Quantization in Nature II

Northeastern Illinois University

Greg Anderson Department of Physics & Astronomy Northeastern Illinois University

February,2008

°c 2004, 2007 G. Anderson Physics III – slide 1 / 35 Northeastern Illinois Overview University

Outline Electric Charge Electric Charge Black Body Black Body Radiation Radiation Photoelectric Photoelectric Eﬀect Eﬀect Compton Scattering Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 2 / 35 Northeastern Illinois Outline University

Outline ◆ Electric Charge Quantization of Charge Black Body ■ Radiation J.J. Thomson’s Experiment Photoelectric ■ Eﬀect Millikan’s Oil Drop Compton Scattering ◆ Blackbody Radiation ■ Blackbody Radiation ■ Planck’s quantum hypothesis ◆ The Photoelectric Eﬀect ◆ X-rays & Compton scattering

°c 2004, 2007 G. Anderson Physics III – slide 3 / 35 Northeastern Illinois University

Outline

Electric Charge Quantization in Nature Charge & Charged Constituents Quantization of Charge The Cathode Ray Tube (CRT) The Electron & Electric Determination of q/m of the electron The Mass Charge Spectrometer The Millikan Oil Drop Experiment Black Body Radiation Photoelectric Eﬀect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 4 / 35 Northeastern Illinois Quantization in Nature University

Outline ◆ Many of the fundamental quantities in nature: Electric Charge Quantization in matter, energy, electric charge come in indivisible Nature Charge & “clumps”. Charged Constituents ◆ Quantization of These indivisible units are known as quanta. Charge The Cathode 1 quantum, 2 quanta, 3 quanta. ... Ray Tube (CRT) Determination of q/m of the Quantization of Matter electron The Mass ◆ Spectrometer Democritus (450 B.C.) The Millikan Oil Drop ◆ Avagadro’s hypothesis (1811). Experiment Black Body Quantization of Charge Radiation Photoelectric −19 Eﬀect q = ne, e =1.6 × 10 C, n =0, ±1, ±2,... Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 5 / 35 Northeastern Illinois Active Learning: Charge Quantization University

Outline Electric charge is quantized. A charged object has a Electric Charge Quantization in surplus or deﬁcit of the number of electrons relative to Nature Charge & protons. Charged Constituents Quantization of For any charged object: Charge The Cathode Ray Tube (CRT) Q = ne, n =0, ±1, ±2,... Determination of q/m of the electron The Mass Spectrometer ◆ Let Ne be the number of electrons in an object The Millikan Oil Drop ◆ Experiment Let Np be the number of protons in an object. Black Body ◮ Radiation Express n in terms of Ne and Np. Photoelectric Eﬀect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 6 / 35 Northeastern Illinois Active Learning: Charge Quantization University

°c 2004, 2007 G. Anderson Physics III – slide 6 / 35 Northeastern Illinois Charge & Charged Constituents University

Outline The total charge of any composite object is the sum of the Electric Charge Quantization in charges of its charged constituents: electrons and protons. Nature Charge & Charged ◆ Ne electrons, each with charge −e contribute: Constituents Quantization of Charge The Cathode Qelectrons = Ne(−e) = −Nee Ray Tube (CRT) Determination of q/m of the electron The Mass Spectrometer ◆ Np protons, each with charge +e contribute: The Millikan Oil Drop Experiment Qprotons = Npe Example Black Body Radiation − + Np = 3 Photoelectric Together they give a total charge: − + Eﬀect + − N = 4 Compton e Scattering Q =(Np − Ne)e − Q = −1e

°c 2004, 2007 G. Anderson Physics III – slide 7 / 35 Northeastern Illinois Quantization of Charge University

Outline

Electric Charge Quantization in Nature Charge & Charged Constituents Quantization of Charge How do we know this? The Cathode Ray Tube (CRT) Determination of q/m of the electron The Mass Spectrometer The Millikan Oil Drop Experiment Black Body Radiation Photoelectric Eﬀect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 8 / 35 Northeastern Illinois The Cathode Ray Tube (CRT) University

Cathode Ray Tube (CRT) Cathode rays carry negative charge, − “cathode rays” J. Perrin 1895. + Glow J.J. Thomson’s discovery of the Cathode Anode electron in 1897.

− High + q/m =1.76 × 1011 C/kg Voltage

Cathode ray tubes (CRT) are the vacuum tube display devices used in computer displays, video monitors, televisions and oscilloscopes, with the exception of LCD displays and plasma screens.

°c 2004, 2007 G. Anderson Physics III – slide 9 / 35 Northeastern Illinois Determination of q/m of the electron University

Outline ⊙ ⊙ ⊙ ⊙ ⊙

Electric Charge Quantization in ⊙ ⊙ ⊙ ⊙ ⊙ Nature F 2 Charge & mv Charged ⊙ ⊙ ⊙ ⊙ ⊙ F = qvB = Constituents R Quantization of Charge R q v The Cathode ⊙ ⊙ ⊙ ⊙ ⊙ = Ray Tube (CRT) m BR Determination of q/m of the ⊙ ⊙ ⊙ ⊙ ⊙ Add a crossed electric ﬁeld: electron The Mass Spectrometer F = q (E + v × B) The Millikan Oil F = q (E + v × B) Drop ⊙ ⊙ ⊙ ⊙ ⊙ Experiment Black Body FB adjust E so that Fnet =0 Radiation ⊙ ⊙ ⊙ ⊙ ⊙ v Photoelectric Eﬀect ⊙ ⊙ ⊙ ⊙ ⊙ q E Compton = 2 Scattering FE m B R ⊙ ⊙ ⊙ ⊙ ⊙

°c 2004, 2007 G. Anderson Physics III – slide 10 / 35 Northeastern Illinois The Mass Spectrometer University

20 Outline Ne Electric Charge ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Quantization in Nature Charge & Charged ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ Constituents Quantization of Charge ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ The Cathode Ray Tube (CRT) Determination of q/m of the ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ electron − − − − − Ion Current The Mass 22 Spectrometer +++++ Ne The Millikan Oil 21 Drop Ne (×10) Experiment 2 2mV Black Body x =2r = Radiation B s q Accelerating Voltage Photoelectric Eﬀect The Mass Spectrometer. Compton Aston et.al. found iso- Scattering Thomson & Francis Aston 1910. topes, elements with diﬀer- ent masses. Resolved in 1932 by discovery of neutron. °c 2004, 2007 G. Anderson Physics III – slide 11 / 35 Northeastern Illinois The Millikan Oil Drop Experiment University

Outline Electric Charge Robert Millikan’s oil drop exper- Quantization in Nature Charge & iment 1910-1913. For suspended Charged Constituents drops: Quantization of Charge qE = Mg The Cathode FE = qE Ray Tube (CRT) Mg Determination of q = q/m of the E electron Fg = Mg The Mass Spectrometer Studying motion at terminal veloc- The Millikan Oil Drop ity Millikan found: Experiment Black Body q = ne, n =0, ±1, ±2,... Radiation Oil drops with mass M Photoelectric Eﬀect and charge q suspended × −19 Compton e =1.6 10 C Scattering between charged plates

°c 2004, 2007 G. Anderson Physics III – slide 12 / 35 Northeastern Illinois The Millikan Oil Drop Experiment II University

Outline Electric Charge Equation of motion Quantization in Nature Charge & dv Charged − − Constituents qE Mg bv = M , Quantization of dt Charge The Cathode FE = qE with b = 6πηr, r = drop radius, η = coef. of viscosity. Ray Tube (CRT) Determination of Terminal velocity when a = dv/dt = q/m of the electron Fg = Mg 0 The Mass − Spectrometer qE Mg The Millikan Oil v = Drop b Experiment Drops achieve terminal velocity immediately. Allow Black Body Radiation Oil drops with mass M drops to drift upwards or downwards a distance L. Rise Photoelectric time: v T = L, fall time v T = L Eﬀect and charge q suspended r r f f Compton Scattering between charged plates

°c 2004, 2007 G. Anderson Physics III – slide 13 / 35 Northeastern Illinois University

Outline

Electric Charge Black Body Radiation Blackbody Radiation Wein’s Displacement Law The Rayleigh-Jeans Equation Black Body Radiation The Ultraviolet Catastrophe Planck’s Quantum Hypothesis Photoelectric Eﬀect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 14 / 35 Northeastern Illinois Blackbody Radiation University

Outline Blackbody radiation: thermal radiation emitted by Electric Charge opaque bodies. (perfect absorbers) Black Body Radiation Oscillating, charged constituents of Blackbody Radiation atoms and molecules produce EM ra- Wein’s

Displacement Ã diation. Law Ã Ã The

Rayleigh-Jeans

Equation Ã Josef Stefan 1879, The Ultraviolet Ã Catastrophe Stefan-Boltzmann Law - Radiated Planck’s

Quantum Ã Power: Hypothesis Ã

Photoelectric Ã Eﬀect R = P/A = σT 4 Compton Scattering Stefan-Boltzmann constant T = Temperature A = Area σ =5.7 × 10−8 W/m2 · K4

°c 2004, 2007 G. Anderson Physics III – slide 15 / 35 Northeastern Illinois Wein’s Displacement Law University

Outline

Electric Charge − Black Body 8πhcλ 5 Radiation u(λ)= ehc/λkT −1 Blackbody Radiation Wein’s Displacement Law The Rayleigh-Jeans Equation Intensity The Ultraviolet Catastrophe Planck’s Quantum Hypothesis wavelength λ Photoelectric Eﬀect Compton Scattering Emission is a maximum at λm (Wilhelm Wien 1893)

−3 λmT = constant = 2.898 × 10 mK

°c 2004, 2007 G. Anderson Physics III – slide 16 / 35 Northeastern Illinois The Rayleigh-Jeans Equation University

Outline

Electric Charge Black Body Radiation Power radiated per unit Blackbody Radiation area Wein’s 1 Displacement R = cU Law The 4 Rayleigh-Jeans Equation U = is the total energy density The Ultraviolet Catastrophe Planck’s Quantum Hypothesis Energy density spectral distrubution function: Photoelectric Eﬀect −4 Compton u(λ) = kTn(λ)=8πkT λ , Scattering n = the number of modes of oscillation per unit volume.

°c 2004, 2007 G. Anderson Physics III – slide 17 / 35 Northeastern Illinois The Ultraviolet Catastrophe University

Outline

Electric Charge Planck’s solution to the ultra- Black Body violet catastrophe: Radiation Blackbody Quantization of Energy Radiation

Wein’s Intensity Displacement Law En = nhf The Rayleigh-Jeans Equation frequency quantum number n = 0, 1, 2, 3,... The Ultraviolet −4 Catastrophe Rayleigh-Jeans: u(λ) = 8πkT λ Planck’s 8πhcλ−5 Quantum Planck’s law: u(λ) = ehc/λkT −1 Hypothesis Photoelectric Planck’s constant Eﬀect Compton −34 Scattering h = 6.626 × 10 J · s Intensity = 4.14 × 10−15 eV · s wavelength

°c 2004, 2007 G. Anderson Physics III – slide 18 / 35 Northeastern Illinois Planck’s Quantum Hypothesis University

Outline Simple Harmonic Oscillator Electric Charge Planck’s solution: Black Body F = −kx Radiation Quantization of Energy Blackbody Radiation m Wein’s Displacement En = nhf Law 0 The Rayleigh-Jeans Equation x(t) = A cos ωt quantum number The Ultraviolet Catastrophe n = 0, 1, 2,... Planck’s ω 1 k Quantum f = = Hypothesis 2π 2π m Photoelectric r Planck’s constant Eﬀect Total energy (Classical) − Compton × 34 · Scattering h = 6.626 10 J s 1 1 1 = 4.14 × 10−15 eV · s E = mv2 + kx2 = kA2 2 2 2

°c 2004, 2007 G. Anderson Physics III – slide 19 / 35 Northeastern Illinois Discrete vs. Continuous Energies University

Outline

Electric Charge Black Body Radiation Blackbody Radiation Wein’s Displacement E = nhf E varies continuously Law The Rayleigh-Jeans Equation The Ultraviolet Catastrophe Planck’s Quantum Hypothesis Photoelectric Eﬀect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 20 / 35 Northeastern Illinois University

Outline

Electric Charge Black Body Radiation Photoelectric Effect Energy in EM Waves The Photo-electric effect Einstein’s Photoelectric Effect Solution Photoelectric Effect Compton Scattering

°c 2004, 2007 G. Anderson Physics III – slide 21 / 35 Northeastern Illinois Energy in EM Waves University

Outline v = c Electric Charge E Black Body Radiation Photoelectric Effect Energy in EM Waves B The Photo-electric effect Einstein’s −2 Solution Energy density in a EM wave B = E/c, c = µ0ǫ0 Photoelectric Effect Compton 1 2 1 2 2 1 2 Scattering u = uE + uB = ǫ0E + B = ǫ0E = ǫ0E0 2 2µ0 2 Classically, the energy in an EM Wave is continuous, and 1 2 independent of frequency. I = 2 ǫ0cE0

°c 2004, 2007 G. Anderson Physics III – slide 22 / 35 Northeastern Illinois The Photo-electric eﬀect University

Outline light Ke Electric Charge f, I Black Body electron Radiation Photoelectric Effect Energy in EM Waves The Photo-electric effect Einstein’s Solution Photoelectric Effect Compton Scattering

Light absorbed and electrons emitted.

Ke = Eabsorbed − binding energy

°c 2004, 2007 G. Anderson Physics III – slide 23 / 35 Northeastern Illinois Active Learning: Photo-electric eﬀect University

Your are a classical physicist from the late 19th century. What would you expect for the two plots below from classical physics?

Ke I = const. Ke f = const.

f I

°c 2004, 2007 G. Anderson Physics III – slide 24 / 35 Northeastern Illinois Active Learning: Photo-electric eﬀect University

Your are a classical physicist from the late 19th century. What would you expect for the two plots below from classical physics?

Ke I = const. Ke f = const.

f I

°c 2004, 2007 G. Anderson Physics III – slide 24 / 35 Northeastern Illinois Nature: Stranger than Fiction University

Image how puzzled and confused these physicists were when experimental observation showed:

Ke I = const. Ke f = const.

f I

°c 2004, 2007 G. Anderson Physics III – slide 25 / 35 Northeastern Illinois Einstein’s Solution University

Outline Electromagnetic radiation is not continuous. Electric Charge Black Body ◆ Light is quantized. Radiation Photoelectric ◆ These quanta are particles (photons). Effect Energy in EM Waves ◆ The energy of a photon is: The Photo-electric effect Einstein’s Solution E = hf Photoelectric Effect Compton Scattering Planck’s Constant: h = 6.626 × 10−34 J · s = 4.14 × 10−15 eV · s

°c 2004, 2007 G. Anderson Physics III – slide 26 / 35 Northeastern Illinois The Photo-electric eﬀect University

K = eVstop = hf − Φ

Φ f0 = h h − stop Vstop = e f f0 Cesium Lithium

V Potassium Sodium

5.0 5.2 5.4 5.6 5.8 6.0 6.2

f(1014 Hz)

°c 2004, 2007 G. Anderson Physics III – slide 27 / 35 Northeastern Illinois Photoelectric Eﬀect University

If the frequency is held ﬁxed in the photoelectric eﬀect and the intensity of the light is increases, which of the following are true: a. The kinetic energy of the emitted electrons increases. b. The kinetic energy of the emitted electrons stays the same. c. The number of electrons emitted per second increases. d. The number of electrons emitted per second stays the same. e. (b) and (c) f. (a) and (d)

°c 2004, 2007 G. Anderson Physics III – slide 28 / 35 Northeastern Illinois Photoelectric Eﬀect University

°c 2004, 2007 G. Anderson Physics III – slide 28 / 35 Northeastern Illinois University

Outline

Electric Charge Black Body Radiation Photoelectric Eﬀect Compton Scattering Light as Particles Compton Compton Scattering Scattering Sample Photon Interactions Pair Production Next

°c 2004, 2007 G. Anderson Physics III – slide 29 / 35 Northeastern Illinois Light as Particles University

Outline Electromagnetic radiation (light) is quantized. The Electric Charge Black Body indivisible particles which comprise light are called Radiation photons. Photoelectric Eﬀect Compton Scattering Energy of a photon: Light as Particles E = hf Compton Scattering Sample Photon Momentum of a photon: Interactions Pair Production E hf h Next p = = = c c λ

°c 2004, 2007 G. Anderson Physics III – slide 30 / 35 Northeastern Illinois Compton Scattering University

Outline 1923 A.H. Compton scatters X-rays from various metals: Electric Charge − Black Body e Radiation Classically Photoelectric Eﬀect γ θ ′ Compton ∆λ = λ − λ =0 Scattering Light as Particles φ Compton Quantum mechanically: Scattering ′ Sample Photon γ Interactions E hf h Pair Production pγ = = = Next Compton wavelength c c λ of the electron: h ∆λ = h (1 − cos φ) mec λc = mec

°c 2004, 2007 G. Anderson Physics III – slide 31 / 35 Northeastern − − Illinois Elastic Scattering: γ + e −→ γ + e University

Outline Before Electric Charge − Black Body γ e Radiation Ã Electron energy & momentum: Photoelectric λ Eﬀect 2 2 2 2 Compton Ee =(pec) +(mec ) Scattering ′ Light as After λ Particles Conservation of energy: Compton Ã Scattering φ Sample Photon 2 ′ Interactions − hf + mec = hf + Ee Pair Production e Next θ pe Conservation of momentum: h h Photon energy & momen- (px) λ = λ′ cos φ + pe cos θ tum: h − (py) 0 = λ′ sin φ pe sin θ hc E = p c = hf = γ γ λ

°c 2004, 2007 G. Anderson Physics III – slide 32 / 35 Northeastern Illinois Sample Photon Interactions University

◆ Outline Absorption & Ionization, i.e. photoelectric eﬀect:

Electric Charge Ã ⇒ − + Black Body Radiation Photoelectric Eﬀect Compton ◆ ∗ Scattering Absorption without ionization e.g., γ + H → H Light as Particles Ã ⇒ Compton Scattering Sample Photon Interactions Pair Production Next ◆ ÃScattering, e.g. Compton scattering ⇒ Ã − −

◆ Pair Production or annihilation

e+ + e− → γ + γ

°c 2004, 2007 G. Anderson Physics III – slide 33 / 35 Northeastern Illinois Electron-Positron Pair Production University

Outline

Electric Charge Black Body Radiation Photoelectric Eﬀect Compton Scattering Light as Particles Compton Scattering Sample Photon Interactions Pair Production Next

Lawrence Berkeley Laboratory/Science Photo Library

°c 2004, 2007 G. Anderson Physics III – slide 34 / 35 Northeastern Illinois Next University

Outline Lecture 08: The Nuclear Atom Electric Charge Black Body ◆ The Nuclear Atom Radiation Photoelectric ■ Atomic Spectra Eﬀect Compton ■ Rutherford’s Nuclear Model Scattering Light as ■ Particles The Bohr Model Compton Scattering ■ X-Ray Spectra Sample Photon Interactions ■ The Franck-Hertz Experiment Pair Production Next

°c 2004, 2007 G. Anderson Physics III – slide 35 / 35