CHE20028 PHYSICAL INORGANIC CHEMISTRY QUANTUM CHEMISTRY LECTURE 1

CHE-20028: PHYSICAL & INORGANIC CHEMISTRY QUANTUM CHEMISTRY: LECTURE 1 Dr Rob Jackson Office: LJ 1. 16 r. a. jackson@keele. ac. uk http: //www. facebook. com/robjteaching

Main reading material (copies available in library) CHE-20028 QC lecture 1 2

For the Quantum Chemistry section … • If you already have: Keeler & Wothers, ‘Chemical Structure & Reactivity’, • see chapter 16 (p 698 -) • But it’s rather dry and mathematical! I’ll also be using some animations developed at the University of St Andrews: see http: //www. st-andrews. ac. uk/~qmanim/ CHE-20028 QC lecture 1 3

Additional ‘light’ reading for Quantum Chemistry • Recommended as an introduction to Quantum Mechanics! • Some of the ideas of the subject are ‘non-intuitive’, and this book provides a good explanation of these. ISBN 9781851687794 http: //dogphysics. com/ CHE-20028 QC lecture 1 4

Why ‘non-intuitive’ ? • Some ideas from QM are hard to accept because of our ‘conditioning’. • For example, the QM interpretation of the Young’s Double Slit experiment* is that a single photon passes through both slits! *http: //en. wikipedia. org/wiki/Double-slit_experiment CHE-20028 QC lecture 1 5

Learning objectives for lecture 1 • To appreciate why quantum mechanics was devised, through the interpretation of the photoelectric effect and Compton effect experiments. • To understand how wave-particle duality applies to light. CHE-20028 QC lecture 1 6

The Photoelectric Effect Experiment: introduction Shine light of variable frequency on a metal surface and see what happens as the light frequency is varied. http: //phet. colorado. edu/en/simulation/photoelectric CHE-20028 QC lecture 1 7

The Photoelectric Effect • Observation: electrons are emitted from a metal surface when light of a particular frequency shines on it. • What is happening? Electrons must be getting energy from the light to enable them to escape from the surface – but how? CHE-20028 QC lecture 1 8

Schematic of the Photoelectric Effect http: //hyperphysics. phy-astr. gsu. edu/hbase/mod 1. html

Why the Photoelectric Effect was difficult to understand at first • Electrons were emitted from the surface only above a certain frequency. • Below that frequency, no electrons were emitted, regardless of the light intensity. • Light was regarded as a wave (from diffraction/interference experiments) so intensity rather than frequency should control the light energy. CHE-20028 QC lecture 1 10

Explanation of the Photoelectric Effect - 1 • The energy of the light must depend on its frequency rather than its intensity. • Light must be behaving as a particle rather than as a wave, with the energy of the particle depending on the light frequency. • The light particles (photons) collide with electrons near the surface and transfer energy to them. CHE-20028 QC lecture 1 11

Explanation of the Photoelectric Effect - 2 • Planck’s equation relates energy and frequency: • E = h (or hf) where (or f) is the frequency of the light (in Hz, s-1) (h is Planck’s constant, 6. 626 x 10 -34 Js) • Light energy is transferred to the electrons. CHE-20028 QC lecture 1 12

Explanation of the Photoelectric Effect - 3 • The electrons must get enough energy from the light to overcome the attraction of the metal nuclei – this amount of energy is called the work function, (M). • The kinetic energy of the electrons emitted from the surface will be the difference between the photon energy and the metal work function: CHE-20028 QC lecture 1 13

Explanation of the Photoelectric Effect - 4 • So we can say that: ½ mev 2 = h - (M) • me is the electron mass, 9. 11 x 10 -31 kg • We can use this expression to calculate the velocity, v of an electron emitted from a metal surface (see problems). CHE-20028 QC lecture 1 14

Explanation of the Photoelectric Effect - 5 • Another useful value is the threshold frequency, 0 • This frequency which must be exceeded to give photons enough energy to enable electrons to escape from the surface. It is obtained from: h 0 = (M), so 0 = (M)/h CHE-20028 QC lecture 1 15

Photoelectric Effect: Experimental Set-up voltmeter light source detector/photocell

How the experiment is performed • Using a variable frequency light source, shine light onto a metal surface. • Determine the light frequency which causes electrons to be emitted. • Measure the energy of the emitted electrons, by applying a voltage across the cell in the opposite direction to balance the voltage of the emitted electrons (using ½ mv 2=Ve) CHE-20028 QC lecture 1 17

Online demonstrations of the Photoelectric Effect Experiment • Interactive demonstrations of the experiment are available online at: http: //lectureonline. cl. msu. edu/~mmp/kap 28/Photo. Effect/photo. htm and at: http: //www. st-andrews. ac. uk/~qmanim/embed_item_3. php? anim_id=23 • Try these! (a demonstration may be attempted in the lecture). CHE-20028 QC lecture 1 18

Application of the Photoelectric Effect: Photoelectron Spectroscopy http: //www. chem. arizona. edu/facilities/pes/facility/PES_description. htm

Information from Photoelectron Spectroscopy • In photoelectron spectroscopy, UV light is shone onto a molecular substance, and the energy of the electrons emitted is measured: • ½ mev 2 = h - I (where I is the ionisation energy, instead of the work function). • The method enables ionisation energies to be obtained. CHE-20028 QC lecture 1 20

Illustration of an application of PES to obtain the energies of electrons in Ar (1 s 2 2 p 6 3 s 2 3 p 6) Note that in this case, X-rays have been used. Spectrum taken from: K Siegbahn et al, ‘ESCA applied to free molecules’ (North-Holland, Amsterdam 1969) Think about what these numbers mean! CHE-20028 QC lecture 1 21

The Compton Effect If light can be described as photons, if they collide with other particles, there should be a change in their momentum (= mass x velocity).

Demonstration of the Compton Effect • Shine a beam of photons at a substance (e. g. carbon), and look for a change in frequency of the photons, caused by a collision with the electrons. • The effect can also be demonstrated by the collision between a beam of photons and a beam of electrons. CHE-20028 QC lecture 1 23

Application: Compton Scattering http: //hyperphysics. phy-astr. gsu. edu/hbase/quantum/comptint. html

Compton Scattering: Experimental Set-up X-ray photons are emitted from the X-ray tube and hit the carbon target. They are then scattered by electrons in the carbon through a range of angles. CHE-20028 QC lecture 1 25

Compton Scattering: analysis • Some light passing through the material is not scattered and shows no momentum change. • Scattered light shows a momentum change by a wavelength change which depends on the angle it is scattered through: = (2 h/mec) sin 2 (½ ) • is the angle the photon is scattered through • me is the electron mass • c is the velocity of light CHE-20028 QC lecture 1 26

Compton Scattering: applications • As well as providing another demonstration that light behaves as a particle, it is used in ‘Compton Telescopes’, for ray astronomy. – In ray astronomy, the region from 1 -30 Me. V is of great interest, but hard to access. • (What wavelength range is this? ) CHE-20028 QC lecture 1 27

Compton telescopes: basic idea • Compton telescopes work on the principle that ray photons from outer space are detected when they are deflected by electrons in a detector. • Their energy is then obtained from angle through which they are scattered. See web sites below for more details (the first will be looked at in the lecture). http: //imagine. gsfc. nasa. gov/docs/science/how_l 2/compton_scatter. html http: //heseweb. nrl. navy. mil/gamma/detector/compton. htm CHE-20028 QC lecture 1 28

Summary: Photoelectric and Compton Effect • Between them, the photoelectric effect and Compton effect experiments proved conclusively that light behaves as a particle at the atomic level. • However, we still need to use the wave behaviour of light to explain optical effects like diffraction and interference. • This leads to the Duality of wave-particle behaviour ( lecture 2). CHE-20028 QC lecture 1 29