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Chapter 6 Electronic Structure of Atoms David P. White Prentice Hall © 2003 Chapter 6 The Wave Nature of Light • All waves have a characteristic wavelength, l, and amplitude, A. • The frequency, f, of a wave is the number of cycles which pass a point in one second. • The speed of a wave, v, is given by its frequency multiplied by its wavelength: c = fλ c is the speed of light Prentice Hall © 2003 Chapter 6 Prentice Hall © 2003 Chapter 6 • Modern atomic theory involves interaction of radiation with matter. • Electromagnetic radiation moves through a vacuum with a speed of 3.00 108 m/s. Prentice Hall © 2003 Chapter 6 Electromagnetic spectrum Example 1: A laser produces radiation with a wavelength of 640.0 nm. Calculate the frequency of this radiation. Example 2: The YFM radio station broadcasts EM radiation at 99.2 MHz. Calculate the wavelength of this radiation (1 MHz = 106 s-1). Prentice Hall © 2003 Chapter 6 Quantized Energy and Photons • Planck: energy can only be absorbed or released from atoms in fixed amounts called quanta. • For 1 photon (energy packet): E = hf = hc/λ where h is Planck’s constant (6.63 10-34 J.s). Prentice Hall © 2003 Chapter 6 The Photoelectric Effect and Photons • If light shines on the surface of a metal, there is a point (threshold frequency) at which electrons are ejected from the metal. Prentice Hall © 2003 Chapter 6 Example 3: (a) A laser emits light with a frequency of 4.69 x 1014s-1. What is the energy of one photon of the radiation from this laser? If the laser emits a pulse of energy containing 5.0 x 1017 photons of this radiation, what is the total energy of that pulse? Prentice Hall © 2003 Chapter 6 Line Spectra and the Bohr Model Line Spectra • Monochromatic light – one λ. • Continuous light – different λs. • White light can be separated into a continuous spectrum of colors. Prentice Hall © 2003 Chapter 6 A prism disperses light from a light bulb • Balmer: discovered that the lines in the visible line spectrum of hydrogen fit a simple equation. • Later Rydberg generalized Balmer’s equation to: 1 RH l h 1 1 2 n1 n22 where RH is the Rydberg constant (1.096776 107 m-1), h is Planck’s constant, n1 and n2 are integers (n2 > n1). Prentice Hall © 2003 Chapter 6 Bohr Model explains this equation • Rutherford assumed the electrons orbited the nucleus analogous to planets around the sun. • However, a charged particle moving in a circular path should lose energy, ie, the atom is unstable • Bohr noted the line spectra of certain elements and assumed the electrons were confined to specific energy states called orbits. Prentice Hall © 2003 Chapter 6 Colors from excited gases arise because electrons move between energy states in the atom. Black regions show λs absent in the light Prentice Hall © 2003 Chapter 6 Bohr Model • Energy states are quantized, light emitted from excited atoms is quantized and appear as line spectra. • Bohr showed that E 2.18 10 18 1 J 2 n where n is the principal quantum number (i.e., n = 1, 2, 3). Prentice Hall © 2003 Chapter 6 • The first orbit has n = 1, is closest to the nucleus, and has negative energy by convention. • The furthest orbit has n close to infinity and corresponds to zero energy. • Electrons in the Bohr model can only move between orbits by absorbing and emitting energy ∆E = Efinal – Einitial = hf Prentice Hall © 2003 Chapter 6 • We can show that 1 hc 1 E hf 2.18 1018 J 2 2 n l n i f • When ni > nf, energy is emitted. • When nf > ni, energy is absorbed Prentice Hall © 2003 Chapter 6 Limitations of the Bohr Model • Can only explain the line spectrum of hydrogen adequately. • Electrons are not completely described as small particles. Prentice Hall © 2003 Chapter 6 The Wave Behavior of Matter • Explores the wave-like and particle-like nature of matter. • Using Einstein’s and Planck’s equations, de Broglie showed: h l mv • The momentum, mv, is a particle property, whereas l is a wave property. Prentice Hall © 2003 Chapter 6 The Uncertainty Principle • Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. • For electrons: we cannot determine their momentum and position simultaneously. • If x is the uncertainty in position and mv is the uncertainty in momentum, then h x·mv 4 Prentice Hall © 2003 Chapter 6 Quantum Mechanics and Atomic Orbitals • Schrödinger proposed an equation that contains both wave and particle terms. • Solving the equation leads to wave functions, ψ (orbitals). • ψ2 gives the probability of finding the electron • Orbital in the quantum model is different from Bohr’s orbit Prentice Hall © 2003 Chapter 6 Prentice Hall © 2003 Chapter 6 • Schrödinger’s 3 QNs: 1. Principal Quantum Number, n. - same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. Prentice Hall © 2003 Chapter 6 2. Azimuthal Quantum Number, l. - depends on the value of n. The values of l begin at 0 and increase to (n - 1). The letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals. 3. Magnetic Quantum Number, ml. - depends on l. Has integral values between -l and +l. Gives the 3D orientation of each orbital. There are (2l +1) allowed values of ml and this gives the no. of orbitals. Total no. of orbitals in a shell = n2 Prentice Hall © 2003 Chapter 6 Prentice Hall © 2003 Chapter 6 • Orbitals can be ranked in terms of energy to yield an Aufbau diagram. Prentice Hall © 2003 Chapter 6 Single electron atom – orbitals with the same value of n have the same energy Prentice Hall © 2003 Chapter 6 Representations of Orbitals The s-Orbitals • • • • All s-orbitals are spherical. As n increases, the s-orbitals get larger & no. of nodes increase. A node is a region in space where the probability of finding an electron is zero, 2 = 0 . For an s-orbital, the number of nodes is (n - 1). Prentice Hall © 2003 Chapter 6 The p-Orbitals • • • • There are three p-orbitals px, py, and pz. The letters correspond to allowed values of ml of -1, 0, and +1. The orbitals are dumbbell shaped and have a node at the nucleus. As n increases, the p-orbitals get larger. Prentice Hall © 2003 Chapter 6 Prentice Hall © 2003 Chapter 6 The d and f-Orbitals • There are five d and seven f-orbitals. • They differ in their orientation in the x, y,z plane Prentice Hall © 2003 Chapter 6 Many-Electron Atoms Orbitals and Their Energies • Orbitals of the same energy are said to be degenerate. • For n 2, the s- and p-orbitals are no longer degenerate because the electrons interact with each other. • Therefore, the Aufbau diagram looks different for manyelectron systems. Prentice Hall © 2003 Chapter 6 Many electron atoms – electrons repel and thus orbitals are at different energies Electron Spin and the Pauli Exclusion Principle • Line spectra of many electron atoms show each line as a closely spaced pair of lines. • Stern and Gerlach designed an experiment to determine why. Prentice Hall © 2003 Chapter 6 2 opposite directions of spin produce oppositely directed magnetic fields leading to the splitting of spectral lines into closely spaced spectra • Since electron spin is quantized, we define ms = spin quantum number = + ½ and - ½ . • Pauli’s Exclusion Principle: no two electrons can have the same set of 4 quantum numbers. • Therefore, two electrons in the same orbital must have opposite spins. Prentice Hall © 2003 Chapter 6 • In the presence of a magnetic field, we can lift the degeneracy of the electrons. Prentice Hall © 2003 Chapter 6 Electron Configurations • • Hund’s Rule Electron configurations - in which orbitals the electrons for an element are located. For degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron. Prentice Hall © 2003 Chapter 6 • • • • Condensed Electron Configurations Neon completes the 2p subshell. Sodium marks the beginning of a new row. Na: [Ne] 3s1 Core electrons: electrons in [Noble Gas]. Valence electrons: electrons outside of [Noble Gas]. Prentice Hall © 2003 Chapter 6 Transition Metals • After Ar the d orbitals begin to fill. • After the 3d orbitals are full, the 4p orbitals begin to fill. • Transition metals: elements in which the d electrons are the valence electrons. Prentice Hall © 2003 Chapter 6 • • • • • Lanthanides and Actinides From Ce onwards the 4f orbitals begin to fill. Note: La: [Xe]6s25d14f0 Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements. Elements Th - Lr have the 5f orbitals filled and are called actinides. Most actinides are not found in nature. Prentice Hall © 2003 Chapter 6 Electron Configurations and the Periodic Table • The periodic table can be used as a guide for electron configurations. • The period number is the value of n. • Groups 1A and 2A have the s-orbital filled. • Groups 3A - 8A have the p-orbital filled. • Groups 3B - 2B have the d-orbital filled. • The lanthanides and actinides have the f-orbital filled. Prentice Hall © 2003 Chapter 6