1. CHE-20004: PHYSICAL CHEMISTRY QUANTUM CHEMISTRY: LECTURE 1 Dr Rob Jackson Office: LJ 1.16 r.a.jackson@keele.ac.uk http://www.facebook.com/robjteaching

2. Main reading material (copies available in library) CHE-20004 QM lecture 12

3. 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! CHE-20004 QM lecture 13 I’ll also be using some animations developed at the University of St Andrews: see http://www.st-andrews.ac.uk/~qmanim/

4. 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. CHE-20004 QM lecture 14 ISBN 9781851687794 http://dogphysics.com /

5. 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-20004 QM lecture 15

6. 6 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-20004 QM lecture 1

7. The Photoelectric Effect Experiment: introduction CHE-20004 QM lecture 17 http://phet.colorado.edu/en/simulation/photoelectric Shine light of variable frequency on a metal surface and see what happens as the light frequency is varied.

8. 8 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-20004 QM lecture 1

9. Schematic of the Photoelectric Effect http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

10. 10 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-20004 QM lecture 1

11. 11 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-20004 QM lecture 1

12. 12 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-20004 QM lecture 1

13. 13 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-20004 QM lecture 1

14. 14 Explanation of the Photoelectric Effect - 4 So we can say that: ½ m e v 2 = h -  (M) m e 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-20004 QM lecture 1

15. 15 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-20004 QM lecture 1

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

17. 17 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-20004 QM lecture 1

18. 18 Online demonstrations of the Photoelectric Effect Experiment Interactive demonstrations of the experiment are available online at: http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/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-20004 QM lecture 1

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

20. 20 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 m e v 2 = h - I (where I is the ionisation energy, instead of the work function). The method enables ionisation energies to be obtained. CHE-20004 QM lecture 1

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

22. 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).

23. 23 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-20004 QM lecture 1

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

25. 25 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.

26. 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:  = (2h/m e c) sin 2 (½  )  is the angle the photon is scattered through m e is the electron mass c is the velocity of light CHE-20004 QM lecture 126

27. 27 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 MeV is of great interest, but hard to access. (What wavelength range is this?) CHE-20004 QM lecture 1

28. 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_l2/compton_scatter.html http://heseweb.nrl.navy.mil/gamma/detector/compton/compton.htm CHE-20004 QM lecture 128

29. 29 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-20004 QM lecture 1