Transcript Lecture 14 (Slides) September 27

Wave Particle Duality – Light and
Subatomic Particles
• In high school physics light was treated as
having both wave like and particle like
character. Diffraction and refraction of light
both exemplify its wave like properties.
Particle like properties of light can also be
demonstrated readily. One way to do this is to
consider the photoelectric effect (see text)
which implies, surprisingly, that light photons
have momentum.
Subatomic Particles – Wave Character
• A number of experiments show that small
particles have observable wave like properties.
Such wave like properties become increasingly
important as one moves to particles of smaller
mass. The electron is the most important of
these particles. Interesting diffraction and
refraction experiments have been conducted
with electrons.
Mathematical Description of Electrons
• The fact that electrons exhibit wave like
behavior suggested that equations used to
describe waves, and light waves in particular,
might be modified to describe electrons. We
will see some familiar mathematical functions
used to describe the electron (e.g. cos θ, sin θ,
eiθ). We will use so-called wave functions (Ψ’s)
to gain insight into the behavior of electrons in
atoms.
De Broglie’s Contribution
• De Broglie used results/equations from
classical physics to rationalize experimental
results which proved that subatomic particles
(and some atoms and molecules) had wave
like properties. He proposed, in particular, that
particles with a finite rest mass had a
characteristic wave length – as do light waves.
8-5 Two Ideas Leading to a New
Quantum Mechanics
• Wave-Particle Duality
– Einstein suggested particle-like
properties of light could explain the
photoelectric effect.
–Diffraction patterns suggest photons
are wave-like.
• deBroglie, 1924
– Small particles of matter may at
times display wavelike properties.
Copyright © 2011 Pearson
Canada Inc.
General Chemistry: Chapter 8
Louis de Broglie
Nobel Prize 1918
Slide 5 of 50
Wave-Particle Duality
E = mc2
h = mc2
h/c = mc = p
p = h/λ
λ = h/p = h/mu
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Canada Inc.
General Chemistry: Chapter 8
Slide 6 of 50
FIGURE 8-16
Wave properties of electrons demonstrated
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Canada Inc.
General Chemistry: Chapter 8
Slide 7 of 50
Probabalistic Description of Electrons
• Classical physics suggests that we should be
able (given enough information) to describe
the behaviour of any body – changes in
velocity, kinetic energy, potential energy and
so on over time. Classical physics suggests that
all energies are continuously variable – a
result which very clearly is contradicted by
experimental results for atoms and molecules
(line spectra/quantized energies).
Uncertainty Principle
• The quantum mechanical description used for
atoms and molecules suggests that for some
properties only a probabalistic description is
possible. Heisenberg suggested that there is a
fundamental limitation on our ability to
determine precise values for atomic or
molecular properties simultaneously. The
mathematical statement of Heisenberg’s socalled Uncertainty Principle is given on the
next slide.
The Uncertainty Principle
h
Δx Δp ≥
4π
Heisenberg and Bohr
FIGURE 8-17
•The uncertainty principle interpreted graphically
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Canada Inc.
General Chemistry: Chapter 8
Slide 10 of 50
Atomic “Diagrams”
• Many simple diagrams of atoms/atomic
structure have limitations. In class we’ll
consider some limitations of the C atom
diagram shown on the next slide.
• Representations of molecules are even more
challenging – at least if we want to consider
the electrons!
The “Carbon Atom”
• Limitations?
e le c tr o n
n e u tr o n
p r o to n
A Molecular Model
Wave Functions and Standing Waves
• If we wish to describe the behaviour of a
system changing over time in three
dimensional space we would need four
variables - three coordinates and time.
Classically, we might wish to describe the
velocity of a satellite re-entering the Earth’s
atmosphere and write, for example, v(x,y,z,t).
Copyright © 2011 Pearson
Canada Inc.
General Chemistry: Chapter 8
Slide 14 of 50
Form of Wave Functions
• For wave functions used to describe the
behaviour of electrons in atoms we could, by
analogy, write Ψ(x,y,z,t). For charged particles
and Coulombic interactions, using spherical
polar coordinates simplifies the mathematical
work greatly. We then write wave functions as
Ψ(r,ϴ,φ,t). It turns out that in many cases the
properties of an electron, atom, or molecule
do not change over time.
Wave Functions and Time
• If the behaviour of an electron, atom or
molecule does not change with time we can
write simpler wave functions, such as Ψ(x,y,z)
or Ψ(r,ϴ,φ). The classical analogy of a system
with wave like behaviour not changing over
time is any object that features standing
waves. In such cases there is no destructive
wave interference. Then wave like properties
should be constant over time.
Standing Waves in Newtonian
Mechanics
• In macroscopic systems with “constant” wave
like properties one sees nodes which do not
move over time. An example would be a guitar
string vibrating with, in the simplest case, two
nodes occurring at each end of the string.
More complex waves are possible for real
systems – which again reflect constructive
rather than destructive wave interference.
Similar considerations apply to electrons.
Wave Mechanics
Standing waves.
Nodes do not undergo
displacement.
λ = 2L, n = 1, 2, 3…
n
FIGURE 8-18
•Standing waves in a string
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General Chemistry: Chapter 8
Slide 18 of 50
FIGURE 8-19
The electron as a matter wave
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Canada Inc.
General Chemistry: Chapter 8
Slide 19 of 50
Dihydrogen Oxide Waves
Sample Term Test 1 Example
• B4. Consider the following reaction
•
•
2 C(s) + O2(g) + 4 H2(g) → 2 CH3OH(g)
∆Hº = –402.4 kJ
•
• [2] (a) Calculate a ΔUº value for the reaction at 25ºC.
•
• [1] (b) How much heat would be released if 10.0 g of CH3OH(g)
is formed from this reaction under constant volume conditions?
• Reminder: The enthalpy change for the reaction as written gives the
amount of heat released when two moles of gaseous methanol are
formed at constant pressure. The internal energy change for the
reaction as written gives the amount of heat released at constant V.
Sample Term Test 1 Example
• [2] A5. A 16.0 L tank contains a mixture of
helium gas at a partial pressure of 125.0 kPa
and nitrogen gas at a partial pressure of 75.0
kPa. If neon gas is added to the tank, what
must the partial pressure of neon be to reduce
the mole fraction of nitrogen to 0.200?
Sample Term Test 1 Example
• [4] B5. A sample of zinc metal reacts
completely with an excess of hydrochloric acid:
• Zn(s) + 2 HCl(aq) → ZnCl2(aq) + H2(g)
•
• The hydrogen gas produced is collected over
water at 25.0ºC. The volume of the gas is 7.80 L,
and the pressure is 0.980 atm. Calculate the
amount of zinc metal in grams consumed in the
reaction. (Vapor pressure of water at 25ºC = 23.8
mmHg.)