Transcript p = mv

FALL SEMESTER 2002
WELCOME TO CHEM 614, A COURSE ON
QUANTUM CHEMISTRY
YOUR INSTRUCTOR IS
Michael A. J. Rodgers
His Office is at PSLB 310
e-mail: [email protected]
Send me your e-mail addresses ASAP
COURSE WEB SITE ADDRESS:
http://www.bgsu.edu/departments/chem/faculty/rodgers/quantum
There is no recommended book, but there is a reference text (see course
outline handout), and I shall loan you a copy of a math book (Barrante) that
you could find useful.
The syllabus for the course is defined by the 12 or so Modules (chapters) that
you will eventually find under the “Modules” page on the Quantum web site.
Today there is just one.
Class meets MWF at 0830. I shall present “lectures” that are based on the
content of the Modules. The Modules contain much more material than I can
cover in the lectures, so you will have to do a lot of reading on your own in
order to complete the homework assignments.
The “pace” of the course will be set by the homeworks. A homework
assignment will be given every week. It is up to you to do the homeworks.
If you complete the homework assignments assiduously you will have no
surprises when the Tests come around.
SPEAKING OF TESTS THERE WILL BE THREE (3)
TEST 1 WILL BE IN EARLY OCTOBER (1 HOUR)
TEST 2 WILL BE IN MID NOVEMBER (1 HOUR)
TEST 3 (THE FINAL) WILL BE HELD AS STIPULATED DURING
FINALS WEEK (2 HOURS),
YOUR GRADE FOR THE COURSE WILL BE CALCULATED
FROM THE POINTS YOU ACCUMULATE ON ALL3 TESTS
POINTS FOR THE FINAL WILL BE WEIGHTED DOUBLE
MODULE 1
FROM PLANCK TO EINSTEIN TO DE BROGLIE TO SCHRÖDINGER…
.
You should be familiar with the major rethinking about the physics of
electromagnetic radiation and matter that occurred at the opening of the 20th
century.
If not, I suggest that you read and digest an account that you will find in any
advanced text on modern physics, physical chemistry, and the like.
At the opening of Module 1 you will find a very brief and hardly sufficient
overview of the historical background to the birth and early growth of quantum
mechanics, the concept of wave-particle duality, and the contributions of the
“greats”.
I urge you to read this historical material and to supplement it from other
sources. It will help you ease into the course material.
Next is a photo with some of the greats in it.
12
8
7
6
1
2
13
3
4
14
9
10
5
1: Langmuir
7: Bragg
13: Pauli
2: Planck
8: Dirac
14: Heisenberg
3: Mme Curie
9: de Broglie
15: Brillouin
4: Lorentz
10: Born
5: Einstein
11: Bohr
6: Debye
12: Schrödinger
15
11
Solvay Conference
Brussels, Belgium, 1927
As a result of his contemplation of the PHOTOELECTRIC EFFECT, Einstein
proposed that when light was emitted from a source, it was not a continuous
wave, but as a beam of minute energy packets (quanta) and this was the way
that it generated electrons on impinging on the sensitive metal surface.
Eventually these light quanta became known as photons.
In 1924 Louis de Broglie proposed that if light (a classical wave) can display
particle-like behavior, then matter (classical particles) should likewise display
wave-like behavior under particular experimental conditions.
This proposal has brought an intriguing symmetry to natural phenomena. Louis
de Broglie argued that the equation that Einstein had arrived at for photons, viz.
l  h/ p
where l is the wavelength, p is the momentum and h is Planck's constant,
should be applicable also to matter. On this concept, l would be the
wavelength of matter waves that are associated with the particle.
Consider a particle of mass m moving with velocity v.
The momentum is given by p = mv
its de Broglie wavelength is given by l = h/mv.
For masses in the kg range, moving with everyday velocities (e.g.,
a fast moving baseball) l is of the order of 10-34 m, a value that is
not observable and of no consequence in everyday life.
However, for an electron traveling at 1% of the speed of light
l~ 10-10 m, i.e. 100 pm
This is in the x-ray spectrum, and clearly measurable.
In fact, it is now commonplace that electron beams of such
character can be employed for diffraction studies (a specific
property of waves) to obtain information on the structure of
crystalline materials.
Thus it seems we have a paradoxical situation:
an electron shows properties of both a particle (which we think of
as having a particular set of spatial coordinates, i.e. localized)
and it shows wave-like properties (in which it cannot be pinned to
a particular set of coordinates).
The paradox is resolved by deciding that an electron (and
electromagnetic radiation) is neither a particle nor a wave but can
show properties of either (but not simultaneously both), depending
on how we carry out the observations.
So electrons and photons resemble one another but they are not
twins.
electrons have rest mass and travel at any velocity less than
3x108 m s-1;
photons have no rest mass and always travel at 3x108 m s-1 in
vacuo.