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Chapter 5 Electrons in Atoms 5.1 Models of the Atom Development of Atomic Models First "modern" model - John Dalton (1808) · J. J. Thomson (1897) · · Ernest Rutherford (1911) · Niels Bohr (1913) · proposed how electrons were arranged around the nucleus proposed in order to explain how light interacts with atoms electrons are in fixed energy levels quantum= · · · Bohr's Model of the Hydrogen Atom Four Assumptions: 1. The electron moves around the nucleus in only certain allowed orbits 2. The energy of these quantized orbits is characterized by an integer, n 3. In order to change energies, an electron must move from one energy level (orbit) to another. No gradual changes are allowed. 4. Upon changing levels, an electron absorbs or emits energy equal to the difference in energy between the two levels. Physical picture: 1 Quantum Mechanical Model Determined the allowed energies an electron can have and how likely it is to find an electron in various locations around the nucleus. Atomic Orbitals · a region of space where there is a high probability of finding an electron For the quantum mechanical model: Quantum Numbers The energy of the electron is expressed in terms of four variables called quantum numbers. These variables can have only certain restricted values in order to solve the wave equation. The Four Quantum Numbers: n the principle quantum number it describes the main energy level or shell it can any positive integer value these energy levels are also called "shells" n=1 n=2 n=3 n=4 2 l the angular momentum quantum number it describes the sublevels or subshells (each energy sublevel corresponds to an orbital of different shape depending on where the electron is likely to be found) it can have any integer value from 0 to n-1 Ex. if n = 3, l can be:0,1,2 Other designations: if l = 0 if l = 1 if l = 2 if l = 4 if l = 3 if n = 1 1sublevel if n = 2 2 sublevels if n = 3 3 sublevels if n = 4 4 sublevels m the magnetic quantum number it describes the orientations of the "orbitals" it can have any integer value from -l . . . +l Ex. if l = 3, m =s the spin quantum number it describes the "spin" of the electron it can have only two possible values The energy of the electron is described in terms of these four quantum numbers. 3 Electron Arrangement in Atoms Electron Configurations/Electron Diagrams Atomic Orbitals For the quantum mechanical model: Energy Levels (shells) Sublevels (subshells) Orbitals The Arrangement of Levels, Sublevels, and Orbitals First Level Second Level Third Level The Arrangement of Electrons Electrons will be represented as arrows: if s=+½ if s=-½ 4 The arrangement of electrons is show by Electron Diagrams Three rules for placing electrons in an atom: Aufbau Principle: An electron diagram for hydrogen (Z=1) An electron diagram for helium (Z=2) An electron diagram for lithium (Z=3) Pauli Exclusion Principle: An electron diagram for nitrogen (Z=7) Hund’s Rule: p. 133 fig. 5.7 A Table: Energy Level Number of Sublevels Number of Orbitals Number of electrons 5 Shapes of Orbitals The 1s The 2s The 2p’s The Famous Diagonal Rule Electron Configurations a shorthand method of drawing electron diagrams 6 list the sublevels and show the number of electrons in each sublevel Examples: Element Electron Diagram Electron Configuration Must know: Diagonal Rule The maximum number of electrons in each sublevel Some Exceptions to the Diagonal Rule · 5.3 Physics and the Quantum Mechanical Model Light Visible light is one form of electromagnetic radiation other forms include: radio waves microwaves infrared radiation ultraviolet X-rays Properties of waves: Amplitude 7 Wavelength The symbol used for wavelength is the Greek letter: λ Wavelengths of visible light are usually expressed in nanometers (nm): 1m = 1 x 109 nm Different colors of visible light have different wavelengths: ROYGBIV Red Orange Yellow Green Blue Indigo Violet low energyhigh energy long wavelengthsshort wavelengths low frequencyhigh frequency Another property of light is frequency defined as the number of wave cycles that pass a given point per unit of time represented by the Greek letter: v Compare two waves: P.139 fig.5.10 Waves with shorter λ's have higher v's Frequency and wavelength are inversely related. where c = the speed of the wave vλ = c 8 For light, c = Example: Calculate the frequency of light which has a wavelength of 588 nm. Max Planck (1900) energy is not continuous, but exists in little units called quanta (singular: quantum) the energy of a quantum of light (a photon) is directly proportional to its frequency Ev E = hv h is Planck's Constant = 6.6262 10-34 J·s Example: Calculate the energy of a single photon of light energy which has a λ = 450 nm. For one mole of photons: Atomic Spectra The spectroscope p.141 fig. 5.12 9 Bohr If the electron can have only certain energies, it can have only certain changes in energy Only certain energies (photons, wavelengths) will be emitted by an atom This will produce a line spectrum called atomic emission spectrum In order to predict which lines would be formed, Bohr calculated the energies of the electron His simplified equation: -1312 kJ n2 If the energies of each level can be calculated, the differences in energies (ΔE) can be calculated. Using E = hv, the frequency and wavelength of the light emitted can be calculated. Example: Calculate the λ of light emitted when an electron falls from level 5 to level 2. 10 Explanation of Atomic Spectra Patterns of Spectral Lines: Energy Levels to Scale: E1 E2 E3 E4 E5 E6 = = = = = = -1312 kJ -328 kJ -146 kJ -82 kJ -52 kJ -36 kJ Lyman seriesBalmer seriesPaschen series- Quantum Mechanics Historical Development 1900 - Max Planck radiant energy (light) has a duel character light has both wave and particle properties 1924 - Louis deBroglie matter also has both wave and particle properties the wave character of matter is important for very small particles (electrons) 1927 - Werner Heisenberg developed a mathematical principle which deals with very small particles The Heisenberg Uncertainty Principle 11 "It is impossible to know exactly both the velocity (energy) and the position of a small particle at the same time." Again, this principle is important only for very small particles like the electron 1926 - Erwin Schrodinger used quantum mechanics to develop a model of the hydrogen atom developed an equation (the wave equation) which treated the electron as a wave The Model: also has quantized energy levels could solve for the energy exactly, but only approximates the position of the electron the position of the electron is expressed interms of probability diagrams. Example: the ground state of hydrogen Homework: 1,2,4,5,7,8,9,10,11,12,14,15,16,17,20,21,29,30,32,33,3 4,35,36,38,39,40,44,45,49,50,51,52,53,54,55,56,57,58,60,61, 62,63,64,68,69,70,71 12 13 14 15