Transcript P301_2009_week3

P301 Lecture 6
“Headlight effect”
This effect is important in medium-energy physics experiments (lots of the
“action” is in the forward direction), and for “synchrotron radiation” sources
(very bright sources of x-rays obtained from highly relativistic electrons or
positrons). See also the spreadsheet “P301_angle_transf.xls” on the web
site.
P301 Lecture 7
“JITT question”
•If you combine Thomson’s original value for the e/m ratio of the
electron with Millikan’s value for the elementary charge, what
would you get for the ratio of the electron mass to the mass of a
hydrogen atom? (you may take the presently accepted value for
the mass of hydrogen atoms).
•8 answered ~ 8e-4 (this is the correct answer to this question)
•7 answered ~ 5.4e-4 (this is the currently accepted value for the ratio, but note that
the text points out Thomson’s original answer was off by about 35%, so it’s not the
correct answer to the question.)
•5 made blunders of various types
•19 didn’t answer
P301 Lecture 6
“Examples from the Text”
•2-44 Given two events (x1,t1) (x2,t2), use a space-time diagram to find the
speed of a frame of reference in which the two events occur simultaneously.
What range of values would be possible for Ds2 in this case?
•2-51 A spacecraft travelling out of the solar system at 0.92c sends back
information at a rate of 400 Hz. At what rate do we receive the information?
•2-78 Calculate the energy needed to accelerate a 10,000kg spacecraft to 0.3c
for intergalactic exploration. Note: the current annual GLOBAL energy
consumption is roughly 1021 J (DVB: suppose you took a year, how many
nuclear power plants would be needed to provide the required power).
P301 Lecture 6
“Michelson Interferometer”
•This is a classic piece of
apparatus (in a more
sophisticated form it is now
being used to search for gravity
waves, see LIGO).
•The version used by M&M
used many more bounces to
increase its sensitivity (see text)
•Basic idea is that a change in
length (or transit time) of either
arm will shift the position of the
observed interference fringes.
•LIGO looks for change in
length on the order of 10-18 m
out of arms that are 4x103 m
long
http://hyperphysics.phy-astr.gsu.edu/HBASE/PHYOPT/michel.html
P301 Lecture 7
“Cathode Rays”
http://en.wikipedia.org/wiki/Cathode_ray
•As early as 1838 Michael
Faraday started exploring the
effects of applying voltages
between metal surfaces inside
evacuated containers (some
crude work even preceded
this).
•1870 Crook’s started looking at
effects with reasonable vacuum
(10-6 atm)
•1897 Thomson measured the
e/m ratio of the particles and
showed they were sub-atomic
in size (mass).
See also: http://books.google.com/books?id=3CMDAAAAMBAJ&pg=PA323#v=onepage&q=&f=false
For an early paper by Thomson describing how he knew that the particles were smaller than atoms.
P301 Lecture 7
“Cathode Rays”
•1897 Thomson measured the
e/m ratio of the particles and
showed they were sub-atomic
in size (mass).
•The diagram on the left shows
the basic manner in which the
beam of “cathode rays” was
created in Thomson’s work.
•The key to the experiment was
to combine crossed electric and
magnetic fields; balancing the
two forces allowed e/m to be
determined.
http://library.thinkquest.org/19662/low/eng/exp-thomson.html
(upper figure; the lower figure I took from a copy of Thomson’s
original paper in Phil. Mag. 44 P293 (1897)).
P301 Lecture 8
“Characteristic spectra of elements”
•For H, in the visible:
1/l = RH( 1/4 - 1/k2 )
Where RH = 1.097x107 m-1
• Balmer series, seen in
1885, similar series for
other values of n2 were
seen in 1908 (n=3), 1916
(n=1), 1922 (n=4) and
1924 (n=5)
•Different elements emit light at certain well-defined wavelengths/frequencies.
•Gases also absorb light at those same frequencies (this was used to discover
Helium, from looking at the sun’s spectrum).
•For hydrogen, there was a particularly simple formula for the wavelengths:
1/l = RH( 1/n2 - 1/k2 )
http://www.physics.uc.edu/~sitko/CollegePhysicsIII/28-AtomicPhysics/AtomicPhysics_files/image006.jpg
P301 Lecture 8
“Millikan oil drop expt.”
Millikan’s number was (in his 1911
paper):
e=4.891(2)x10-10 st.coul .(1.63x10-19
C)
A later (1913) paper then revised this
to 4.774(9)x10-10 st. Coul. (1.54 x10-19
C)
•Make small drops of oil in an atomizer (through this process they also
pick up an electric charge)
•Let the drops fall under gravity (in air) with an opposing electric field of
variable size.
•Compare rates of “fall” (or rise) with and without field.
•Vary charge by bringing a radioactive source nearby
•Look at the statistics and determine the “quantum” of charge
http://en.wikipedia.org/wiki/Oil-drop_experiment
P301 Lecture 8
“Millikan oil drop expt.”
•Apparatus figure, and final compilation of
data in an early Millikan paper
R. A. Millikan Phys. Rev. 32 p349 (1911) “The isolation of an ion, a precision
measurement of its charge, and the correction of Stokes law”
P301 Lecture 8
“JITT question”
•You first start to see a piece of metal glowing when its temperature reaches
about 550oC. At this temperature, at what wavelength is the peak in the
spectrum emitted by the metal (assumed to be a black body)? Can you see
this wavelength?
•23 answered 3.5 um, and no you cannot see it (wavelength too long)
•3 answered with other numbers
•15 didn’t answer.
P301 Lecture 8
“Black body radiation.”
http://en.wikipedia.org/wiki/Black_body
•All objects made of charged particles emit em-radiation if they are at a
temperature above absolute zero.
•If the body absorbs light at all frequencies equally (it is “black”) then we can
describe the process using statistical techniques (see P340); classsical statistical
physics predicts the divergent spectrum shown above, the other spectra show
what is found experimentally.
•What do you notice about the experimental curves?
Cavity Radiation
An common realization of a black body, consider a box with a small hole in
it that is in thermal equilibrium with the electromagnetic fields (sometimes
thought of as a gas of photons).
P301 Lecture 9
“Black body radiation.”
http://us.fluke.com/usen/products/CategoryTI?PK=InfraredImaging&g
clid=CLnssMje6ZwCFSBN5QodGyW3rQ
And
http://support.fluke.com/findsales/Download/Asset/3359026_6251_ENG_A_W.PDF
We know that infrared cameras can be used to see things “in the dark”, they can
also be used to find hot objects (such as overheating components in electrical
panels.
How do these devices work?
P301 Lecture 9
“Wien’s distribution”
•Many books point out that both the
long and short wavelength ends of
the spectrum had been described
(at least empirically) before Planck’s
work, the short wavelength end of
the spectrum was described by a
result due to Wien that these same
books often don’t bother to discuss:
I(f,T) ~ f3 e–af/T
http://en.wikipedia.org/wiki/Wien_approximation
•Note that in this formula T appears
(almost) to set the frequency scale,
and this observation is the origin of
the Displacement law that bears
Wien’s name.
P301 Lecture 9
“Planck’s Hypotheses”
•The energy in the oscillators producing the radiation in a black body (or cavity) is
constrained to take on only values that are an integral multiple of hf:
Ef = nhf
(where n is an integer and f is the frequency)
•The oscillators only exchange energy with the EM waves in the cavity in units given by the
above “quantum”:
DE = hf
•Planck had expected to be able to take the limit where h-> 0 at the end of his calculation,
but a finite value for h agreed with experiment and an infinitesimal one didn’t. He wasn’t
happy about this turn of events, but he accepted it as a route to get to the right answer for
the time being.
I(f,T) = 2hf3/c2(ehf/kT – 1 )
P301 Lecture 8
“CMB fit to BB spectrum”
•The plot on the right shows data from the
FIRAS instrument on the original COBE
satellite experiment. The measurement of
interest here was the set of residuals (i.e.
the lower plot of the differences between the
measured spectrum and that of a true black
body)
•The curves correspond to various non-ideal
BB spectra:
•100 ppm reflector (e)
•60 ppm of extra hot electrons adding
extra 60ppm of energy just about 1000
yrs after the big bang (m before, y after
this time)
http://www.astro.ucla.edu/~wright/CMB.html
P301 Lecture 9
“Photoelectric Effect”
http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod2/pelec.gif
Used to measure
contact
potentials
Light
PE effect was discovered in stages
ranging from 1839 (Becquerel
photo-currents in solutions thru
1902 (Lenard, dependence on
frequency)
Apparatus from R. A. Millikan Phys. Rev. 7 355 (1916)
P301 Lecture 9
“Photoelectric Effect”
Basic phenomenology of the Photoelectric effect (ca. 1902):
1. The kinetic energy of the photoelectrons is independent of the
INTENSITY of the incident light.
2. The maximum kinetic energy of the photoelectrons, for a given
material, depends only on the light’s frequency.
3. There is a threshold frequency below which no photoelectrons are
produced, irrespective of the intensity. The smaller the work function
of the material, the smaller the threshold frequency for photoelectron
production.
4. The number of photoelectrons produced is proportional to the light
intensity (assuming freq. is above the threshold value).
1905: Einstein explained all of these results by assuming that Planck’s
hypothesis corresponded to reality, it was not just a convenient
accounting trick. This is what won Einstein the Nobel Prize.
Electrons are liberated by absorption of single quanta of light
E=hf.
P301 Lecture 9
“Photoelectric Effect”
Data from R. A. Millikan Phys. Rev. 7 355 (1916)
P301 Lecture 9
“Photoelectric Effect”
Data from R. A. Millikan Phys. Rev. 7 355 (1916)
Note Millikan’s value is 6.56e-27 erg-sec; presently accepted value is 6.626e-27 erg sec
P301 Lecture 9
“X-Rays”
•Experimental results on the absorption of xrays from C. G. Barkla Phil. Mag. 17 (1909)
P301 Lecture 9
“X-Rays”
http://www.google.com/imgres?imgurl=http://www.amptek.com
•Ka and Kb lines from various elements
(Mosely)
http://en.wikipedia.org/wiki/Moseley%27s_law