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Quantization • Matter is not continuous – it is quantized. – Idea dates back to Democritus (Greece, 450 BC). – First scientific arguments appear in 18th – 19th century • Eg, Avogadro’s claim that 22.4 liter volume of a gas contains the same number of molecules at standard conditions. • Towards the end of 19th century, first hints that electric charge is also quantized. – Later, found that light is also quantized. • These discoveries led to the development of quantum mechanics. – Very different understanding of the natural laws. Quantization of Charge • Early hints: – Faraday (mid 1800’s) found that he always needed the same amount of charge to decompose equal amount of material in electrolysis: Q = NA e – Later estimates of NA led to the first measurements of e. – Zeeman (1896): splitting of spectral lines emitted by atoms in strong magnetic field. • Thomson (1897): discovered electron using cathode ray tubes. Fm = qvB Thomson’s Experiment Fe = qE v = E/B • Two parts: • First pass the cathode rays through a crossed field. – Magnetic and electric force cancel, giving the speed of the rays. • Then put the ray in another magnetic field. +q qvB = mv 2 / R q v = m BR Direct measurement of the chargeto-mass ratio. Thomson’s Experiment • Repeated with different gases in the tube, different metals for the cathode etc. • Always the same answer: e 11 = 0.7 × 10 C/kg m • Conclude that cathode rays consist of particles, common to all metals. • But still don’t know the charge. Millikan’s Oil Drop Experiment • Spray oil into a space between two metal plates. – Interaction with the nozzle charges the oil drops. • Change electric field until a drop floats in the air. qE = mg • Estimate m from the size of the drop. • Found that each drop’s charge was a multiple of an elementary unit e, which he measured: – e = 1.601 x 10-19 C Blackbody Radiation • When light falls on a body, it is partly reflected and partly absorbed. – Light colored objects reflect more. • Absorbed light increases the internal energy of the body. – Atoms move faster, electrons accelerate, and therefore produce electromagnetic radiation – light. – This process reduces the temperature (and internal energy) of the body. • When the absorption and emission rates are equal, the body is in equilibrium with the environment. • So: all bodies continually emit radiation, whose intensity is dependent of the body temperature. Stefan-Boltzmann Law • Stefan empirically found that the power per unit area emitted by a black body is: R = σT 4 σ = 5.67 x 10-8 W/m2/K4 (Stefan’s constant). • Boltzmann later proved it in statistical physics. Visible part of the spectrum is • Rate only depends on only populated if T>600 °C temperature – no other property of the body matters. Wien’s Displacement Law • The spectrum (frequency content) also only depends on λmaxT = 2.9 × 10−3 mK temperature. Example • A star’s spectrum is observed to peak at 1 µm. The star emits 100 times the power of the Sun. How large is the star? Blackbody Energy Density Spectrum • Best blackbody is a cavity with a small opening. Blackbody Spectrum • Rayleigh-Jeans: 8πkT u (λ ) = λ4 • Planck: u (λ ) = 8πhc 1 λ5 e hc / λkT − 1 e hc / λkT ≈ 1 + hc / λkT • Large λ: 8πhc λkT 8πkT = 4 u (λ ) ≈ 5 λ hc λ • Small λ: u (λ ) ≈ 8πhc λ 5 e − hc / λkT →0 Recover Rayleigh-Jeans at large wavelengths Blackbody Spectrum • Planck’s constant, measured to be h = 6.626 x 10-34 Js • Recover Wien’s Law • Recover Stefan-Boltzmann Law Example • What should be the temperature of the Earth? – Greenhouse effect and global warming. /m2 (1-a) Blackbody Spectrum: Sun Tsun = 5778 K Emits mostly in the visible and infrared parts of the spectrum. Atmosphere is transparent in the visible band. Blackbody Spectrum: Earth TE = 20 C Emits predominantly in the infrared part of the spectrum Atmosphere partly absorbs in this band. Greenhouse Effect • Simple model – Earth with albedo (reflection) in visible – Atmosphere with some absorption in infrared and transparent in visible. • Leads to an increase in the Earth’s temperature. • What causes the absorption in the atmosphere? – Gases: greenhouse effect. – Mostly water, but also CO2, CH4 and others. "Absorption spectrum of liquid water" by Kebes at English Wikipedia. Water Absorption Spectrum: 4.2 micron 15 micron "Absorption spectrum of liquid water" by Kebes at English Wikipedia. Pulling things together: - Significant part of the Earth’s emission spectrum is absorbed by the atmospheric gases, leading to the greenhouse effect. - Changing the composition of the atmosphere can modify the magnitude of the greenhouse effect: global warming Evidence for Global Warming http://www.ipcc.ch/report/ar5/ From the latest (fifth) assessment report of the Intergovernmental Panel on Climate Change (IPCC). - Founded by the World Meteorological Organization and the UN Environment Programme. Evidence for Global Warming http://www.ipcc.ch/report/ar5/ Drivers of Global Warming http://www.ipcc.ch/report/ar5/ Models require anthropogenic contributions to explain the observed data. Natural effects (volcanic eruptions, solar cycle effects) alone cannot explain the data. Strong evidence that CO2 emission dominates the changes in the greenhouse effect. Photoelectric Effect • Light kicks out electrons from a material. • First hint: Hertz experiments with spark gaps (1887). – Observed that if light is present, it is easier for sparks to jump a gap (i.e. they can jump a larger gap). • Lenard (1900) conducted a series of experiments with a cathode ray tube. Photoelectric Effect • Increasing voltage increases collection of cathode rays (electrons), until they are all collected. • Negative voltage repels electrons. No signal if 1 2 mv = eV0 2 Stopping Potential • Increasing light intensity increases the maximum signal, but it does not change V0. – Changing the light frequency does! Photoelectric Effect • Einstein solved the problem in 1905, using Planck’s quantization of energy. • Light consists of quanta (photon) each of energy hν. • A photon enters the cathode and gives its energy (and momentum) to an electron. – If it takes energy φ (work function) to remove the electron from the material, the electron will have energy hν-φ. 1 2 • The stopping potential is then: eV0 = mvmax = hν − φ 2 – It does not depend on the light intensity (rate of photons), but linearly depends on the light frequency. Photoelectric Effect • Millikan later measured the stopping potential as a function of frequency. – The slope yields h/e, in agreement with Planck’s value. – V0 = 0 gives the measurement of the work potential, for the material used. • Typically a few eV. h φ V0 = ν − e e Demos • 7A10.10 - Discharging Aluminum Plate • 7A10.12 - Photoelectric Charging • 7A10.30 - Stopping Potential Example • A light source at wavelength 555 nm radiates at 100 W. If the human eye can register 10 photons/sec, how far could the source be placed (and still be seen by eye). X-rays • Roentgen also worked with cathode ray tubes (1895+). • He found that cathode rays generate new “rays” when they interact with the glass tube. – These rays typically pass through materials opaque to light, and can activate photographic film (or fluorescent screen). • Don’t bend in magnetic field, don’t seem to do interference, called them X-rays. • Produced by accelerated charges (electrons), so they are a form of light. – Generally, radiation formed in this way is called bremsstrahlung (German for breaking radiation). X-rays • Generated by electrons with V ~ 10 kV. • So, electron’s (and X-ray’s) energy is ~10 keV. • Or, X-ray wavelength is of order 0.1 nm = 10-10 m = 1 Å. • This is of the same scale as spacing between atoms in a crystalline lattice. • So, use different planes of atoms in the crystal to do interferometry. 2d sin θ = mλ Bragg Condition By changing the incident angle, can measure the spectral content of the incoming wave. • Found that the spectrum is material dependent! • Continuous component, expected from bremsstrahlung. • Sharp lines (characteristic spectrum) dependent on the cathode target material. – Quantum atomic structure. • Continuum stops at λm. – Independent of material. – Dependent on the CRT voltage. – Corresponds to highest energy electrons produced in CRT: V↑, Ek↑, νm↑, λm↓ X-Rays Bragg Spectrometer Demo • 7A60.50 - Microwave Bragg Diffraction Compton Effect • Scattering of photons off of electrons – Electron absorbs part of the incoming energy and momentum. – Have to do it relativisticaly. Compton Effect • Compton confirmed this experimentally. • Used CRT with molybdenum to generate monochromatic beam of photons of wavelength 0.0711 nm. • Smashed them into graphite target, producing scattered photons. • Measured the content of scattered photons with a Bragg spectrometer.