Chapter 6 Electronic structure of atoms light photons spectra Heisenberg s uncertainty principle atomic orbitals electron configurations the periodic table 6.1 The wave nature of light Visible light is a form of electromagnetic radiation, or radiant energy. Radiation carries energy through space 1
Electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. The number of waves passing a given point per unit of time is the frequency For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency. All electromagnetic radiation travels at the same velocity The wavelength and frequency of light is therefore related in a straightforward way: Blackboard examples 1. what is the wavelength of UV light with ν = 5.5 x 10 15 s -1? 2. what is the frequency of electromagnetic radiation that has a wavelength of 0.53 m? Wave nature of light successfully explains a range of different phenomena. 2
Thomas Young s sketch of two-slit diffraction of light (1803) 6.2 Quantized Energy and Photons Some phenomena cannot be explained using a wave model of light. 1. Blackbody radiation 2. The photoelectric effect 3. Emission spectra Hot Objects and the Quantization of Energy Heated solids emit radiation (blackbody radiation) In 1900, Max Planck investigated black body radiation, and he proposed that energy can only be absorbed or released from atoms in certain amounts, called quanta The relationship between energy, E, and frequency is: The Photoelectric Effect and Photons The photoelectric effect provides evidence for the particle nature of light and for quantization. 3
Einstein proposed that light could have particle-like properties, which he called photons. Light shining on the surface of a metal can cause electrons to be ejected from the metal. Below a threshold frequency no electrons are ejected Light has wave-like AND particle-like properties Blackboard examples 1. MRI body scanners operate with 400 MHz radiofrequency energy. How much energy does this correspond to in kilojoules/mol? 2. A mole of yellow photons of wavelength 527 nm has kj of energy. 6.3 Line Spectra and the Bohr Model Line spectra Radiation composed of only one wavelength is called monochromatic. When radiation from a light source, such as a light bulb, is separated into its different wavelength components, a spectrum is produced, 4
White light passed through a prism provides a continuous spectrum Bohr s Model Rutherford assumed that electrons orbited the nucleus analogous to planets orbiting the sun; however, a charged particle moving in a circular path should lose energy Niels Bohr noted the line spectra of certain elements and assumed that electrons were confined to specific energy states. These he called orbits. 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 5
The Energy States of the Hydrogen Atom Colors from excited gases arise because electrons move between energy states in the atom. Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. Bohr showed mathematically that where n is the principal quantum number (i.e., n = 1, 2, 3 ) and R H is the Rydberg constant. 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 move between orbits by absorbing and emitting energy in quanta (E = hν). The ground state = the lowest energy state The amount of energy absorbed or emitted by moving between states is given by Blackboard examples 1. When the electron in a hydrogen atom moves from n = 6 to n = 2, is light emitted or absorbed? 2. What is its wavelength (in nm)? 6
Limitations of the Bohr Model The Bohr Model has several limitations: However, the model introduces two important ideas: 1. the energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers 6.4 The wave behavior of matter Louis de Broglie posited that if light can have material properties, 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 the term used to describe wave characteristics of material particles. 7
Blackboard examples 1. What is the wavelength of a bullet (7.5 g) traveling at 700 ms -1? 2. At what speed must a 3.0 mg object be moving in order to have a de Broglie wavelength of 5.4 10-29 m? The Uncertainty Principle Heisenberg s uncertainty principle: The dual nature of matter sets a fundamental limit on how precisely we can know the location and momentum of an object. Heisenberg dreamt up the gamma ray microscope to explain his uncertainty principle. A source of photons is used to illuminate an electron fired from the left of the picture. The position of the electron can be determined from the scattering of the photons into the telescope at the bottom right of the picture. Heisenberg related the uncertainty of the position, x, and the uncertainty in momentum (mv) to a quantity involving Planck s constant: 8
6.5 Quantum Mechanics and Atomic Orbitals Erwin Schrödinger proposed an equation containing both wave and particle terms. The solution of the equation is known as a wave function, Ψ (psi), and describes the behavior of a quantum mechanical object, like an electron. Ψ 2 is called the probability density. It gives the electron density for the atom. Orbitals and quantum numbers If we solve the Schrödinger equation we get wave functions and corresponding energies. 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 principal quantum number, n must be a positive integer n = 1,2,3,4, the angular momentum quantum number, l 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). the magnetic quantum number, m l maximum value depends on l, can take integral values from l to + l Blackboard examples 1. Tabulate the relationship among values of n, l and m l through n = 4. 9
Orbitals can be ranked in terms of energy; as n increases energy level spacing becomes smaller. 6.6 Representations 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 The p orbitals p orbitals are dumbell-shaped with two lobes and a node at the nucleus 3 values of m l, 3 different orientations The d orbitals d orbitals have two nodes at the nucleus 10
Three of the d orbitals lie in a plane bisecting the x-, y-, and z-axes Two of the d orbitals lie in a plane aligned along the x-, y-, and z-axes Four of the d orbitals have four lobes each One d orbital has two lobes and a collar 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 Therefore, the energy-level diagram looks slightly different for many-electron systems Electron Spin and the Pauli Exclusion Principle Line spectra of many-electron atoms show each line as a closely spaced pair of lines. 11
Stern and Gerlach designed an experiment to determine why. A beam of atoms was passed through a slit and into a magnetic field and the atoms were detected: Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction. Electron spin is quantized: How do we show spin? Pauli s exclusion principle states that: 6.8 Electron Configurations Electron configurations tell us how the electrons are distributed among the various orbitals of an atom. When writing ground-state electronic configurations: 12
Hund s Rule For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized Blackboard examples 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 Blackboard examples 1. Draw the condensed electron configurations of Li, Na and P. Transition Metals After Ca the 3d orbitals begin to fill. The block of the periodic table in which the d orbitals are filling represents the transition metals. 13
6.9 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. Blocks of elements in periodic table related to which orbital is being filled Note that the 3d orbitals fill after the 4s orbital. Similarly, the 4f orbitals fill after the 5s orbitals. Anomalous Electron Configurations There are elements that appear to violate the electron configuration guidelines: When atomic number > 40, energy differences are small and other anomalies often occur. These usually act to reduce electron repulsions. 14