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

[email protected]

http://www.facebook.com/robjteaching

Main reading material(copies available in library)

CHE-20004 QM 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/

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/

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


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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

The Photoelectric Effect Experiment: introduction


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.

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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?


Schematic of the Photoelectric Effect

http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html

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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.


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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.


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• 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.


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• 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:


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• 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).


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• 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:

h0 = (M), so 0 = (M)/h


Photoelectric Effect: Experimental Set-up

light source

voltmeter

detector/photocell

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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)


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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).


Application of the Photoelectric Effect: Photoelectron Spectroscopy

http://www.chem.arizona.edu/facilities/pes/facility/PES_description.htm

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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.


Illustration of anapplication of PES to obtain

the energies of electrons in Ar

(1s2 2s2 2p6 3s2 3p6)

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!

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).

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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.


Application: Compton Scattering

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

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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.

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

• c is the velocity of light


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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?)


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


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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: physical chemistry quantum chemistry: lecture 1 dr rob jackson office: lj 1.16...

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