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Prentice Hall © 2003Chapter 6 Chapter 6 Electronic Structure of Atoms David P. White

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Prentice Hall © 2003Chapter 6 All waves have a characteristic wavelength,, 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 The Wave Nature of Light

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Prentice Hall © 2003Chapter 6

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Prentice Hall © 2003Chapter 6 Modern atomic theory involves interaction of radiation with matter. Electromagnetic radiation moves through a vacuum with a speed of 3.00 10 8 m/s.

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Electromagnetic spectrum

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Prentice Hall © 2003Chapter 6 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 = 10 6 s -1 ).

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Prentice Hall © 2003Chapter 6 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). Quantized Energy and Photons

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Prentice Hall © 2003Chapter 6 If light shines on the surface of a metal, there is a point (threshold frequency) at which electrons are ejected from the metal. The Photoelectric Effect and Photons

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Prentice Hall © 2003Chapter 6 Example 3: (a) A laser emits light with a frequency of 4.69 x 10 14 s -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 10 17 photons of this radiation, what is the total energy of that pulse?

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Prentice Hall © 2003Chapter 6 Line Spectra Monochromatic light – one λ. Continuous light – different λs. White light can be separated into a continuous spectrum of colors. Line Spectra and the Bohr Model

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A prism disperses light from a light bulb

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Prentice Hall © 2003Chapter 6 Balmer: discovered that the lines in the visible line spectrum of hydrogen fit a simple equation. Later Rydberg generalized Balmer’s equation to: where R H is the Rydberg constant (1.096776 10 7 m -1 ), h is Planck’s constant, n 1 and n 2 are integers (n 2 > n 1 ).

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Prentice Hall © 2003Chapter 6 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. Bohr Model explains this equation

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Prentice Hall © 2003Chapter 6 Colors from excited gases arise because electrons move between energy states in the atom. Black regions show λs absent in the light

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Prentice Hall © 2003Chapter 6 Bohr Model Energy states are quantized, light emitted from excited atoms is quantized and appear as line spectra. Bohr showed that where n is the principal quantum number (i.e., n = 1, 2, 3).

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Prentice Hall © 2003Chapter 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 = E final – E initial = hf

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Prentice Hall © 2003Chapter 6 We can show that When n i > n f, energy is emitted. When n f > n i, energy is absorbed f

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Prentice Hall © 2003Chapter 6 Limitations of the Bohr Model Can only explain the line spectrum of hydrogen adequately. Electrons are not completely described as small particles.

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Prentice Hall © 2003Chapter 6 Explores the wave-like and particle-like nature of matter. Using Einstein’s and Planck’s equations, de Broglie showed: The momentum, mv, is a particle property, whereas is a wave property. The Wave Behavior of Matter

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Prentice Hall © 2003Chapter 6 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 The Uncertainty Principle

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Prentice Hall © 2003Chapter 6 Schrödinger proposed an equation that contains both wave and particle terms. Solving the equation leads to wave functions, ψ (orbitals). ψ 2 gives the probability of finding the electron Orbital in the quantum model is different from Bohr’s orbit Quantum Mechanics and Atomic Orbitals

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Prentice Hall © 2003Chapter 6

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Prentice Hall © 2003Chapter 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.

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Prentice Hall © 2003Chapter 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, m l. - depends on l. Has integral values between -l and +l. Gives the 3D orientation of each orbital. There are (2l +1) allowed values of m l and this gives the no. of orbitals. Total no. of orbitals in a shell = n 2

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Prentice Hall © 2003Chapter 6

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Prentice Hall © 2003Chapter 6 Orbitals can be ranked in terms of energy to yield an Aufbau diagram.

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Prentice Hall © 2003Chapter 6 Single electron atom – orbitals with the same value of n have the same energy

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Prentice Hall © 2003Chapter 6 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). Representations of Orbitals

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Prentice Hall © 2003Chapter 6 The p-Orbitals There are three p-orbitals p x, p y, and p z. The letters correspond to allowed values of m l 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.

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Prentice Hall © 2003Chapter 6

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Prentice Hall © 2003Chapter 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

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Prentice Hall © 2003Chapter 6 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 many- electron systems. Many-Electron Atoms

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Many electron atoms – electrons repel and thus orbitals are at different energies

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Prentice Hall © 2003Chapter 6 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.

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2 opposite directions of spin produce oppositely directed magnetic fields leading to the splitting of spectral lines into closely spaced spectra

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Prentice Hall © 2003Chapter 6 Since electron spin is quantized, we define m s = 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.

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Prentice Hall © 2003Chapter 6 In the presence of a magnetic field, we can lift the degeneracy of the electrons.

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Prentice Hall © 2003Chapter 6 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. Electron Configurations

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Prentice Hall © 2003Chapter 6 Condensed Electron Configurations Neon completes the 2p subshell. Sodium marks the beginning of a new row. Na: [Ne] 3s 1 Core electrons: electrons in [Noble Gas]. Valence electrons: electrons outside of [Noble Gas].

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Prentice Hall © 2003Chapter 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.

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Prentice Hall © 2003Chapter 6 Lanthanides and Actinides From Ce onwards the 4f orbitals begin to fill. Note: La: [Xe]6s 2 5d 1 4f 0 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.

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Prentice Hall © 2003Chapter 6 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. Electron Configurations and the Periodic Table

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