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 6Synchrotron Radiation facilities

The Advanced Photons Source at Argonne National Lab (Chicago) has 40 or more beam lines devoted to materials research, biochemistry, …

http://www.aps.anl.gov/Beamlines/Beamlines_Map/index.html

P301 Lecture 7“More Relativity Examples”

•Synchrotron Radiation: The APS ring circulates electrons at an energy of 7GeV. What is the speed of those electrons (express as a deviation from c).

•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 to reach this speed, how many nuclear reactors would be needed to provide the required power. If you had an antimatter drive, how much antimatter fuel would you need?).

P301 Lecture 6“Michelson Interferometer”

http://hyperphysics.phy-astr.gsu.edu/HBASE/PHYOPT/michel.html

•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•Also the device at the heart of an FTIR spectrometer

P301 Lecture 6“LIGO”

http://www.jb.man.ac.uk/research/pulsar/images/Ligo_hanford.jpg

•This is one of two large Michelson interferometers built in the US (one in Richland Washington state, the other in Livingston Louisiana).

P301 Lecture 7“Cathode Rays”

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)).

•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.

P301 Lecture 7“Cathode Rays”

In this case, both the figure and the above paragraph giving the main result are from a copy of Thomson’s original paper in Phil. Mag. 44 P293 (1897)).

•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.

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).

•9 answered ~ 8e-4 (this is the correct answer to this question)•9answered ~ 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. RTFQ!!)•5 made blunders of various types (typically units!)•~12 didn’t answer

•NOTE: The original number for the m/q ratio in Thompson’s paper was about “1.2e-7”. Although he did not explicitly give units, it is clear from later writings that he was employing “electronmagnetic units” (emu) of electric charge. In these units the current value of the ratio is 5.7x10-8 (emu/g), which is a slightly bigger difference than the book suggests

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 Crookes 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=falseFor an early paper by Thomson describing how he knew that the particles were smaller than atoms.

Discovery of X-rays

http://www.medcyclopaedia.com/library/radiology/chapter01.aspx

First “medical” x-ray (of the hand of Roentgen’s wife) Dec. 1895

"If one passes the discharges of a fairly large Ruhmkorff induction coil through a Hittorf vacuum tube, a sufficiently evacuated Lenard or Crooke’s tube, or a similar apparatus, and if one covers the tube with a rather closely fitting envelope of thin black cardboard, one observes in the completely darkened room that a piece of paper painted with barium platinocyanide lying near the apparatus glows brightly or becomes fluorescent with each discharge, regardless of whether the coated surface or the other side faces the discharge apparatus. The fluorescence is still visible at a distance of 2 m from the apparatus ..."(Roentgen's original communication, translated by Otto Glasser.)Note: others had seen mysteriously fogged photo plates near their apparatus several years earlier, but not understood the significance.

P301 Lecture 8“Characteristic spectra of

elements”

http://en.wikipedia.org/wiki/Gas-filled_tube

•Gas discharges in tubes filled with various gases:

•He, Ne, Ar, Kr, Xe [top row]

•H2, D2, N2, O2, Hg [bottom row]

•If you use a spectrometer (typically using a diffraction grating) you can identify specific lines of emission (and absorption) for the various gases (each has its own distinct “fingerprint”)

P301 Lecture 8“Characteristic spectra of

elements”

http://www.physics.uc.edu/~sitko/CollegePhysicsIII/28-AtomicPhysics/AtomicPhysics_files/image006.jpg

•Different elements emit light at certain well-defined wavelengths/frequencies.•Gases also absorb light at those same frequencies, as shown in the fourth figure above (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/= RH( 1/n2 - 1/k2 ) (n<k)

•For H, in the visible: 1/= 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)

P301 Lecture 8“Millikan oil drop expt.”

http://en.wikipedia.org/wiki/Oil-drop_experiment

•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

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)

P301 Lecture 8“Millikan oil drop expt.”

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”

•Apparatus figure, and final compilation of data in an early Millikan paper

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.

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).

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

P301 Lecture 8“Black body radiation.”

•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?

http://en.wikipedia.org/wiki/Black_body

P301 Lecture 9“Black body radiation.”

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?

http://us.fluke.com/usen/products/CategoryTI?PK=InfraredImaging&gclid=CLnssMje6ZwCFSBN5QodGyW3rQ Andhttp://support.fluke.com/find-sales/Download/Asset/3359026_6251_ENG_A_W.PDF

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–f/T

•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.http://en.wikipedia.org/wiki/Wien_approximation

P301 Lecture 9“Planck’s Forumula”

•Max Planck looked into the problem of Blackbody radiation in the late 19th century and discovered a result that interpolated between the low-frequency Rayleigh-Jeans result and the high-frequency Wein law, and did a great job of describing the data over the whole range of frequencies:

I(f,T) = 2hfc2(ehf/kT – 1 )]

f- frequency of the light; k- Boltzmann’s constant; c- speed of light; h a new constant relating energy and frequency. A little while later he developed a theoretical justification for this formula based on two assumptions:

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”:

E = 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) = 2hfc2(ehf/kT – 1 )]

P301 Lecture 8“CMB fit to BB spectrum”

http://www.astro.ucla.edu/~wright/CMB.html

•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 ()•60 ppm of extra hot electrons adding extra 60ppm of energy just about 1000 yrs after the big bang ( before, y after this time)

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod2/pelec.gif

P301 Lecture 9“Photoelectric Effect”

Apparatus from R. A. Millikan Phys. Rev. 7 355 (1916)

Light

Used to measure contact potentials

PE effect was discovered in stages ranging from 1839 (Becquerel photo-currents in solutions thru 1902 (Lenard, dependence on frequency)

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