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Wednesday, November 29, 2006 Modern Physics

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Light as a Particle

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Quantum Physics Physics on a very small scale is “quantized”. Quantized phenomena are discontinuous and discrete. Atoms can absorb and emit energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.

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Quantum physics centers on light Visible spectrum Electromagnetic spectrum

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Light is a ray We know from geometric optics that light behaves as a ray. This just means it travels in a straight line. When we study ray optics, we ignore the nature of light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.

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But light is also a wave! We will study the wave nature of light in more depth later in the year. In quantum optics, we use one equation from wave optics. c = f – c: 3 x 10 8 m/s (the speed of light in a vacuum) – : wavelength (m) (distance from crest to crest) – f: frequency (Hz or s -1 )

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And light behaves as a particle! Light has a “dual nature”. In addition to behaving as a wave, it also behaves like a particle. It has energy and momentum, just like particles do. This particle behavior shows up under certain circumstances. A particle of light is called a “photon”.

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Calculating photon energy The energy of a photon is calculated from it the frequency of the light. E = hf – E: energy (J or eV) – h: Planck’s constant J s 4.14 eV s – f: frequency of light (s -1, Hz)

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Conceptual checkpoint Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser? – Neither! They both have the same energy per photon. The big one has more power. Which has more energy in its photons, a red laser or a green laser? – The green one has shorter wavelength and higher frequency. It has more energy per photon.

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The “electron-volt” (eV) The electron-volt is the most useful unit on the atomic level. If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy. 1 eV = J

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Sample Problem What is the frequency and wavelength of a photon whose energy is 4.0 x J?

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Sample Problem The bonding energy of H 2 is kcal/mol. Determine the frequency and wavelength of a photon that could split one atom of H 2 into two separate atoms. (1 kcal = 4186 J).

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Sample Problem How many photons are emitted per second by a He-Ne laser that emits 3.0 mW of power at a wavelength of nm?

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Wednesday, December 6, 2006 Atomic Energy Levels

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Announcements Sign in; pick up worksheet and homework score sheet Due next Wednesday – Worksheet Due today – Modern HW #1

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Quantized atomic energy levels This graph shows allowed quantized energy levels in a hypothetical atom. More stable states are those in which the atom has lower energy. The more negative the state, the more stable the atom. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state more stable less stable

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Quantized atomic energy levels The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionization or dissociation level. The lowest allowed energy is called the ground state. This is where the atom is most stable. States between the highest and lowest state are called excited states. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state

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Quantized atomic energy levels Transitions of the electron within the atom must occur from one allowed energy level to another. The atom CANNOT EXIST between energy levels. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state

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Absorption of photon by atom When a photon of light is absorbed by an atom, it causes an increase in the energy of the atom. The photon disappears. The energy of the atom increases by exactly the amount of energy contained in the photon. The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.

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Absorption of photon by atom When a photon is absorbed, it excites the atom to higher quantum energy state. The increase in energy of the atom is given by E = hf. 0 eV -10 eV Ground state EE

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Absorption Spectrum When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum. Therefore, a spectrum with dark bands in it is called an absorption spectrum.

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Absorption Spectrum Absorption spectra always involve atoms going up in energy level. 0 eV -10 eV ionized

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Emission of photon by atom When a photon of light is emitted by an atom, it causes a decrease in the energy of the atom. A photon of light is created. The energy of the atom decreases by exactly the amount of energy contained in the photon that is emitted. The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.

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Emission of photon by atom When a photon is emitted from an atom, the atom drops to lower quantum energy state. The drop in energy can be computed by E = hf. 0 eV -10 eV Excited state EE

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Emission Spectrum When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum. Therefore, a spectrum with bright bands in it is called an emission spectrum.

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Emission of photon by atom Emission spectra always involve atoms going down in energy level. 0 eV -10 eV ionized

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Sample Problem A.What is the frequency and wavelength of the light that will cause the atom shown to transition from the ground state to the first excited state? B.Draw the transition. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state

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Sample Problem A.What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state? B.Draw the transition. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state

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Sample Problem A.The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum? B.Draw the transitions. 0.0 eV -1.0 eV -3.0 eV -5.5 eV eV Ionization level Ground state (lowest energy level) First excited state Second excited state Third excited state

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Wednesday, December 13, 2006 Photoelectric effect

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Announcements Atomic transitions worksheet is due. Clicker quiz. Modern Physics #2 due January 3

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Remember atoms can absorb photons We’ve seen that if you shine light on atoms, they can absorb photons and increase in energy. The transition shown is the absorption of an 8.0 eV photon by this atom. You can use Planck’s equation to calculate the frequency and wavelength of this photon. 0.0 eV eV Ionization level Ground state (lowest energy level) -4.0 eV

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Photoelectric Effect Some “photoactive” metals can absorb photons that not only ionize the metal, but give the electron enough kinetic energy to escape from the atom and travel away from it. The electrons that escape are often called “photoelectrons”. The binding energy or “work function” is the energy necessary to promote the electron to the ionization level. The kinetic energy of the electron is the extra energy provided by the photon. 0.0 eV eV Ionization level Ground state (lowest energy level) -8.0 eV Work function Kinetic energy Photon energy e-

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Photoelectric Effect Photon Energy = Work Function + Kinetic Energy hf = + K max K max = hf – – K max : Kinetic energy of “photoelectrons” – hf: energy of the photon – : binding energy or “work function” of the metal. 0.0 eV eV Ionization level Ground state (lowest energy level) -8.0 eV Work Function Kinetic energy Photon energy e-

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Sample problem Suppose the maximum wavelength a photon can have and still eject an electron from a metal is 340 nm. What is the work function of the metal surface?

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Sample problem Zinc and cadmium have photoelectric work functions given by W Zn = 4.33 eV and W Cd = 4.22 eV. A) If illuminated with light of the same frequency, which one gives photoelectrons with the most kinetic energy? B) Calculate the maximum kinetic energy of photoelectrons from each surface for 275 nm light.

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Question The photoelectric equation is K max = hf – . Suppose you graph f on horizontal axis and K max on vertical. What information do you get from the slope and intercept? Slope: Planck’s Constant Intercept: -

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The Photoelectric Effect experiment The Photoelectric Effect experiment is one of the most famous experiments in modern physics. The experiment is based on measuring the frequencies of light shining on a metal, and measuring the energy of the photoelectrons produced by seeing how much voltage is needed to stop them. Albert Einstein won the Nobel Prize by explaining the results.

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Photoelectric Effect experiment metal (+) A V Collector (-) e- light e- At voltages less negative than Vs, the photoelectrons have enough kinetic energy to reach the collector. If the potential is V s, or more negative than V s, the electrons don’t have enough energy to reach the collector, and the current stops. light

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Experimental determination of the Kinetic Energy of a photoelectron The kinetic energy of photoelectrons can be determined from the voltage (stopping potential) necessary to stop the electron. If it takes 6.5 Volts to stop the electron, it has 6.5 eV of kinetic energy.

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Strange results in the Photoelectric Effect experiment Voltage necessary to stop electrons is independent of intensity (brightness) of light. It depends only on the light’s frequency (or color). Photoelectrons are not released below a certain frequency, regardless of intensity of light. The release of photoelectrons is instantaneous, even in very feeble light, provided the frequency is above the cutoff.

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Voltage versus current for different intensities of light. V I VsVs I1I1 I2I2 I3I3 Vs, the voltage needed to stop the electrons, doesn’t change with light intensity. That means the kinetic energy of the electrons is independent of how bright the light is. “Stopping Potential” Number of electrons (current) increases with brightness, but energy of electrons doesn’t!

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Voltage versus current for different frequencies of light. V I V s,1 f1f1 f2f2 V s,2 f3f3 V s,3 f 3 > f 2 > f 1 Vs changes with light frequency. That means the kinetic energy of the photoelectrons is dependent on light color. “Stopping Potential” Energy of electrons increases as the energy of the light increases.

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Wednesday, January 3, 2007 Photoelectric effect simulation laboratory

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Announcements Put modern physics homework #2 in folder today if you’ve got it - – extension to Friday due to holiday break. Clicker quiz. Simulation laboratory: lab report due next week.

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Graph of Photoelectric Equation f K max K max = h f - y = m x + b slope = h (Planck’s Constant) (binding energy) Cut-off frequency

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Photoelectric simulations Link for simulated photoelectric effect experiment – otoEffect/photo.htm otoEffect/photo.htm

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Assignment Run the photoelectric experiment for both metals. You must collect at least 5 data points for each metal. Graph the data such that Planck’s constant can be determined from the slope, and the work function can be determined from the y- intercept. Your report will consist of two data tables and two graphs, one for each metal, done in Excel. You must do a proper curve fit for your data, and clearly indicate Planck’s constant, the work function, and the cut-off frequency for each metal. Reports are due one week from today. They may be ed to me, or stored in the folder for your period on the N: drive. If necessary, you may print your report out and submit it as hard-copy.

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Wednesday, January 10, 2007 Nuclear Decay

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Announcements Due Today: Photoelectric Excel Laboratory Clicker quiz. Modern #3 due next week.

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A typical nucleus C 12 6 Element name Atomic mass: protons plus neutrons Atomic number: protons

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Isotopes Isotopes have the same atomic number and different atomic mass. Isotopes have similar or identical chemistry. Isotopes have different nuclear behavior. Examples:

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Uranium isotopes U U

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Nucleons Nucleons are particles that exist in the nucleus of an atom. Proton Charge: +e Mass: 1 amu Neutron Charge: 0 Mass: 1 amu p 1 1 n 1 0

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Nuclear reactions Nuclear Decay: a spontaneous process in which an unstable nucleus ejects a particle and changes to another nucleus. – Alpha decay – Beta decay Beta Minus Positron Fission: a nucleus splits into two fragments of roughly equal size. Fusion: Two nuclei combine to form another nucleus.

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Decay Reactions Alpha decay – A nucleus ejects an alpha particle, which is just a helium nucleus. Beta decay – A nucleus ejects a negative electron. Positron decay – A nucleus ejects a positive electron. Simulations – ty/radioactivity.html ty/radioactivity.html

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Alpha Decay Alpha particle (helium nucleus) is released. Alpha decay only occurs with very heavy elements.

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Beta ( - ) Decay A beta particle (negative electron) is released. Beta decay occurs when a nucleus has too many neutrons for the protons present. A neutron converts to a proton. An antineutrino is also released.

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Positron ( + ) Decay Positron (positive electron) is released. Positron decay occurs when a nucleus has too many protons for the neutrons present. A proton converts to a neutron. A neutrino is also released.

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Neutrino and Anti-Neutrino Proposed to make beta and positron decay obey conservation of energy. These particles possess energy and spin, but do not possess mass or charge. They do not react easily with matter, and are extremely hard to detect.

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Gamma Radiation, Gamma radiation is electromagnetic in nature. Gamma photons are released by atoms which have just undergone a nuclear reaction when the excited new nucleus drops to its ground state. The high energy in a gamma photon is calculated by E = hf.

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Calculation of energy released in nuclear reactionss 1.Add up the mass (in atomic mass units, u) of the reactants. You can find the mass in Appendix E of your textbook. 2.Add up the mass (in atomic mass units, u) of the products. 3.Find the difference between reactant and product mass. The missing mass has been converted to energy. 4.Convert mass to kg ( 1 u = 1.66 x kg) 5.Use E = mc 2 to calculate energy released.

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Sample Problem Complete the reaction, identify the type of decay, and calculate the energy.

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Sample Problem Complete the reaction, identify the type of decay, and calculate the energy.

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Wednesday, January 17, 2007 Nuclear Fusion and Fission

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Announcements Due Today: Assignment #3 Clicker quiz Modern #4 due next week.

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Fission Fission occurs when an unstable heavy nucleus splits apart into two lighter nuclei, forming two new elements. Fission can be induced by free neutrons. Mass is destroyed and energy produced according to E = mc2.

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Neutron-induced fission Neutron-induced fission produces a “chain reaction.” What does that mean? Nuclear power plants operate by harnessing the energy released in fission in by controlling the chain reaction. Nuclear weapons depend upon the initiation of an uncontrolled fission reaction.

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Critical Mass The neutrons released from an atom that has undergone fission cannot immediately be absorbed by other nearby fissionable nuclei until they slow down to “thermal” levels. How can this concept be used to explain why a chain reaction in nuclear fission will not occur unless a “critical mass” of the fissionable element is present at the same location?

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Nuclear Reactors Nuclear reactors produce electrical energy through fission. Advantages are that a large amount of energy is produced without burning fossil fuels or creating greenhouse gases. A disadvantage is the production of highly radioactive waste. Another simulation appears at – University of Wisconsin Nuclear Reactor Tour

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Nuclear Weapons Nuclear weapons have been used only twice, although they have been tested thousands of times. Weapons based on nuclear fission involve slamming together enough material to produce an uncontrolled fission chain reaction. Nagasaki, Japan Little Boy was dropped on Hiroshima and contained U-235 produced in Oak Ridge, TN.

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Fission Fission occurs only with very heavy elements, since fissionable nuclei are too large to be stable. A charge/mass calculation is performed to balance the nuclear equation. Mass is destroyed and energy produced according to E = mc 2.

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Sample problem Complete the following reaction and determine the energy released.

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Fusion Fusion occurs when two light nuclei come together to form a new nucleus of a new element. Fusion is the most energetic of all nuclear reactions. Energy is produced by fusion in the sun. Fusion of light elements can result in non-radioactive waste. He 2 2 H 1 1 H 1 1

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Fusion Fusion is the reaction that powers the sun, but it has not been reliably sustained on earth in a controlled reaction. Advantages to developing controlled fusion would be the tremendous energy output and the lack of radioactive waste products. Disadvantages are – we don’t know if we’ll be technical able to do it on earth!

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Sample Problem You fuse a free proton with a free neutron to form a deuterium nucleus. How much energy is released?

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Mass defect This strange term is used to indicate how much mass is destroyed when a nucleus is created from its component parts. The mass defect is generally much, much less than the mass of a proton or neutron, but is significant nonetheless. The loss of mass results in creation of energy, according to E = mc 2.

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Sample problem What is the mass defect of 12 C in atomic mass units? How does this relate to mass in kg and energy in eV and J?

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Wednesday, January 24, 2007 Wave-Particle Duality

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Announcements Due in folder today -- Modern #4 You will do Modern #5 in lunch bunch today. Next Wednesday – Free Response Problems in packet will be due at beginning of Lunch Bunch; we’ll correct them during Lunch Bunch. – Homework Quiz will be given. – We’ll review for the exam. Clicker Quiz

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Wave-Particle Duality Waves act like particles sometimes and particles act like waves sometimes. This is most easily observed for very energetic photons (gamma or x-Ray) or very tiny particles (elections or nucleons).

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Particles and Photons both have Energy We know from mechanics that a moving particle has kinetic energy – E = K = ½ mv 2 However, a particle really has most of its energy locked up in its mass. – E = mc 2 A photon’s energy is calculated using its frequency – E = hf

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Particles and Photons both have Momentum We know from mechanics that a particle that is moving has momentum – p = mv For a photon – p = h/ – Check out the units! They are those of momentum.

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Particles and Photons both have a Wavelength A photon of light has a wavelength, since light is also a wave – = c/f Hard as it may be to believe, particles also have wavelengths – = h/p where p = mv – This is referred to as the deBroglie wavelength and is pronounced for very tiny particles.

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We have experimental proof of Wave- Particle Duality Compton scattering – Proof that photons have momentum. – High-energy photons collided with electrons exhibit conservation of momentum. Davisson-Germer Experiement – Verified that electrons have wave properties by proving that they diffract. – Electrons were “shone” on a metal surface and acted like light by diffraction and interference.

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Sample problem What is the momentum of photons that have a wavelength of 620 nm?

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Sample problem What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?

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Wednesday, January 31, 2007 Review for Exam

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