2Introduction What is a “quantum”? The special theory of relativity did not answer all questions about matter.Blackbody radiation?Photoelectric effect?Spectral lines from gas discharge tubes?
3Between 1900 and 1930 quantum mechanics was developed to help explain the behavior of atoms, molecules, and nuclei.It modifies our ideas concerning the physical world.
4Famous scientists involved in the development of the quantum theory: EinsteinBohrSchrodingerde BroglieHeisenbergBornDirac
5We will discuss:The photoelectric effectThe Compton effectX-rays
6Blackbody Radiation And Planck’s Hypothesis Thermal radiationEmitted by an object at any temperatureThe radiated spectrum depends upon the temperature and other properties of the object.Incandescent light bulb demonstrationIt is produced by accelerating charged particles near the surface of the object.
8Blackbody Radiation What is a blackbody? It is an ideal system that absorbs all radiation incident upon it.It is also a perfect emitter of radiation as a function of temperature.
9When the temperature of a blackbody increases: The total maximum intensity of the emitted radiation increasesThe peak of the energy distribution shifts toward the shorter wavelengths (higher frequencies).27.2, 27.3
11Wien’s displacement law T is the absolute temperature.It can be used to determine the temperature of objects by measuring their peak emitted wavelengthFinding the temperature of stars
12Planck’s Hypothesis Planck Developed a better equation for predicting blackbody radiationThis overcame the weaknesses of the Wien displacement law.Originated the concept of submicroscopic electric oscillators (resonators)
13Planck’s first assumption The resonators could only have discrete amounts of energy (En) given byn is a positive integer called the principle quantum numberh = x J.s
14Planck’s second assumption The resonators emit discrete units of light that are called photons.
15Electron TransitionsElectrons jump from one quantum state (energy level) to another.
16Photon EnergyEquation for the energy of a photon274
17The electron will absorb or radiate energy only when it changes quantum states.
18Plank’s TheoryThe key point of Planck’s theory is the radical assumption of quantized energy states.This development marked the birth of the quantum theory.Most scientists (including Planck!) didn’t consider the quantum to be realistic.
19The Photoelectric Effect When light is incident upon certain metallic surfaces, electrons are emitted from the surfaces. (Figure 27.5)This is called the photoelectric effect.The emitted electrons are called photoelectrons.It was first discovered by Hertz.275
20Important concepts involving the photoelectric effect: Stopping potential (DV)A negative potential can stop the electrons.Cutoff frequency (fc)No electrons are emitted for incident light below this frequency.Inconsistent with the wave theory27.4
21Other important concepts: The maximum KE of the photoelectrons is independent of light intensity.The maximum KE of the photoelectrons increases with increasing light frequency.Electrons are emitted from the surface almost instantaneously.27.4
22Einstein received the Nobel Prize in 1921 for successfully explaining the photoelectric effect in 1905.He said that all electromagnetic waves can be considered as a stream of photons.Each photon has a discrete energy E.
23Einstein’s view:A photon can give up all of its energy (hf) to a single electron in the metal.Electrons emitted from the surface of the metal possess KE.
24The Work Function f is called the work function of the metal. It represents the minimum energy (in eV) needed to free an electron from the metal.
25Photoelectric effects: No emission occurs below the cutoff frequency and the KE increases with frequency.KEmax is independent of the intensity of the light.Doubling the light intensity doubles the number of electrons emitted.27.5, 38-1,
29Uses for the photoelectric cell: Sound tracks on motion picture filmUsed to control outdoor lightsGarage door safetyElevator safetyAnalyzing bacterial growthUsed in “Breathalyzers”272
30X-RaysAccidentally discovered in 1895 by Wilhelm Roentgen while he was studying electrical discharges in low pressure gases.The nature of the mysterious radiation was unknown, thus the name x-rays.They traveled at the speed of light.They were unaffected by electric or magnetic fields.They were not a beam of charged particles.
31The formation of x-rays is like an inverse photoelectric effect.
32X-ray photons are produced when high speed electrons are suddenly decelerated. Electrons striking a metal target is one method.X-ray tubes27.8
33The x-ray spectrum Two distinct features Broad continuous spectrum Bremsstrahlung (braking radiation)A number of sharp linesCharacteristic x-rays
40X-rays are also used to examine paintings for authenticity.
41Diffraction of X-Rays by Crystals Max von Laue suggested the possibility of using crystals as a diffraction grating to diffract the x-rays.Their wavelength could now be determined.It is about 0.10 nm27.11
42Diffraction gratings cannot be used with x-rays because the slits are much too wide. Crystals work well because the spacing between the atoms acts like a 3-dimensional grating.Sodium chloride crystals may be used.A Laue diffraction pattern is observed.
43Bragg’s LawThe condition for constructive interference is given by Bragg’s law.Bragg and his son shared a Nobel Prize in 1915.
45The Compton EffectCompton directed a beam of x-rays at a block of graphite.The scattered x-rays had a slightly longer wavelength than the incident x-rays.This meant that the scattered x-rays had a lower energy.276, 27.18
46The Compton EffectThe change in wavelength (Dl) is called the Compton shift.The Compton effect demonstrated that photons behave like particles.
47The Compton Effect The Compton shift is given by (h/mec) is called the Compton wavelength27.16
48The Compton Effect (h/mec) = 0.00243 nm (h/mec) is called the Compton wavelength(h/mec) = nm
49The Compton EffectThe Compton shift depends upon the scattering angle but not upon the wavelength.
50The Compton EffectThe photoelectric effect and the Compton effect both involve the loss or gain of kinetic energy.Photons lose energyElectrons gain KE.
51Pair Production And Pair Annihilation Can a photon produce a single charged particle?
52Pair Production And Pair Annihilation In pair production, a photon is converted completely into mass.Electron-positron pairs can be formed.What is a positron?
53Photons And Electromagnetic Waves Light has a dual nature.It has the properties of both waves and particles.The wave nature is difficult to detect at high frequencies.The particle nature is difficult to detect at low frequencies.
54The Wave Properties Of Particles Light has a dual nature but particles can also exhibit wave properties.Matter has a dual nature as well.
55The Wave Properties Of Particles de Broglie postulated that because photons have wave and particle characteristics, perhaps all forms of matter have a dual nature.A highly revolutionary ideaHe said that electrons have wave properties.
56The Wave Properties Of Particles Equation for the momentum of a photon
57The Wave Properties Of Particles Equation for the de Broglie wavelength of a particle
58The Wave Properties Of Particles Both equations have wave and particle characteristics.
59The Wave Properties Of Particles Davisson and Germer accidentally discovered that electrons can exhibit diffraction.They confirmed de Broglie’s prediction.274, 25-6
60The Wave Properties Of Particles Application: The Electron MicroscopeIt relies on the wave characteristics of electrons.It has a much greater resolving power.High energy electrons have very short wavelengths.All microscopes detect details close in size to the wavelength being used.Resolution is 100x better than light microscopes.
61The Wave Function The Schrodinger equation: Described the manner in which waves change in space and timeIs a key element in the theory of quantum mechanicsIs as important in quantum mechanics as Newton’s laws are in classical mechanicsDeals with the probability of finding a particle in a particular location
62The Uncertainty Principle Quantum theory predicts that it is impossible to make simultaneous measurements of a particle’s position and velocity with infinite accuracy.This is called the Heisenberg uncertainty principle.
63The Uncertainty Principle If Dx is made very small, Dpx will be large and vice versa.Position and momentum cannot both be measured with accuracy simultaneously.277, 278
64The Uncertainty Principle The measuring procedure itself limits the accuracy of the measurements.
65The Uncertainty Principle The uncertainty principle also states thatIt is also impossible to simultaneously measure the energy of a particle in an infinitely short interval of time
66The Uncertainty Principle Experiments designed to reveal the wave character of an electron will diminish its particle character.
67The Uncertainty Principle Experiments designed to reveal the particle character of an electron will diminish its wave character.
68The Uncertainty Principle The Heisenberg uncertainty principle predicts that all molecular motion will not cease at absolute zero.
72The Scanning Tunneling Microscope It’s operation is based upon the concept of “tunneling” which was understood in the 1920s but the microscope wasn’t built until the 1980s when the technology became available.
73The Scanning Tunneling Microscope The scanning tunneling microscope (STM) is being replaced by the atomic force microscope (AFM).