Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Chapter 6 Electronic Structure of Atoms Chemistry, The Central Science, 11th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Overview of Chapter 6 Electronic Structure of Atoms Review/On your own: EMR Waves:, and E relationships Older theories of the atom Basics of Bohr’s theory Heisenberg’s Uncertainty Principle Erwin Schrödinger’s idea about the wave function/probabilities of finding an electron, quantum numbers Use of orbital names – s, p, d, f – in quantum numbers Electron configuration and orbital diagrams, including the application of Aufbau, Hund’s and Pauli’s rules/principles s, p, d, f blocks in the periodic table Anomalous electron configurations

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Overview of Chapter 6 Electronic Structure of Atoms Details not required: Bohr’s model – application of E = h to the hydrogen spectrum, incorporating the Rydberg constant Louis de Broglie and matter waves New Material: Use of numbers for quantum numbers The presence of nodes in relation to orbitals Degenerate orbitals vs energy levels in multi-electron atoms = h mv

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy A mystery in the early 20th century involved the emission spectra observed from energy emitted by atoms and molecules.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Line Spectrum Radiation of only wavelength = monochromatic Continuous spectrum = radiation of whole array of wavelenghs Line spectrum = radiation of a few specific wavelengths

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy (Hydrogen Spectrum) 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).

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy (Hydrogen Spectrum) 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy (Hydrogen Spectrum) 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

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy (Hydrogen Spectrum) First orbit: n = 1, closest to the nucleus Furthest orbit: n is close to infinity, E = 0 Electrons can move between orbits by absorbing or emitting energy in quanta:  E = E f – E i = h

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy (Hydrogen Spectrum) Ground state = lowest energy state (E i ) Excited state = higher energy state (E f ) See notes for equation for excited states.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy details not required The amount of energy absorbed or emitted by moving between energy states can be calculated by the equation:  E = −R H ( ) 1nf21nf2 1ni21ni2 - where R H is the Rydberg constant, 2.18  10 −18 J, and n i and n f are the initial and final energy levels of the electron.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy details not required In your 4-page packet: E n = x joule n 2 See how this is applied to the difference between two energy levels:

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Nature of Energy details not required  E = −R H ( ) 1nf21nf2 1ni21ni2 - where R H is the Rydberg constant, 2.18  10 −18 J, and n i and n f are the initial and final energy levels of the electron.  E = E f - E i = (-2.18  10 −18 J) 1 – 1 n 2 f n 2 i ( )  E = h = hc => = hc so we can use  E to  E determine  of energy jump

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Sample Exercise 6.4 (p. 222) Using the figure above, predict which of the following electronic transitions produces the longest wavelength spectral line: n = 2 to n = 1, n = 3 to n = 2, or n = 4 to n = 3.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Practice Exercise 6.4 Indicate whether each of the following electronic transitions emits energy or requires the absorption of energy: a) n = 3 to n = 1; b) n = 2 to n = 4.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Limitations of the Bohr Model It cannot explain the spectra of atoms other than hydrogen. Electrons do not move about the nucleus in circular orbits.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. What We can Learn from Bohr’s Model Electrons exist only in certain energy levels described by quantum numbers. Energy gain or loss is involved in moving an electron from one energy level to another.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Wave Nature of Matter (details not required) Louis de Broglie presented the idea that if light can have material properties, matter should exhibit wave properties. He demonstrated that the relationship between mass and wavelength was = h mv

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Wave Nature of Matter (details not required) The momentum, mv, is a particle property, whereas is a wave property. Matter waves is the term used to describe wave characteristics of material particles.  in one equation de Broglie summarized the concepts of waves and particles as they apply to low-mass, high-speed objects.  X-ray diffraction and electron microscopy to study small objects.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Sample Exercise 6.5 (p. 223) (not required) What is the wavelength of an electron with a velocity of 5.97 x 10 6 m/s? You will need the following conversion factor: 1 J = kg m 2 s 2 (0.122 nm or 1.22 Å)

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Practice Exercise 6.5 (not required) Calculate the velocity of a neutron whose de Broglie wavelength is 500. pm. (mass of a neutron = 1 amu = x g) (799 m/s)

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. The Uncertainty Principle (details not required) Heisenberg’s uncertainty principle: We cannot determine the exact position, direction of motion, and speed of subatomic particles simultaneously. For electrons: We cannot determine their momentum and position simultaneously. (  x) (  mv)  h4h4

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Mechanics Erwin Schrödinger proposed an equation containing both wave and particle terms. It is known as quantum mechanics.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Mechanics (details not required) 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Mechanics (details not required) A region of high electron density is one where there is a high probability of finding an electron.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Quantum Numbers 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Origin of Orbital Names s – sharp (or use sphere) p – principal (peanut) d – diffuse (daffodil or daisy) f – fundamental (funky) Names come from the spectrum analysis, e.g. the hyperfine splitting of the d-line of the sodium spectrum

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Origin of Orbital Names Pauling, General Chemistry, 1970, footnote: "The use of the letters s, p, d, and f has a curious origin; they are the initial letters of the adjectives [above], which happened to be used by spectroscopists in the period around 1890 to describe different observed spectral series of the alkali metals. These letters accordingly are not abbreviations of words that describe the orbitals in a meaningful way."

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Principal Quantum Number (n) (review) Same as Bohr’s n As n becomes larger, the atom becomes larger and the electron is further from the nucleus

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) Depends on the value of n 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. This quantum number defines the shape of the orbital.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Angular Momentum Quantum Number (l) note new notation Value of l0123 Type of orbitalspdf

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) depends on l: (2l + 1) possible values of m l gives the 3-D orientation of each orbital Allowed values of m l are integers ranging from -l to 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Magnetic Quantum Number (m l ) (note new notation) Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Sample Exercise 6.6 (p. 228) a)Without referring to Table 6.2, predict the number of subshells in the fourth shell, that is, for n = 4. b) Give the label for each of these subshells. c) How many orbitals are in each subshell?

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Practice Exercise 6.6 a)What is the designation for the subshell with n = 5 and l = 1? b)How many orbitals are in this subshell? c)Indicate the values of m l for each of these orbitals.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. 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.

Electronic Structure of Atoms © 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. p Orbitals The value of l for p orbitals is 1. They have two lobes with a node between them.

Electronic Structure of Atoms © 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.

Electronic Structure of Atoms © 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many- electron atoms, orbitals on the same energy level are no longer degenerate.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Spin Quantum Number, m s This led to a fourth quantum number, the spin quantum number, m s. The spin quantum number has only 2 allowed values: +1/2 and −1/2.

Electronic Structure of Atoms © 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Electron Configurations (review) 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Orbital Diagrams (review) 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Hund’s Rule (review) “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc.

Electronic Structure of Atoms © 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.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies in Electron Configuraton Some irregularities occur when there are enough electrons to half- fill s and d orbitals on a given row.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies in Electron Configuration For instance, the electron configuration for copper is [Ar] 4s 1 3d 5 rather than the expected [Ar] 4s 2 3d 4.

Electronic Structure of Atoms © 2009, Prentice-Hall, Inc. Some Anomalies in Electron Configuration This occurs because the 4s and 3d orbitals are very close in energy. These anomalies occur in f-block atoms, as well.