Download 4.8-Quantum Mechanics

 The Bohr model describes definite electron energy levels
within atoms
 Bohr’s model only applied to hydrogen – it has been
replaced by more sophisticated models.
 Quantum Mechanics is the present model – it incorporates
the wave and particle nature of matter.
Quantum effects are only noticeable on the atomic scale
Erwin Shroedinger (1925)
- Developed a system of wave
mechanics based upon de
Broglie’s matter waves
 2
8 2 m
E  V    0

2
2
x
h
rate of change of the rate
of change of the
wavefunction with distance
The energy of
the particle
wave
The electrical
potential in which
the particle is
travelling
 Due to the wave nature of matter, the exact position and
momentum of an electron cannot be determined.
A two dimensional standard distribution
Interference of light waves
(wave nature)
Interference of electrons
(wave nature)
electrons
The Strange World of Quantum Physics
One Photon Or
Electron
Where does it hit the screen??
Let’s watch one at a time…
Screen
Screen
Given ONE photon, we cannot predict exactly where it will hit.
We can only predict the PROBABILITY that it will hit a certain place
on the screen: i.e., we can predict the pattern that many photons will
make!!
Hyperlink to folder with video!
Shroedinger’s math treated multiple electrons as
waves interfering in three dimensions.
Water hitting
water
Vibrations on
a drum skin
Max Born (1926)
-  2 represents the probability of a
particle’s position at a particular time.
“The normalized position wavefunctions for hydrogen, given in spherical coordinates are:”
 The region where the probability of finding an electron is
high is called the electron cloud, or orbital
3D Orbitals
Free and trapped quantum particles
Schroedinger’s wave equation,
and Born’s interpretation, can
equally be applied to “free”
particles, or those which are
trapped
Classically, a particle trapped
in a potential well cannot
escape….
….but a trapped quantum
particle (eg a particle in an
atomic nucleus) can tunnel out
of the well, even when it does
not have sufficient energy to
climb over the barrier
Heisenburg and Schrodinger developed sets of equations
that give the probability of any event in atomic physics
 including why some spectral lines are brighter
than others (some electron transitions are more likely to
occur so with a large number of atoms, there are more
atoms emitting that wavelength)
•The duality of matter makes it impossible to develop a set
of equations that tells us both exactly where an electron is
and what its momentum might be (Heisenburg’s
Uncertainty Principle)
•the Uncertainty Principle and other quantum mechanical
effects are not noticeable for large objects because of the
large number of atoms
Quantum mechanics also explains why all the electrons in
any atom do not fall into the ground state; no two electrons
can have the same exact state (distance from the nucleus,
energy, direction of rotation, etc.)
Quantum theory also gives the
number of electrons possible in each
of the energy levels (and therefore
the number of elements in each
period of the periodic table)
•Dirac developed equations that treated light
as either a wave or as a particle
•Dirac’s equations also predicted the
existence of antimatter, particles that are the
exact opposite of the regular particles (antielectron, antiproton, antineutron)
Dirac’s Theory
Dirac’s theory removed the paradox of particle-wave
duality:
It showed that if a particle was probed in a way that was
meant to demonstrate its particle like properties - it
would appear to be a particle…...
…….if it was probed in a way that was meant to demonstrate
its wave like properties - it would appear to be a wave
It seems that it is our own inability to conjure up an
appropriate or adequate mental picture of photons,
atoms, electrons and other quantum particles that is at
the heart of the particle-wave duality paradox
Why is quantum physics important?
All of physics, chemistry and the biosciences, as well as
almost all of modern technology rely upon quantum mechanics
Semiconductors, microelectronics, magnetism,
superconductivity, lasers, radioactivity, solar
energy, computers, polymers, batteries, recording
media, microwave ovens, mobile phones, medical
imaging, pharmaceuticals etc etc etc………..all
require a detailed knowledge of the quantum world
…...and quantum theory has never let us down
Some paradoxes do remain , but each time a test is carried
out to resolve a paradox quantum mechanics is only
strengthened.
The
story
so
far
The first 25 years of the 20thCentury saw a dramatic change in
the way that physicists viewed the nature of matter and
electromagnetic radiation
Quantum mechanics had provided a radically different
description of the substance of the universe to that offered
by Classical Physics
Each experimental test of Quantum Mechanics reinforced
the new theory and provided yet more evidence for:
Wave-particle duality of both light and matter
A probabilistic rather than deterministic view of
the Universe in which uncertainty is a physical
concept
A quantisation of energy
An underlying symmetry in which both
particles and antiparticles play a role
But...
Quantum Physics had revolutionary impact upon our
understanding of light and matter at the atomic level but...
…despite these dramatic developments our perception and
experience of the world around us has not significantly
changed
The physical laws developed by Newton and by Maxwell
continued to provide a perfectly adequate description of
the every day world - and still do today
However, at precisely the same time that Quantum
Mechanics was demonstrating the complete inadequacy of
these Classical Laws at an atomic scale, developments were
taking place which showed that they were also inadequate on
the scale of the Universe
These developments changed our perception of time itself!!