physics 3313 - lecture 6brandta/teaching/sp2010/lectures/phys3313-lec6.pdfrayleigh-jeans formula •...

Physics 3313 - Lecture 6

2/8/10 13313 Andrew Brandt

Monday February 8, 2010Dr. Andrew Brandt

1. HW1 Due today HW2 weds 2/10

2. Electron+X-rays

3. Black body radiation

4. Compton Effect

5. Pair Production

• 3.1 Discovery of the X Ray and the Electron• 3.2 Determination of Electron Charge• 3.3 Line Spectra (defer to next chapter)• 3.4 Quantization• 3.5 Blackbody Radiation• 3.6 Photoelectric Effect (last lecture)• 3.7 X-Ray Production• 3.8 Compton Effect• 3.9 Pair Production and Annihilation

CHAPTER 3The Experimental Basis of Quantum Theory


1895 J.J. Thomson’s Discover’s Electron • Thomson used an evacuated cathode-ray tube (vacuum tube with a high

voltage) to show that the cathode rays were negatively charged particles (electrons) by deflecting them in electric and magnetic fields.

Used force equations to determine q/m for electron, charge later determined by Millikan Oil drop experiment


• Thomson’s method of measuring the ratio of the electron’s charge to mass was to send electrons through a region containing a magnetic field perpendicular to an electric field.

Thomson’s Experiment


An electron moving through the electric field is accelerated by a force:

Electron angle of deflection:

The magnetic field deflects the electron against the electric field force.

The magnetic field is adjusted until the net force is zero.

Charge to mass ratio:

Calculation of e/m


Calculation of the oil drop charge• Used an electric field and

gravity to suspend a charged oil drop.

• Mass is determined from Stokes’s relationship of the terminal velocity to the radius and density.

• Magnitude of the charge on the oil drop.

• Thousands of experiments showed that there is a basic quantized electron charge. C


3.5: Blackbody Radiation• When matter is heated, it emits radiation (visible light, CW

blacksmith, Return of King). • All objects radiate energy continuously with a frequency that

depends on temperature.• Ability to radiate related to ability to absorb—thermal

equilibrium• Black body is ideal object that absorbs all radiation

independent of frequency (radiation enters small whole bounces around until absorbed)


Rayleigh-Jeans Formula• Lord Rayleigh used the classical theories of electromagnetism

and thermodynamics to show that the blackbody spectral distribution should be

• Missed it by that much! The disagreement for small wavelengths (data goes to zero while theory increases with 4th

power!) became known as “the ultraviolet catastrophe” and was one of the outstanding exceptions that classical physics could not explain.2/8/10 83313 Andrew Brandt

• Planck assumed that the radiation in the cavity was emitted (and absorbed) by some sort of “oscillators” that were contained in the walls. He used Boltzman’s statistical methods to arrive at the following formula that fit the blackbody radiation data (note exponential damping at small wavelengths!)

• Planck made two modifications to the classical theory:1) The oscillators (of electromagnetic origin) can only have certain

discrete energies determined by En = nhf, where n is an integer, f is the frequency, and h is called Planck’s constant. h = 6.6261 × 10−34 J·s.

2) The oscillators can absorb or emit energy in discrete multiples of the fundamental quantum of energy given by

Planck’s Radiation Law

Planck’s radiation law


Wien’s Displacement Law• The intensity (λ, T) is the total power radiated per unit area

per unit wavelength at a given temperature.• Wien’s displacement law: The maximum of the distribution

(from taking derivative with respect to wavelength) shifts to smaller wavelengths as the temperature is increased.

• Ex: 2.7K cosmic background radiation from Big Bang 1.1 mm microwaves in 1964 sky survey(1978 Nobel prize for Penzias+Wilson)


Stefan-Boltzmann Law• Can also use Planck’s formula to derive an expression for the

total power radiated increases with the temperature:

• This is known as the Stefan-Boltzmann law, with the constant σ experimentally measured to be 5.6705 × 10−8 W / (m2 · K4).

• The emissivity є (є = 1 for an idealized blackbody) is simply the ratio of the emissive power of an object to that of an ideal blackbody and is always less than 1.


What is Light?• Both wave and particle theory needed.• Quantum theory: light has individual photons… but frequency is a wave

phenomenon• Two different interpretations of intensity• Wave theory average magnitude of EM wave over a complete

cycle• Photon description I=Nhυ• Both descriptions must give the same intensity if they are valid so• Consider double slit experiment: for large N observer looking at screen

would see a double slit interference pattern (continuous distribution)• However, for small N, see a flash of light as one photon at a time goes

through either slit (quantum phenomena), but if you wait a long time you would see an interference pattern

• How can photon interfere with itself ? (sounds vaguely immoral)

2/8/10 3313 Andrew Brandt 12

2

0I cEε=

2N E∝

What is Light (2)?• Must conclude that is the probability of finding a photon at a certain

place and time—each photon has a wave associated with it; the intensity of wave a given place on the screen determines the likelihood that a photon will arrive there

• Light travels as a wave, but deposits and absorbs energy like a particle (or a series of particles)

• Wave-particle duality: need both pictures (outside of our everyday life experience!)

• It not a wave nor a particle…it’s a WARTICLE


2E

X-Rays• 1895 Roentgen found that when fast moving electrons strike matter a

highly penetrating unknown radiation (X-Ray) is produced. He found certain characteristics of X-Rays: they1) travel in straight lines2) are unaffected by E+B fields (what does this imply?)3) can pass through opaque materials4) can expose photographic plates

• He also observed that faster electrons yield more penetrating X-Raysand that increasing the number of incident electrons yields higher intensity X-Rays


More X-Rays• Soon it became obvious that X-Rays are EM waves• Accelerating charges produce EM waves (basis for radio

transmitters)• How does an electron produce X-Rays?• What happens as an electron interacts with matter?• It decelerates: bremsstrahlung (“braking radiation”)• Higher atomic number nuclei cause more energetic brem.

(energy loss is more important for light particles like electron—NLC)


Measuring X-Ray Wavelength• Scattering of X-Rays off Crystal (draw)• Use crystals as a diffraction grating−need crystals since d must be on order of a

wavelength (λ) for diffraction effects to be observed and λ is very small (0.01 to 10 nm) for X-Rays.

• Small wavelength implies large υ, so if X-Ray has several orders of magnitude smaller wavelength than light, it has several orders of magnitude higher energy

2/8/10 3313 Andrew Brandt 16http://www.wwnorton.com/college/chemistry/gilbert/tutorials/ch10.htm

Inverse P.E. Effect• X-Ray production is an inverse photoelectric effect: electron in/photon out,

instead of vice-versa• Small wavelength implies large υ, so if X-Ray has several orders of

magnitude smaller wavelength than light, it has several orders of magnitude higher energy

• For photoelectric effect:• For X-Rays can neglect binding energy, since X-Ray is so energetic:

where V is the accelerating potential of X-Ray machine and the frequency is maximum when the electron gives all of its energy to a single photon

• Duane-Hunt formula for X-Ray production:


maxeV hv=

6

min1.24 10hc V m

eV Vλ

−×= =

hν φ= −max 0KE eV=

http://www.spineuniverse.com/videos/x-rays/http://www.spineuniverse.com/videos/x-rays/

Compton Effect• Can photon be treated like a particle when it interacts with an electron?

• Consider conservation of momentum and energy, and also have an additional constraint that the loss in photon energy yields an equivalent gain in electron KE:


hv hv KE′− =

Compton Effect• some math occurs on blackboard yielding:

• where is called the ComptonWavelength, and has a value of 2.4 pm for electrons

• this is largest when?

• Compton scattering is the main way that X-Rays lose energy when passing through matter; visible light has long wavelength so small wavelength shift is less noticeable

• Experimentally Compton effect initially not verified! • The problem was that electrons in matter are not free—some are tightly

bound and if whole atom recoils the large mass implies a small wavelength shift (when this is corrected for, the Compton picture is validated)


(1 cos )hmc

λ λ φ′ − = − ch

mcλ =

φ π=

Other X-ray stuff• http://www.nature.com/news/2009/090728/full/news.2009.744.html• http://www.livescience.com/strangenews/reason_demkina_050128.html• http://www.dailymotion.com/video/x1z82o_xray-vision_creation


http://www.nature.com/news/2009/090728/full/news.2009.744.html�

Pair Production• In pair production a photon of sufficient energy can create an

electron/positron pair.• How much energy? •

• Charge conserved, for energy and momentum conservation need the nucleus (Ex. 2.5)

• Opposite of pair production is annihilation


22 .511 2em c MeV≥ = ×

e e γγ+ − →


Energy Loss in Matter


Photons and Gravity

hpcν

=

hmvcν

=

2

hvmc

=

E pc hν= =

for v=c

effective mass of photon, implies light affected by gravity

Black hole—so much gravitational force that photons cannot escape

physics 3313 - lecture 6brandta/teaching/sp2010/lectures/phys3313-lec6.pdfrayleigh-jeans formula •...

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