che-20028 QC lecture 1 - Rob Jackson's Website

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CHE-20028: PHYSICAL & INORGANIC 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-20028 QC lecture 1
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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/
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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/
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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.
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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
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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?
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Schematic of the Photoelectric
Effect
http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.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.
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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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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.
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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:
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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).
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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
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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 mv2=Ve)
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Online demonstrations of the
Photoelectric Effect Experiment
• Interactive demonstrations of
experiment are available online at:
the
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).
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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 mev2 = h - I (where I is the ionisation
energy, instead of the work function).
• The method enables ionisation energies
to be obtained.
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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!
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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.
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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.
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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?)
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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).
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