2009, Prentice-Hall, Inc. Light Equations • • • • • c= c is the speed of light (3.0 x 108 m/s) lambda is the wave length (in m, cm, or nm) represents the frequency (waves/s or hertz) http://www.astronomynot es.com/light/s3.htm • E=h • E is energy (in joules) • h is Planck’s Constant (h= 6.626 x 10-34J s) • is frequency • E=h(c/ ) http://sunflower.bio.indiana.edu/~rhangart/courses/b373/lecturenotes/photomorph/sinewave.gif 4.2 The Quantum Model of the Atom • Louis deBroglie • Werner Heisenberg • Based on the photoelectric effect concept of light behaving as both a wave and a particle, deBroglie applied this to electrons, or quantized energies of Bohr’s orbits • Through experimentation, deBroglie showed the wavelike property of electrons through diffraction (bending of a wave) and interference (waves overlap resulting in higher or lower energy) • Electrons are detected by their interactions with photons. Because photons have about the same energy as electrons, any attempt to locate a specific electron with a photon knocks the electron off its course. Therefore, the Heisenberg Uncertainty Principle • States that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle. http://hackensackhigh.org/~rkc2/diffraction.jpg Quantum Theory: Describes mathematically the wave properties of electrons or other very small particles treating e- as waves and using Heisenberg’s and De Broglie’s principles. Quantum Mechanical Model of Atom (Schrodinger’s Model) Erwin Schrödinger, in developing a quantum-mechanical model for the atom, began with a classical equation for the properties of waves. He modified this equation to take into account the mass of a particle and the de Broglie relationship between mass and wavelength. The important consequences of the quantum-mechanical view of atoms are the following: (http://www.cartage.org.lb/en/themes/sciences/chemistry/Generalchemistry/Atomic/Electronicstructure/Electronicstructures/Quantum/Quantum.htm-) 1. 2. 3. 4. The energy of electrons in atoms is quantized. The number of possible energy levels for electrons in atoms of different elements is a direct consequence of wave-like properties of electrons. The position and momentum of an electron cannot both be determined simultaneously. The region in space around the nucleus in which an electron is most probably located is what can be predicted for each electron in an atom. Electrons of different energies are likely to be found in different regions. The region in which an electron with a specific energy will most probably be located is called an atomic orbital. Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics. © 2009, Prentice-Hall, Inc. Quantum Mechanics • The wave equation is designated with a lower case Greek psi (). • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. © 2009, Prentice-Hall, Inc. Quantum Numbers • Schrodinger arrived at three functions while solving the wave equation for electrons and came up with three quantum numbers, each corresponding to a property of atomic orbital. The fourth quantum number was later introduced to clarify the spin of electrons. use(http://www.google.com/search?hl=en&q=wave+mechanical+model) • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. © 2009, Prentice-Hall, Inc. Principal Quantum Number (n) • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 1. © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. Value of l 0 1 2 3 Type of orbital s p d f © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (ml) • The magnetic quantum number describes the three-dimensional orientation of the orbital. • Allowed values of ml are integers ranging from -l to l: −l ≤ ml ≤ l. • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (ml) • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells. © 2009, Prentice-Hall, Inc. Orbitals and Electron Capacity of the First Four Principle Energy Levels Maximum Principle Number of Number of Type of number of energy level orbitals per orbitals per sublevel electrons (n) type level(n2) (2n2) 1 2 3 4 s 1 s 1 p 3 s 1 p 3 d 5 s 1 p 3 d 5 f 7 1 2 4 8 9 18 16 32 s Orbitals • The value of l for s orbitals is 0. • They are spherical in shape. • The radius of the sphere increases with the value of n. © 2009, Prentice-Hall, Inc. s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. © 2009, Prentice-Hall, Inc. p Orbitals • The value of l for p orbitals is 1. • They have two lobes with a node between them. © 2009, Prentice-Hall, Inc. d Orbitals • The value of l for a d orbital is 2. • Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. © 2009, Prentice-Hall, Inc. Energies of Orbitals • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate. © 2009, Prentice-Hall, Inc. Energies of Orbitals • As the number of electrons increases, though, so does the repulsion between them. • Therefore, in manyelectron atoms, orbitals on the same energy level are no longer degenerate. © 2009, Prentice-Hall, Inc. Spin Quantum Number, ms • In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. • The “spin” of an electron describes its magnetic field, which affects its energy. © 2009, Prentice-Hall, Inc. Spin Quantum Number, ms • This led to a fourth quantum number, the spin quantum number, ms. • The spin quantum number has only 2 allowed values: +1/2 and −1/2. © 2009, Prentice-Hall, Inc. Pauli Exclusion Principle • No two electrons in the same atom can have exactly the same energy. • Therefore, no two electrons in the same atom can have identical sets of quantum numbers. © 2009, Prentice-Hall, Inc. 5.2 Electron Configurations According to the aufbau principle, electrons occupy the orbitals of lowest energy first. According to the Pauli exclusion principle, an atomic orbital may describe at most two electrons. To occupy the same orbital, two electrons must have opposite spins Hund’s rule states that electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. Electron Configurations • This shows the distribution of all electrons in an atom. • Each component consists of – A number denoting the energy level, © 2009, Prentice-Hall, Inc. Electron Configurations • This shows the distribution of all electrons in an atom • Each component consists of – A number denoting the energy level, – A letter denoting the type of orbital, Animation: http://intro.chem.okstate.edu/WorkshopFolder/Electronconfnew.html © 2009, Prentice-Hall, Inc. Electron Configurations • This shows the distribution of all electrons in an atom. • Each component consists of – A number denoting the energy level, – A letter denoting the type of orbital, – A superscript denoting the number of electrons in those orbitals. © 2009, Prentice-Hall, Inc. Orbital Diagrams • Each box in the diagram represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the relative spin of the electron. © 2009, Prentice-Hall, Inc. Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.” © 2009, Prentice-Hall, Inc. Periodic Table • We fill orbitals in increasing order of energy. • Different blocks on the periodic table (shaded in different colors in this chart) correspond to different types of orbitals. © 2009, Prentice-Hall, Inc. Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row. © 2009, Prentice-Hall, Inc. Some Anomalies For instance, the electron configuration for copper is [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. © 2009, Prentice-Hall, Inc. Some Anomalies • This occurs because the 4s and 3d orbitals are very close in energy. • These anomalies occur in f-block atoms, as well. © 2009, Prentice-Hall, Inc. 5.2 Exceptional Electron Configurations Why do actual electron configurations for some elements differ from those assigned using the aufbau principle? – Some actual electron configurations differ from those assigned using the aufbau principle because half-filled sublevels are not as stable as filled sublevels, but they are more stable than other configurations. – Exceptions to the aufbau principle are due to subtle electron-electron interactions in orbitals with very similar energies. – Copper has an electron configuration that is an exception to the aufbau principle. It is 1s22s22p63s23p64s13d10 Instead of 1s22s22p63s23p64s23d9 http://www.tannerm.com/Quick_atom/hund.gif Electron Configuration Theories • Aufbau’s Principle: An electron occupies the lowest-energy orbital that can receive it. • Pauli’s Exclusion Principle: No two electrons in the same atom can have the same set of four quantum numbers. • Hund’s Rule: Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin. Aufbau principle: Lowest energies first 1s, 2s, 2p, 3s, 3p, 4s 3d, 4p, 5s It follows the periodic table Electron Configurations in Groups Group 1A elements -- there is only one electron in the highest occupied energy level. Group 4A elements -there are four electrons in the highest occupied energy level. noble gases are the elements in Group 8A Electron Configuration and Orbital Filling Practice Write the electron a. Li: atomic number 3 configuration and orbital filling for 1s22s1 _ a. Li b. Mg b. Mg: atomic number 12 1s22s22p63s2 c. Si _ _ _ c. Si: atomic number 14 1s22s22p63s23p2 _ _ _ _ Ways to Represent Electron Configuration 1. Expanded Electron Configuration 2. Condensed Electron Configurations 3. Orbital Notation 4. Electron Dot Structure Write the above four electron configurations for a) oxygen b) zinc c) zinc ion d) cu ion. Quantum Number Terms • Ground State: Lowest energy state of an atom • Excited State: A state in which an atom has a higher potential energy then it has in its ground state • Orbital: A 3D region around the nucleus that indicates the probable location of an electron • Quantum Numbers: Specify the properties of atomic orbitals and the properties of electrons in orbitals • Principle Quantum Number: (n) Indicates the main energy level occupied by the electron. • Angular Momentum Quantum Number: (l) Indicates the shape of the orbital. • Magnetic Quantum Number: (m) Indicates the orientation of an orbital around the nucleus. • Spin Quantum Number: (+1/2, -1/2) Indicates the two fundamental spin states of an electron in an orbital Chapter 4 Objectives • • • • • • • • • • • • • • • • Explain the mathematical relationship between the speed, wavelength and frequency of electromagnetic radiation (problems) Know that X rays, gamma rays and UV rays have short wavelength and high energy, radio waves have long wavelength and low energy Discuss the dual wave-particle nature of light Discuss the significance of the photoelectric effect and the line emission spectrum of hydrogen to the development of the atomic model Describe the Bohr model of the hydrogen atom, draw the Bohr model and label the parts Compare and contrast Thompson, Rutherford and the Bohr models (at least three similarities and three differences) Discuss Louis de Broglie’s role in the development of the quantum model of the atom Compare and contrast the Bohr model and the quantum model of the atom State Heisenberg uncertainty principle Explain how Heisenberg uncertainty principle and the Schroedinger wave equation led to the idea of atomic orbitals List the four quantum numbers and describe their significance Relate the number of sublevels corresponding to each of an atom’s main energy level, the number of orbitals per sublevel and the number of orbitals per main energy level List the total number of electrons needed to fully occupy each main energy level State the Aufbau principle, the Pauli exclusion principle and Hund’s rule Write electron configurations for elements on the chapter 1 packet list using orbital notation, electron configuration notation and noble gas notation Explain why the electron configurations of chromium and copper do not follow Aufbau’s principle?