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Unit 12: Part 3
Quantum Mechanics and
Atomic Physics
Overview
Matter Waves: The de Broglie Hypothesis
The Schrödinger Wave Equation
Atomic Quantum Numbers and the Periodic
Table
The Heisenberg Uncertainty Principle
Particles and Antiparticles
Matter Waves: The de Broglie
Hypothesis
The momentum of a photon is given by:
The de Broglie hypothesis is that particles
also have wavelengths, given by:
Matter Waves: The de Broglie
Hypothesis
It can be shown that the allowed orbits
in Bohr’s theory of the hydrogen atom
are those that contain an integral
number of de Broglie wavelengths
around their circumference.
Matter Waves: The de Broglie
Hypothesis
Electrons can be
observed to diffract
from crystals whose
plane spacing is close
to the electron
wavelength, just as Xrays do. Diffraction is
purely a wave
phenomenon.
The Schrödinger Wave Equation
The Schrödinger wave equation describes the
electron wave and how it propagates in space
and time.
The solution to the Schrödinger equation is
called the wave function. It gives the
probability of finding the electron at any
location.
The Schrödinger Wave Equation
The most probable
place to find the
electron is at the Bohr
radius, but the
probability is significant
near the radius as well.
The Schrödinger Wave Equation
Another prediction of this equation is tunneling;
a particle has some probability of appearing on
the “wrong” side of a barrier. This effect is used
in the operation of a scanning tunneling
microscope, and is
responsible for some forms
of radioactive decay.
Atomic Quantum Numbers and the
Periodic Table
The energy of an electron orbit is
characterized by its quantum number, n.
Within the same energy level, different values
of the orbital angular momentum are possible.
Atomic Quantum Numbers and the
Periodic Table
Electrons with the same energy and angular
momentum can have different values of the z
component of angular momentum.
Atomic Quantum Numbers and the
Periodic Table
Finally, each
electron possesses
a quantity called
“spin,” which can be
in either of two
directions.
Atomic Quantum Numbers and the
Periodic Table
This table summarizes the different quantum
numbers and their allowed values.
Atomic Quantum Numbers and the
Periodic Table
For multielectron atoms,
the electrons fill the
quantum states in order
of increasing energy. For
each “shell” (energy
level) there are
subshells corresponding
to different values of l.
Atomic Quantum Numbers and the
Periodic Table
This diagram illustrates the different energy
levels.
Atomic Quantum Numbers and the
Periodic Table
The Pauli exclusion principle states that no
two electrons in an atom can have the same
values of all four quantum numbers; that is,
no two electrons can be in the same quantum
state.
Atomic Quantum Numbers and the
Periodic Table
This shows how energy levels fill up, one
electron per state:
Atomic Quantum Numbers and the
Periodic Table
As n increases, the total number of states per
shell increases as well.
Atomic Quantum Numbers and the
Periodic Table
The periodic table was originally organized by
putting elements with similar chemical behavior
in columns of increasing mass. Comparing with
electron configurations, we see that the
elements in each column have the same
number of electrons in their outer shell, called
valence electrons.
Atomic Quantum Numbers and the
Periodic Table
Atomic Quantum Numbers and the
Periodic Table
The periods in
the periodic
table
correspond to
the outermost
shell being
filled.
The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle:
It is impossible to know simultaneously an
object’s exact position and momentum.
In order to understand this, we need to
consider how we would measure an
object’s position and momentum.
The Heisenberg Uncertainty
Principle
Any observation is going to
involve interacting with the
object in one way or
another. If we shine light on
a book, the book’s
momentum doesn’t really
change very much. If we
shine light on an electron,
though, the electron’s
momentum changes a lot.
The Heisenberg Uncertainty
Principle
There is a lower limit on how small the
product of the uncertainty in position and the
uncertainty in momentum can be:
The smallness of Planck’s constant means
that uncertainty effects are observable only
in atomic particles.
The Heisenberg Uncertainty
Principle
The uncertainty principle can also be
expressed in terms of energy and time; the
faster you measure energy (or the shorter the
lifetime of an excited state), the more
uncertain it is.
This leads to natural
broadening of spectral
lines.
Particles and Antiparticles
When quantum mechanics was expanded to
include relativity (Paul A. M. Dirac), it
predicted that there should be an antiparticle
to the electron. This particle has been
observed, and is called the positron.
If an X-ray passes sufficiently close to a
nucleus, an electron–positron pair may be
created. The X-ray must have at least as
much energy as the rest energies of the
electron and positron:
Particles and Antiparticles
In this picture, the magnetic
field serves to deflect the
electron and positron in
opposite directions, making
them easier to detect.
Particles and Antiparticles
Positrons don’t last long
once they’ve been produced,
though; they annihilate
almost immediately with
nearby electrons, producing
X-rays in the process.
Review
Photon momentum:
de Broglie hypothesis: particles also have a
wavelength:
Atomic electrons are described by a
wave function, which gives the
probability of finding the electron at a
particular position.
Review
Electron orbital energies are determined
mainly by the principal quantum number, n.
The orbital quantum number gives the
electron’s angular momentum.
The magnetic quantum number gives the z
component of the electron’s angular
momentum.
The spin quantum number gives the direction
of the electron’s spin.
Review
Exclusion principle: no two electrons in the
same atom can have exactly the same set of
quantum numbers.
Uncertainty principle: position and momentum,
or energy and time, cannot be simultaneously
measured with arbitrary accuracy.
Review
Pair production is the creation of a particle and
its antiparticle; pair annihilation is the opposite.