Chapter 7 Ebbing and Gammon Quantum Theory of the Atom Modern chemistry dates from the late 1700 s and early 1800 s But it was not until the early 1900 s that the role of electrons in chemical bonds began to be understood It soon became known that the electrons circling the nucleus of an atom had an order to them both in terms of location and energy that could not be explained by the same laws of physics used to predict the behavior of planets and baseballs The Wave Nature of Light As strange as it may seem much of our present understanding of the electronic structure of atoms has come from the analysis of the light emitted or absorbed by substances Light infrared visible and ultraviolet is a member of a family electromagnetic radiation of seemingly quite different phenomenon x rays radio waves heat from a glowing rod Although the members of the electromagnetic radiation family seem very different they all have several characteristics in common All members of this family carry energy through space All members move through a vacuum at 3 00 x 108 m s the so called speed speed of light All members move through space as waves The waves are characterized by an amplitude a wavelength and a frequency 1 The energy of the wave E is directly proportional to the frequency and inversely proportional to the wavelength That is E h hc h Planck s constant The work of Niels Bohr Building on Rutherford s model of the atom and some earlier work by Max Planck and Albert Einstein the Danish physicist Niels Bohr published his quantum theory of the hydrogen atom in 1914 Why did Bohr start with hydrogen Although Bohr s work has been greatly expanded and even some of his original ideas have been dropped the core of his ideas are still the basis for modern theories of electronic structure Bohr was the first to use the concept of quantized electron energies for this he eventually won the Nobel prize in physics What is meant by quantized electron energies Bohr was able to show that these allowed energies depended on a single variable which he gave the symbol n and called the principal quantum number n can have only whole integer values beginning with 1 That is n 1 2 3 4 5 6 2 Bohr developed the following equations which allowed him to calculate the energy of the allowed energy levels in an atom and the radius of the electron s orbit E 2 18x10 18 Z2 n2 joules r 52 9 n2 Z pm Show effect of these two equations on the electron energy and distance from the nucleus For 1 electron systems H He1 Li2 etc Bohr s equations reproduced experimental results very nicely but it did not work very well at all for systems with more than 1 electron Show relationship between n values and emitted or absorbed light Modern theories have only slightly changed Bohr s original concepts of quantized energy states and that electrons only gained or lost energy when they changed energy states 3 The Modern Model The modern model used by chemists to calculate the electronic structure of atoms was developed by the Austrian physicist Erwin Schrodinger His mathematical model allows scientists to calculate both electronic energies and the most probable region orbital where each electron will be located Probability Orbital Description Orbital The region in space outside the nucleus where a particular electron is most likely to be found Energy Description Schrodinger s model requires four numbers to describe the energy and orbital of any electron The four numbers needed are called the quantum numbers The Quantum Numbers n l ml ms n principal quantum number n 1 2 3 4 5 6 7 In general as n increases the energy of the electron is increasing and the distance of the electron away from the nucleus is getting larger This is the same as in the Bohr model Remember from before E 2 18x10 18 Z2 n2 joules r 52 9 n2 Z pm l azimuthal Q N sub level Q N l 0 1 2 3 4 n 1 The value of l defines the shape of the electron s orbital The value of l is also used to identify the subshell of the electron 4 ml magnetic Q N ml l 0 l This Q N tells us the number orbitals contained in a subshell ms spin Q N ms 1 2 or 1 2 This Q N describes the spin state of the electron Once the 4 quantum numbers have been correctly assigned based on the above requirements the energy of the electron can be calculated Do some 3 4 2 1 2 type questions Pauli exclusion principle No two electron in any atom can have exactly the same energy or No two electrons in any atom can have the exact same set of 4 quantum numbers 5 Energy shells and sub levels the use of n and l All electrons with the same value of n are said to be in the same energy shell shell name K L M N n 1 2 3 4 All electrons with the same value of l are said to be in the same subshell subshell name s p d f g l 0 1 2 3 4 h i j k 5 6 7 8 Do complete n l ml ms tables for boron oxygen phosphorous and argon Define Paired electrons and Hund s Rule State if each of the following electronic configurations is allowed in an atom If the configuration is not permissible state what is wrong n 1 l 0 ml 0 mS n 3 l 1 ml 2 mS n 6 l 4 ml 4 mS n 13 l 13 ml 9 mS n 0 l 0 ml 0 mS 6 Review of Q N How many subshells in the n 3 shell The n 6 shell Name the possible subshells in the n 3 shell For n 6 How many orbitals in each subshell How many electrons in each orbital How many electrons in each subshell Total number of electrons possible in n 3 shell n l subhell name ml Number of orbitals Number of electrons 1 0 1s 0 1 2 2 0 2s 0 1 2 1 2p 1 0 1 3 6 0 3s 0 1 2 1 3p 1 0 1 3 6 2 3d 2 1 0 1 2 5 10 0 4s 0 1 2 1 4p 1 0 1 3 6 2 4d 2 1 0 1 2 5 10 3 4f 3 2 1 0 1 2 3 7 14 0 5s 0 1 2 1 5p 1 0 1 3 6 2 5d 2 1 0 1 2 5 10 3 5f 3 2 1 0 1 2 3 7 14 4 5g 4 3 2 1 0 1 2 3 4 9 18 3 4 5 Show how the values in this table are connected to the 4 areas of electron grouping in the periodic table 7 Orbital Shapes 8