Modern Physics Quantum Effects 1773 – 1829

Objectives  Explain the photoelectric effect and recognize that quantum theory can explain it, but wave theory cannot  Explain the Compton effect, and describe it in terms of the momentum and energy of a photon

Modern physics  Microscopic realm  Atoms and subatomic particles

Classical Physics (Newtonian)  Macroscopic objects  Marbles to moons  Pendulums to planets  Springs to stars

Classical Physics  Debate over light and matter Isaac Newton – beam of particles Isaac Newton – beam of particles Christian Huygens – wave theory Christian Huygens – wave theory Observed phenomena Observed phenomena ReflectionReflection RefractionRefraction InterferenceInterference DiffractionDiffraction Electric charge was once thought to be a fluid “Phlogiston,” a substance released by combustion “Luminiferous aether,” a medium for transporting light

Maxwell’s Equations 1831 – 1879

Heinrich Hertz  “The wave theory of light is, from the point of view of human beings, a certainty” 1857 – 1894

Properties of Light and Matter  Light frequency frequency wavelength wavelength energy energy amplitudeamplitude intensityintensity continuous continuous velocity velocity v = λƒ = cv = λƒ = c v = 3x10 8 m/sv = 3x10 8 m/s  Matter mass mass momentum momentum energy energy potentialpotential kinetickinetic discrete discrete velocity velocity v  cv  c

Disaster Strikes!

Wave Theory Can’t Explain

Blackbody Radiation  Objects absorb certain colors (wavelengths) and reflect others  Objects that are heated glow with different colors related to their temperature  An ideal “blackbody” absorbs all incident light, and emits radiation based only on its temperature  Classical wave mechanics can’t explain the distribution of wavelengths given off by a blackbody TB Pg. 626

Photoelectric Effect  Electrons are emitted when light strikes certain metallic surfaces Interaction starts immediately (no “absorption” time) Interaction starts immediately (no “absorption” time) Only occurs when light waves reach a certain minimum frequency Only occurs when light waves reach a certain minimum frequency Kinetic energy of electrons increases with frequency of the light wave Kinetic energy of electrons increases with frequency of the light wave Number of electrons is proportional to the intensity of the light Number of electrons is proportional to the intensity of the light TB Pg. 628

From a Wave Perspective  Electrons require energy to break their molecular bonds  Energy of a wave is related to its intensity (brightness)  Low intensity light of any frequency might take longer to be absorbed, but should still work  High intensity should give electrons more energy  Kinetic energy (velocity) of the electrons should increase with the intensity of the light

Laws of Photoelectric Emission  I. The rate of emission of photoelectrons is directly proportional to the intensity of incident light  II. The kinetic energy of photoelectrons is independent of the intensity of the incident light  III.The maximum kinetic energy of photoelectrons varies directly with the difference between the frequency of the incident light and the cutoff frequency

Photoelectric Effect  Impossible to explain with wave mechanics  Light is behaving like a particle

Photoelectric Effect  Binding energy of the electron is related to the wave frequency & Planck’s constant h = Planck’s constant h = Planck’s constant = 6.63 x joule·second= 6.63 x joule·second

Work Function  Minimum energy needed to free an electron where f 0 = the threshold frequency  Kinetic energy of the electron (K = ½mv 2 ) W = hf 0 K = hf ­ hf 0 TB Pg. 630

Quantization  Energy is “quantized” Specific amount required (“all or nothing”) to free the electron Specific amount required (“all or nothing”) to free the electron Any additional energy increases the velocity (kinetic energy) of the electron Any additional energy increases the velocity (kinetic energy) of the electron  Light and other forms of radiation consist of discrete bundles of energy Called “photons” Called “photons”

Light is Quantized  “Quantized” means light comes in discrete bundles, rather than a continuous spectrum “Discreteness” is the essence of a particle “Discreteness” is the essence of a particle Light behaves as a particle when it interacts with electrons Light behaves as a particle when it interacts with electrons  A different way of looking at light!

Quantized Quantities  We live in a quantized universe (integral multiples) Mass Mass Atoms Atoms Charge Charge Elementary charge (±1.60 x C)Elementary charge (±1.60 x C) Energy Energy Radiation emitted or absorbedRadiation emitted or absorbed Fundamental quantity (hf)Fundamental quantity (hf)

Compton Effect  X-rays bombarding graphite Arthur Holly Compton, 1922 Arthur Holly Compton, 1922 Electrons ejected from graphite Electrons ejected from graphite Scattered X-rays had a longer wavelength than the incident energy Scattered X-rays had a longer wavelength than the incident energy Energy and momentum gained by the electrons equal the energy and momentum lost by the X-ray photons Energy and momentum gained by the electrons equal the energy and momentum lost by the X-ray photons TB Pg. 635

Question  Which results in photoelectrons with more energy, a dim blue light or a bright red light? TB Pg. 632

More Questions  If the brightness of the light shining on a photosensitive surface increases, what happens to the photocurrent?  If you decrease the frequency of the light falling on the surface, what happens to the current?  If you make the light dim, do you have to wait longer for a photon to be ejected? TB Pg. 635

Practice  A photon has 2.11 electronvolts of energy. What is the energy in joules? What is its frequency and color? (1eV = 1.6 x J) Given: E = 2.11 eV h = 6.63 x J·s E = hf Find: E = ? (J) f = ? (Hz) color = ?

Answer Given: E = 2.11 eV h = 6.63 x J·s E = hf Find: E = ? (J) f = ? (Hz) color = ?

Practice  The threshold wavelength of sodium is 536 nm. What is the work function of sodium in eV? What is the work function of sodium in eV? If ultraviolet radiation with a wavelength of 348 nm falls on sodium, will electrons be ejected, and if so, and what is their energy in eV? If ultraviolet radiation with a wavelength of 348 nm falls on sodium, will electrons be ejected, and if so, and what is their energy in eV?

Answer  Find the work function using Planck’s constant and 0

Answer  Use Einstein’s photoelectric equation to find the energy of the electron