Chapter 6 - Electronic Structure of Atoms 6.1 The Wave Nature of Light To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation Visible light is an example of electromagnetic radiation Electromagnetic radiation carries energy through space Electromagnetic radiation is made up of self-propagating transverse oscillating waves of electric and magnetic fields Frequency: number of complete waves that pass a certain point per unit of time For waves traveling at the same velocity: All electromagnetic radiation moves at the same speed (speed of light) 1
Wavelength and frequency of electromagnetic radiation are always related in a straightforward way: Wavelength long (fewer cycles per second) frequency low Wavelength short (more cycles per second) frequency high This relationship is expressed by the following equation: = c (nu) frequency (lambda) wavelength c speed of light 2
Examples 1. What is the wavelength of visible light with = 4.9 x 10 14 s -1? 2. What is the frequency of electromagnetic radiation that has a wavelength of 514 nm? Wave nature of light successfully explains a range of different phenomena Thomas Young's sketch of two-slit diffraction (1803) 3
6.2 Quantized Energy and Photons Three phenomena that wave model cannot explain: 1. Blackbody radiation 2. The photoelectric effect 3. Emission spectra Hot Objects and the Quantization of Energy Hot objects emit radiation (blackbody radiation) Problem solved in 1900 by Max Planck who assumed energy can only be absorbed or released by atoms only in certain amounts The energy of a single quantum equals a constant times the frequency of the radiation: 4
The Photoelectric Effect and Photons The photoelectric effect provides evidence for the particle nature of light as well as for its quantization Einstein assumed that light traveled in energy packets called photons If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal Below the threshold frequency, no electrons are ejected Conclusion - Light has wave-like and particle-like properties 5
Examples 1. 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? 2. A mole of UV photons of wavelength 320 nm has kj of energy. 6.3 Line Spectra and the Bohr Model Line Spectra Radiation composed of a single wavelength is said to be monochromatic When radiation from a light source, such as a light bulb, is separated into its different wavelength components, a spectrum is produced, 6
Sunlight passing through a prism produces a continuous spectrum Bohr s Model Rutherford assumed that electrons move in circular orbits around the nucleus Niels Bohr noted the line spectra of certain elements and assumed that electrons were confined to specific energy states called orbits. 7
Bohr s model is based on three postulates: 1. Only orbits of specific radii are permitted for electrons in an atom 2. An electron in a permitted orbit has a specific energy 3. Energy is only emitted or absorbed by an electron as it moves from one allowed energy state to another The Energy States of the Hydrogen Atom The colours observed from excited gases are due to electrons moving between energy states in the atom Bohr showed mathematically that where n is the principal quantum number (i.e., n = 1, 2, 3 ) and R H is the Rydberg constant. 8
The first orbit in the Bohr model has n = 1 and is closest to the nucleus. The furthest orbit in the Bohr model has n = and corresponds to E = 0. Electrons in the Bohr model can only jump between orbits by either absorbing or emitting energy in quanta (E = h ). The ground state = the lowest energy state The amount of energy absorbed or emitted by moving between states is given by the following equation 9
Examples 1. When the electron in a hydrogen atom moves from n = 5 to n = 1, is light emitted or absorbed? 2. What is its wavelength (in nm)? Limitations of the Bohr Model The Bohr Model has some limitations: The model introduces two important ideas: 1. Electrons exist only in certain energy levels described by quantum numbers (energy of electron quantitized) 10
6.4 The Wave Behaviour of Matter Louis de Broglie - if light can behave like particles, matter should exhibit wave properties de Broglie proposed that the characteristic wavelength of the electron or of any other particle depends on its mass, m, and on its velocity, v Matter waves is used to describe the wave characteristics of material particles Examples 1. What is the wavelength of an electron (9.11 x 10-31 kg) traveling at 1.0 x 10 7 ms -1? 2. At what speed must a 150.0 mg object be moving in order to have a de Broglie wavelength of 5.4 10-29 m? 11
The Uncertainty Principle sets a fundamental limit on how precisely we can know the location and momentum of an object Heisenberg dreamt up a gamma ray microscope to explain his uncertainty principle Heisenberg related the uncertainty of the position ( x) and the uncertainty in momentum (mv): 6.5 Quantum Mechanics and Atomic Orbitals Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. The solution of the equation is known as a wave function, (psi). Orbitals and Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. 12
The probability density (or electron density) described by an orbital has a characteristic energy and shape. The energy and shape of orbitals are described by three quantum numbers. These arise from the mathematics of solving the Schrödinger equation. The values of n are integers 0 maximum value is (n-1), i.e. l = 0,1,2,3 (n-1) use letters for l (s, p, d and f for l = 0, 1, 2, and 3) Values are integers ranging from -l to l: l m l l. Examples 1. Tabulate the relationship among values of n, l and m l through n = 4. 13
Orbitals can be ranked in terms of energy. 6.6 Representation of Orbitals The s orbitals All s orbitals are spherical As n increases, the s orbitals get larger As n increases, the number of nodes increases 14
The p orbitals p orbitals are dumbell-shaped 3 values of m l The d orbitals d orbitals have two nodes at the nucleus 15
6.7 Many-Electron Atoms Orbitals and Their Energies In a many-electron atom, for a given value of n, the energy of an orbital increases with increasing value of l The result is that the electron-level diagram looks different for manyelectron systems Electron Spin and the Pauli Exclusion Principle It was observed in the line spectra of many-electron atoms that each line appeared as a closely spaced pair of lines. Electrons have an intrinsic property, called electron spin, that causes each electron to behave as if it were a sphere spinning on its own axis 16
Stern and Gerlach designed an experiment to determine why. A beam of atoms was passed through a slit and into a magnetic field. Two spots were found in the experiment one to electrons with one spin and the other to electrons with opposite spin Electron spin is quantized. The spin magnetic quantum number is denoted by Wolfgang Pauli determined the principle that governs arrangements of electrons in many-electron atoms Pauli s exclusion principle states that: 17
6.8 Electron Configurations The electron configuration of an atoms tell us the way in which the electrons are distributed among the various orbitals of an atom Important rules to follow when writing ground-sate electronic configurations: 1s 1s 1s 2s Hund s Rule For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized 18
Example 1. Draw the electron configurations of Li, Be, B, C, N, O, Ne and Na. Condensed Electron Configurations Electron configurations may be written using a shorthand notation (condensed electron configuration): 1. Write the core electrons corresponding to the noble gas in square brackets 2. Write the valence electrons explicitly 19
Example 1. Draw the condensed electron configurations of Li, Na, Al and K. Transition Metals The block of the periodic table in which the d orbitals are filled represents the transition elements or transition metals 20
The Lanthanides and Actinides The lanthanide elements or rare earth elements are the 14 elements which correspond to the filling of the 4f orbitals The actinide elements are built up by filling the 5f orbitals 6.9 Electron Configurations and the Periodic Table The outermost electrons are called the valence shell electrons 21
The periodic table is a great tool for determining electron configurations. Blocks of elements in periodic table related to which orbital is being filled: 22
Anomalous Electron Configurations There are certain elements that appear to violate the electron configuration rules: When atomic number > 40, 23