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CHE-20004: PHYSICAL CHEMISTRY QUANTUM CHEMISTRY: LECTURE 1 Dr Rob Jackson Office: LJ 1.16

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. Main reading material (copies available in library). For the Quantum Chemistry section …. If you already have:

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CHE-20004: PHYSICAL CHEMISTRY QUANTUM CHEMISTRY: LECTURE 1 Dr Rob Jackson Office: LJ 1.16

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  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 1

  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! I’ll also be using some animations developed at the University of St Andrews: see http://www.st-andrews.ac.uk/~qmanim/ CHE-20004 QM lecture 1

  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. ISBN 9781851687794 http://dogphysics.com/ CHE-20004 QM lecture 1

  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 1

  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 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-20004 QM lecture 1

  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. 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 frequencyshould control the light energy. CHE-20004 QM lecture 1

  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. 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 10-34Js) • Light energy is transferred to the electrons. CHE-20004 QM lecture 1

  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. Explanation of the Photoelectric Effect - 4 • So we can say that: ½ mev2 = 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-20004 QM lecture 1

  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 voltmeter light source detector/photocell

  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 mv2=Ve) CHE-20004 QM lecture 1

  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. 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 mev2 = 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 (1s2 2s2 2p6 3s2 3p6) 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!

  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. 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. 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/mec) sin2 (½) • is the angle the photon is scattered through • me is the electron mass • cis the velocity of light CHE-20004 QM lecture 1

  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 1

  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

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