Dr. Bill Pezzaglia

Part I

Updated: 2010Apr19

Quantized Radiation(Particle Theory of Light)

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Quantum Mechanics

A. Classical vs Quantum Theory

B. Black Body Radiation

C. Photoelectric Effect

D. Atomic Physics

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A. Classical vs Quantum Theory

1. Discussion in class. Essentially classical theory assumes:

• Causality (causes must precede effects, i.e. can’t go backwards in time)

• Determinism: classical theory assumes can measure quantities to infinite precision

• Objectivity: classical theory assumes measurement does not affect the system

• Two Models: particles (things) which can be localized vs waves (fields) which are non-local. Fields mediate the forces between particles

Quantum theory upsets these ideas

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2. Is light a Wave or Particle 4

• Newton’s corpuscular theory: light is a particle• 1678 Huygens: light is a wave• Foucault measures speed of light is slower in

water (favors wave theory)• 1801 Young’s diffraction experiment proves it’s a

wave, and gives a way to measure its size• Waves are

very small,around500 nm

3a. Electromagnetic Theory• 1831 Michael Faraday proposes Electric and Magnetic

Fields

• 1860 Maxwell shows changing electric field creates magnetic field, changing magnetic field creates electric. Derives wave solutions, with speed exactly “c” the speed of light.

• Proposes these waves are “light”

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3b. The Electromagnetic Spectrum• 1888 Hertz produces “radio” waves• 1895 Rontgen produces X-rays• 1900 Paul Villard discovers gamma rays• They are all part of the “electromagnetic

spectrum”, of which visible light is a small piece.

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3c Wavespeed

c = speed of light

f = frequency (Hertz)

= wavelength

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fc

B. Black Body Radiation

1. Stephan Boltzmann Law

2. Wien’s Law

3. Black Body Radiation

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1a. Temperature• 1851 Lord Kelvin’s temperature scale

• Conversion: 0 K = -273 C

• Temperature isa measure ofaverage energy

• 0K is absolutezero

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1b. Josef Stefan’s Law 1879• Experimentally shows total output of light

of a hot dense (black) body is proportional to 4th power of the temperature (in Kelvin)

• Power (watts)=AT4

• =5.67x10-8 Watts/(m2-K4)• A=surface area

• 1884 Ludwig Boltzmann (formerstudent of Stefan) derives formulafrom thermodynamics.

• I was a guest speaker (Sept 2005) at theJosef Stefan Institute in Slovenia.

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1c. Inverse Square Law

• 1604 Kepler proposes intensity of light drops of with square of distance (?)

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•Charles Soret measures solar flux to be about 1400 Watts/m2 at surface of the earth.

•Stefan uses this to estimatetemperature of sun to be 5700 K.

2a. Wien’s Displacement Law

• 1893 shows that the “color” of black body is inversely proportional to temperature

• Wien’s constant=2,898,000 nm-K

• So T=6000K gives=483 nm

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T

2b. Black Body Curve

• Willhelm Wien getsNobel Prize 1911

• 1894 coins term“black body”

• The black body emitsall colors, but whereit peaks is describedby Wien’s law

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2c. Color Indexing• If we can measure the color of a star, we can

calculate its temperature• Measure magnitude of star through color filters• Color Index=C.I. = B-V is measure of

temperature of star.

• Standard Filters• U filter 370 nm• B filter 440 nm• V filter 550 nm

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3a. Black Body Theory• Maxwell: hot atoms vibrate, acting

like small antennas, radiating electromagnetic waves

• Wien tries to give theory to explain shape of curve, but it fails in IR

• Rayleigh (1900) & Jeans (1905) have another theory, but it fails in UV, blowing up to infinite energy (the “ultraviolet catastrophe”).

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3b. Max Planck’s Theory

• 1900 Max Planck ad-hoc proposes that vibrations are “quantized”, i.e. come in steps of n=1, 2, 3, rather than continuous.

• Energy: E=nhfn=integer quantum numberf=frequency of oscillationh is “Planck’s Constanth=6.626x10-34 Joule-Sec

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3c. Planck Radiation Law• His theory exactly matched the experimental

measurements of the black body radiation curve

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k = Boltzmann Constant (1.3810-23 Joule/Kelvin)

C. Photoelectric Effect

1. Phenomena Discovered

2. The Experiment

3. Einstein’s Photon Theory

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1. Discovery of Effect

• Hertz 1887 found discharge of a spark gap was greater when illuminated by light from another spark gap. Glass inserted between stopped effect(note glass absorbs uv light)

• 1888 Hallwachs discovers that negatively charge electroscope will discharge when UV light is shined on it, but not with visible light. No effect for positive charged electroscope.

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1b. Work Function

There is a certain amount of energy required to free an electron from the metal (between 2 and 3 volts)

• Cesium 1.9 volts• Calcium 2.7 volts• Magnesium 3.6 volts

Use energy of light to add energy and “bump off” electrons.

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(2a) 1899 Lenard’s Experimental 21

(2b) Lenard’s Experimental Results

•At a certain (negative) retarding voltage, the current stops.

•This tells us the electrons had (at least) energy eV0

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(2c) Findings

• More intense light, more current, but electrons do not have more energy (stopping voltage unchanged)

• Higher frequency light, electrons have higher energy (bigger stopping voltage)

• Below a certain threshold frequency of light, there is NO current, regardless of the intensity

• Even when intensity is so low that it should take an hour to give enough energy to overcome the work function of the metal, if photon is above the threshold, the effect is instantaneous.

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(3a) The Photon

•1905 Einstein proposes that its light that is quantized

•Proposes light is a particle,called the “photon”

•Uses idea to explain the“photoelectric effect”

•Energy of a single Photon:

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hc

hfE

3b. Einstein

•1905 proposed Photon concept, with quantized energy E=hf

•Emission is caused by ONE photon bumping off ONE electron. Photon frequency must be such that energy is above work function

•Millikan makes precise measurement of stopping voltage vs frequency and gets straight line (different for each metal), with slope (h/e) and intercept gives work function.

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D. Atomic Physics

1. Discrete Spectra

2. Kirchhoff’s Laws

3. Model of Atom

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1a. Dark Line Spectra• 1802 Wollastan sees lines in solar spectra

• 1814 Fraunhofer Labelsthem A, B, C, D

• Later measures over 500 lines!

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1b. Solar spectrum47

1c. Bright Line Spectra• 1857 Bunsen’s burner, a clean

flame with no color• 1859 Kirchhoff suggest using it

to study spectra of elements in flame

• Each element has a unique set of “bright line” (emission) spectra

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2a. Kirchhoff’s Laws30

2b. Gustav R Kirchhoff (1860)31

His three laws:

1. A hot dense body will emit a continuous spectrum

2. A hot transparent gas will emit emission line spectrum

3. A cool transparent gas in front of a source of continuous spectrum will produce absorption spectra.

2c. Spectral Analysis32

•1861 Kirchhoff identifies elements in the sun from Fraunhofer lines

•1868 Janssen finds a line that can’t be identified during solar eclipse

•1870 Lockyer & Frankland verify its an unknown element they name “Helium”. Helium is not discovered on the earth until 1895 !

The absorption lines match emission lines. Hence you can use them to identify elements in stars.

3a. Rydberg Formula 33

• 1885 Balmer comes up with formula that explains the Hydrogen lines (“Balmer Series”)

• 1888 Rydberg improves formula, where n1=2, n2={3,4,5}

•1895 Paschan Series discovered in IR, described by n1=3•1908 Lyman Series discovered in UV, described by n1=1

3b. Atomic Theory34

• 1808 Dalton’s theory of atoms

• 1897 Thomson discovers electron

• 1911 Rutherford’s experiment implies dense core to atom (nucleus)

3c. Atomic Theory35

• 1911 Rutherford’s suggest planetary model of atom, electrons orbit nucleus

• But, it would be unstable!

• Electrons wouldimmediatelyradiate and crashinto nucleus.

3d. Niels Bohr (Nobel Prize 1922)36

• 1913 Bohr proposes“quantized orbits” to atom.

3e. Emission and Absorption37

3f. Emission & Absorption38

3g. Spectral Series39

References40

• McEvoy & Zarate, “Introducing Quantum Theory” (Totem Books, 1996)