Transcript P301_2009_week5

P301 Lecture 12
“Bohr’s Hypotheses”
Bohr formulated the following ad hoc model:
1. Atoms exist only in certain stable “stationary states”
2. The dynamic equilibrium of these stationary states is determined by
the laws of classical physics, but the way the atoms interact with the
electromagnetic field of light waves is not
3. The emission and absorption of EM waves by atoms takes place
ONLY in conjunction with a transition between two stationary states,
with the frequency of the emitted light being determined according to
the Planck hypothesis:
|E1 – E2 |= hf
4. The (orbital) angular momentum of the electron in a stationary state
can only take on values given by integral multiples of Planck’s
constant divided by 2p Ln = nh/2p
It is this last hypothesis that is the truly new (revolutionary) idea
from Bohr himself, the other three are pretty much inescapable
and/or had been provided by someone else already.
P301 Lecture 13
“Moseley’s Law”
http://chimie.scola.ac-paris.fr/sitedechimie/hist_chi/text_origin/moseley/Moseley-article.htm
Lb
La
Lg
Ka
Kb
NOTES:
•Moseley started to catalogue characteristic
x-ray energies (and therefore frequencies)
using a technique we’ll discuss next week.
• He developed the above empirical relations
for the frequencies, determined that atomic
number, not weight, was the relevant
parameter to explain the periodicity of the
periodic table (e.g. he reversed the positions
of Ni and Fe; K and Ar), and predicted the
existence of three (and only three) previously
undiscovered elements (Z=43, 61, and 75;
later: Tc, Pm, and Re) “between Al and Au”
P301 Lecture 13
“Characteristic X-ray production”
NOTES:
•Barkla first discovered “characteristic xrays” in 1909, several years before Bohr,
the Braggs, and Moseley did their work.
•The “shell” model of the atom, which
arises from Bohr’s model for H, is very
useful even when considering multielectron atoms
• The various “shells” (K, L, M, N, etc.,
corresponding to increasing values for “n”
in the Bohr model) are typically split into a
few (or several) individual energy levels
that are much more closely spaced than
the separation between the shells.
•We will start to explore the smaller
splittings later in the course.
It's electrons are easier to excite than the other two
P301 Lecture 13
“JITT question”
• It's electrons are easier to excite than the other two
•because its the only one with the spikes
•Tungsten Z=74 Lambda = 2.281261535*e-11m -› off chart Molybdenum
Z=42 Lambda = 7.231911195*e-11m -› Bingo! Chromium Z=24 Lambda =
2.298079909*e-10m -› off chart [right, except at 35kV, the Ka lines of W
don’t get excited; the L lines are out of the wavelength window.]
•Characteristic x-rays are the result of electron excitation. The electrons in
Cr are bound too tightly for excitation to occur under the given conditions,
and the electrons in W have less energy than those in Mo, so the peaks are
absent. [reasoning is correct, but the roles of Cr and W are reversed.]
It's electrons are easier to excite than the other two
P301 Lecture 13
“JITT question”
What is the key similarity, and what is the key difference between the
inelastic collisions discussed in the context of the Franck-Hertz experiment
and those you studied in Physics I?
Similarities:
•Momentum is conserved in both cases, but kinetic energy is not [most did
not clearly answer this part of the question, those that did got it right]
Differences:
•It's not a loss of mechanical to thermal in the atomic case, and the loss is
QUANTISED in the atomic case. [11 concentrated on the quantized nature
of the loss, with several others remarking on the energy-dependence of the
loss, which almost amounts to the same thing].
Several of you were confused about the essential aspects of the problem:
•Objects only stick together in “perfectly inelastic” collisions in classical
physics and the inelastic nature has little to do with relative size of the
objects involved, therefore these are red herrings.
•ENERGY is conserved in inelastic collisions (as everywhere) it is kinetic
energy that is not conserved.
Franck-Hertz Experiment
http://hyperphysics.phy-astr.gsu.edu/HBASE/FrHzL.html
Fig. at right shows optical emission from Neon gas in
a F-H tube. In regions where the electrons have
enough energy to excite the neon atoms, the atoms
emit visible light when they relax back to their ground
state (from about 19eV to about 16.7 eV)
Franck-Hertz Experiment
Fig. at right shows the energy levels
for Hg (from the instructions for the FH experiment in our P309 lab).
In the grounds state of Mercury, there
are two electrons in the 6s level, and
the other levels shown are
unoccupied.
How many of you recognize this?
The Structure of DNA: Rosalind Franklin and X-ray Diffraction
http://www.pbs.org/wgbh/nova/photo51/pict-01.html
http://www.pbs.org/wgbh/nova/photo51/pict-04.html#fea_top
http://i6.photobucket.com/albums/y250/PhotozOnline/pwcrit1_03-03.jpg
Bragg’s Law
Bragg’s
Law
q
d sin(q)
You get constructive interference only
if:
2dsin(q) = nl
This gets the right answer, but it is
slightly unsatisfying (why do you
consider planes of atoms rather than
the atoms themselves, it doesn’t
explain why some plane sets diffract
and others don’t, and it doesn’t give
you relative intensities of the various
reflections, but it is easy to remember
and it is very useful as a quick answer
to give you much of the right
phenomenology.
Laue Diffraction
From “Techniques of X-ray
Diffraction by B. D. Cullity
http://www.anl.gov/Media_Center/News/2005/photo/050930_biocars-hirez.jpg
Test this out:
http://www.jhu.edu/signals/fourier2/index.html
http://demonstrations.wolfram.com/WavepacketForAFreeParticle/
Silicon powder diffraction
(Baxter lab)
Real X-ray apparatus
Laue setup with digital “film”
Single crystal setup w 2-D detector
http://www-xray.fzu.cz/xraygroup/www/laue.html
http://www.rigaku.com/xrd/rapid.html
“Powder” Diffraction
http://www.bruker-axs.de/index.php?id=x_ray_diffraction
http://pubs.usgs.gov/info/diffraction/xrd.pdf
Bragg’s
Law
q
d sin(q)
You get constructive interference only
if:
2dsin(q) = nl
This gets the right answer, but it is
slightly unsatisfying (why do you
consider planes of atoms rather than
the atoms themselves, it doesn’t
explain why some plane sets diffract
and others don’t, and it doesn’t give
you relative intensities of the various
reflections, but it is easy to remember
and it is very useful as a quick answer
to give you much of the right
phenomenology.
P301 Lecture 13
“Characteristic X-ray production”
NOTES:
•Barkla first discovered “characteristic xrays” in 1909, several years before Bohr,
the Braggs, and Moseley did their work.
•The “shell” model of the atom, which
arises from Bohr’s model for H, is very
useful even when considering multielectron atoms
• The various “shells” (K, L, M, N, etc.,
corresponding to increasing values for “n”
in the Bohr model) are typically split into a
few (or several) individual energy levels
that are much more closely spaced than
the separation between the shells.
•We will start to explore the smaller
splittings later in the course.
P301 Exam I Review
•Philosophy:
•The most important things in this course are developing an
understanding and appreciation for how we know what we know about
things that are very small or moving very fast.
•You should develop some understanding of what very small and very
fast mean, but you needn’t be overly concerned with memorizing
specific constants or formulae.
•You should be able to understand the key experimental results, their
significance in shaping our current view in the world, and how their
data are collected and interpreted.
•You should also understand and be able to use the various formulae
we have derived and or presented in this class to quantify the
sometimes strange phenomena involved (but recall you’ll have a
formula sheet, so memorizing them is not essential).
P301 Exam I Review
•NO CALM QUESTION FOR MONDAY!!!
•Exam Mechanics:
•Covers material from chapters 1 through section 5.1
•1 side of 8.5x11” formula sheet is allowed. It is not to be a
general note sheet
•5 questions (50 points, but 9 “parts” worth 5 or 10 points each)
•One question has multiple parts with answers from earlier
parts feeding later parts, if you have the right method on a
later part but use an incorrect answer from the earlier part,
you get full credit!!
•A mix of descriptive and computational answers.
•Tables from the inside front lay-out of the text will be provided.
•Exam will start at 11:10.
•Office Hours:
•Friday 1:30 to 3:30
•Monday 8:40 to 10:30.
•No office hours Monday afternoon.
P301 Exam I Review
•Important experiments:
•Relativity
•Michelson-Morley experiment
•Muon lifetime observations from cosmic rays.
•Doppler Effect (expanding Universe, binary stars, extra-solar planets,
SMOKEY, …).
•Synchrotron radiation (transformation of angles in relativity).
•Quantum Mechanics
•Cathode-ray tube experiments
•e/m of the electron
•X-rays: Bremsstrahlung, characteristic
•Photo-electric effect
•Franck-Hertz experiment
•Line spectra of gasses
•Compton effect
•Discovery of the positron (antiparticles in general)
•Rutherford scattering
•Bragg/Laue scattering
•Moseley’s law
P301 Exam I Review
•Important ideas:
•Relativity
•Speed of light is a universal constant irrespective of (initial) FoR.
•Lorentz transformation: time dilation/ Lorentz-Fitzgerald contraction.
•Relativistic mass, energy, momentum
•Transformation of angles
•Doppler Effect
•Space-time diagrams
•The invariance of interval
•Electricity and magnetism are intimately connected
•Quantum Mechanics
•Light is quantized (Blackbody radiation and hf=E, Compton and PE
effects)
•Electric charge is quantized and electrons are much lighter than atoms
•Anti-particles exist
•Atoms have internal structure and dynamics (electrons, atomic spectra,
X-rays, radioactivity, chemistry, Rutherford’s experiment).
•We can understand atoms in terms of quantize light and angular
momentum (Bohr)
•We can explain the periodic table (sort of) Moseley
P301 Exam I Review
•Example descriptive questions:
•Identify and provide BRIEF descriptions of 4 important experimental
results that came out of the study of electric currents in vacuum tubes
or such tubes back-filled with dilute gas.
•Provide a sketch showing the essential elements of the apparatus
used by Millikan to quantify individual elementary charges.
•Identify 3 of the crucial postulates Bohr used in constructing his model
of the atom.
•Identify 2 experimental results that shaped Bohr’s construction of the
atom.
•BRIEFLY describe two important results published by Einstein in
1905.
•Describe, BRIEFLY, the phenomenon known as the Ultra-Violet
Catastrophe and how Planck’s quantum hypothesis avoids this failure
of classical theory.
•(these last two are of the right style, but probably deal with
subjects we did not cover in enough detail to be worth more than 5
points on the exam, if they would be asked at all).
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