P301 Lecture 11
“Scattering experiments”
•The rate at which you
detect particles has to be
proportional to the incident
flux (particles/cm2.sec),
and it is a rate (particles
counted in a certain
direction per unit time).
•Conventionally, therefore,
the scattering probability is
expressed as a “cross
Section” (i.e. has
dimensions of an area).
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/imgnuc/ruthgeo.gif
s(q) = {Z21Z22e4/[256p2e2oK2sin4(q/2)]} (4.13) in T&R,
[rewritten as a cross-section per nucleus, the count rate in the detector is this
cross section times the incident flux (Ni), times the number of nuclei per unit area
(nt), integrated over the angular acceptance of the detector]
P301 Lecture 13
“Fine Structure constant”
a= {e2/[2eohc} (or e2/4peo’hbar’c)
•lc/2pao = a (Ratio of Compton wavelength to Bohr radius,
almost)
•2|Eo|/mec2 = a2 (the Hartree is the natural energy unit for
Chemistry, and it is a2 * the rest energy)
•re = e2/(mc24peo)= a2ao (the classical radius of the electron,
This shows up in cross sections for light
scattering off of electrons.)
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
“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?
•Like any inelastic collision, energy is not conserved; however, a certain
quantized level of energy must be obtained by the electron before an
inelastic collision can occur. [several expressed something like this; energy
is in fact conserved, it is only KE that is not conserved.]
•Similarity: momentum is conserved in both while KE isn't ; Difference: the
type energy loss is different [many got this similarity, though few
encapsulated the whole answer as succinctly. What is the difference in the
energy loss?]
I
Franck-Hertz Experiment
Accelerate electrons
through a gas-filled
tube and measure the
current getting to the
anode. What happens
if electrons scatter off
the atoms?
http://www.phy.davidson.edu/ModernPhysicsLabs/f-hertz.html
Franck-Hertz Experiment
If the scattering is
elastic, then nothing
dramatic happens,
you measure average
transfer of charge
from cathode to
anode (per unit time),
and this is essentially
independent of the
electron’s path).
http://www.phy.davidson.edu/ModernPhysicsLabs/f-hertz.html
Franck-Hertz Experiment
What if the collision is
inelastic?
http://www.phy.davidson.edu/ModernPhysicsLabs/f-hertz.html
Franck-Hertz Experiment
If the electron loses
so much energy that it
does not arrive at the
grid with enough
energy to climb the
potential to the
anode, it cannot
contribute to the
anode current, and Ic
drops.
http://www.phy.davidson.edu/ModernPhysicsLabs/f-hertz.html
Franck-Hertz Experiment
http://hyperphysics.phy-astr.gsu.edu/HBASE/FrHzL.html
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.
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.
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
Section 5.1: 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.
“Powder” Diffraction
http://www.bruker-axs.de/index.php?id=x_ray_diffraction
http://pubs.usgs.gov/info/diffraction/xrd.pdf
Silicon powder diffraction
(Baxter lab)
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
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
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 (I give constants, you have your own
formula sheet).
•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 be able to
summarize/describe these in no more than 4 or 5 sentences, and/or
have a short unambiguous name for each.
•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 FRIDAY!!!
•HW4 solutions posted tonight, any answers submitted after
solutions are posted will not be graded.
•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 and I would like it handed in with your answers
•5 questions (50 points, but 8 “parts” worth 5 or 10 points each)
•If a 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 and will last to 12:10.
•Please answer in PEN (Blue or black).
•Office Hours:
•Wed. 2:00 to 3:30
•Thursday 1:30 to 3:00
•Friday 9:45 to 10:45; No office hours Friday 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
•Millikan Oil drop experiment
•Black-body spectrum
•Discovery of the positron (antiparticles in general)
•Rutherford scattering
•Bragg/Laue scattering
•Moseley’s law
•Radioactivity
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 3 important experimental
results that came out of the study of electric currents in vacuum tubes
or such tubes back-filled with dilute gas.
•Provide an annotated 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 and briefly describe three observations or phenomena extant
prior to Bohr’s development of his atomic model which suggested that
atoms had internal structure and dynamics. (Q1 on 2009 test).
•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).
P301 Exam I Review
•Example answers:
•Identify and provide BRIEF descriptions of 3 important experimental
results that came out of the study of electric currents in vacuum tubes
or such tubes back-filled with dilute gas.
•Line spectra from gas discharge tubes: Each element emitted
characteristic pattern of light (sharp lines at specific frequencies)
when excited by cathode rays.
•e/m ratio: Crossed magnetic and electric fields acting on cathode
rays allowed Thomson to show that the e/m ratio for these rays
was much larger than that for atoms.
•X-rays: Roentgen discovered new penetrating radiation was
released for high enough accelerating voltages
•Photo-electric effect: light promotes the evolution of electrons
from a metal surface, but frequency plays a crucial role in
contradiction to predictions of classical physics.
•Franck-Hertz expt: passing electrons through a tube with some
gas can be used to see quantize excitation of the gas atoms
(provided you have an accelerating grid combined with a small
retarding voltage between the grid and collecting anode).
If F is always perpendicular to v, then F=mga (see problem 2-55). Use this
to prove that a relativistic particle moving perpendicular to a magnetic field
orbits with a radius R=p/qB (p momentum, q charge of the particle). What B
field is needed to hold protons with a kinetic energy of 230 MeV in a 15m
circle? (how about 1.5 m, comparable to a medical cyclotron)?
2-56,61
5-DVB
The “<111>” family of planes in Si has a d-spacing of 0.313556 nm, through
what angle would you expect a Cu Ka1 x-ray (l=0.1540598 nm) to be
scattered by this family of planes?
EM radiation with l=100 nm is incident upon a hydrogen atom that is
at rest and in its ground state. What is the highest state to which this atom
(treated within the Bohr model) can be excited?
4- 30
3-
DVB Question: why do they say max. kinetic energy here?