Modern Physics. Light as a Particle

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1 Day 1 Modern Physics NOTE: each topic is sectioned into days numbered from 1 to 7. This would be a good pace to follow as you make your way through the unit. If you learn one section per day, you will be done in one week!

2 Modern Physics Light as a Particle

3 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.

4 Quantum physics centers on light Visible spectrum Electromagnetic spectrum

5 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.

6 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 = lf c: 3 x 10 8 m/s (the speed of light in a vacuum) l: wavelength (m) (distance from crest to crest) f: frequency (Hz or s -1 )

7 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.

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

9 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.

10 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

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

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

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

14 Atomic Energy Levels Day 2

A different look AT an Old companion Line

15 A different look AT an Old companion Line Spectra vs. Continuous Spectra Line Spectrum - contains only certain colors Only certain lines of color appear in the spectrum Continuous Spectrum - contains all the colors A continuous band of colors appears in the spectrum

16 The Crayon Perspective

17 Spectroscope activity Look at an incandescent bulb (Continuous spectrum) Look at a fluorescent bulb (Line spectrum, nearly continuous)

18 The Bohr Model First there was Rutherford. Nuclear Model of the atom: electrons have energy and orbit the nucleus. Then there was Planck. Energy is Quantized (stairs), not continuous (a ramp): there must be energy levels(or steps ) for the electrons to orbit at. It may help to equate the word quantum with level.

19 The Bohr Model: Anything but Bohring Niels Bohr thought, the energy of the electrons orbiting a nucleus must be quantized. So he came up with different energy levels ( quantums ) for the electrons. He gave the energy levels (quantums) numbers. These are what we call Quantum numbers. They are abbreviated with an n and the level number. (For example: n 1 is the first energy level)

When an electron absorbs a photon of high enough energy (or, high enough

20 The Bohr Model: Anything but Bohring The lowest energy level (n 1 ) is called the ground state. When an electron absorbs a photon of high enough energy (or, high enough frequency), that electron jumps to the next energy level. Any energy level where an electron is higher than the ground state is called an excited state.

21 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. more stable less stable Ionization level Third excited state Second excited state First excited state Ground state (lowest energy level) 0.0 ev -1.0 ev -3.0 ev -5.5 ev ev

22 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. Ionization level Third excited state Second excited state First excited state Ground state (lowest energy level) 0.0 ev -1.0 ev -3.0 ev -5.5 ev ev

23 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. Ionization level Third excited state Second excited state First excited state 0.0 ev -1.0 ev -3.0 ev -5.5 ev Ground state (lowest energy level) ev

24 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.

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

26 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.

27 -10 ev Absorption Spectrum Absorption spectra always involve atoms going up in energy level. ionized 0 ev

28 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.

29 -10 ev 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 DE = hf. Excited state l 0 ev DE

30 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.

31 -10 ev Emission of photon by atom Emission spectra always involve atoms going down in energy level. ionized 0 ev

32 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? Ionization level B. Draw the transition. 0.0 ev Sample Problem Third excited state -1.0 ev Second excited state -3.0 ev First excited state -5.5 ev Ground state (lowest energy level) ev

33 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. Sample Problem Ionization level 0.0 ev Third excited state -1.0 ev Second excited state -3.0 ev First excited state -5.5 ev Ground state (lowest energy level) ev

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

35 Photoelectric effect Day 3

36 Review Slide: 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. Ionization level Ground state (lowest energy level) 0.0 ev -4.0 ev ev

37 Photon energy 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. e- Ionization level Kinetic energy 0.0 ev -8.0 ev 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. Work function Ground state (lowest energy level) ev

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

39 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? Sample problem

40 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. Sample problem

41 Question The photoelectric equation is K max = hf f. 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: -f

42 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.

43 Photoelectric Effect At If the voltages potential less is negative V s, or more than negative Vs, the than photoelectrons V s, the have electrons enough don t kinetic have energy enough to energy reach to the reach collector. the collector, and the current stops. light experiment Collector (-) metal (+) e- e- e- e- e- e- e- e- e- e- e- V e- e- e- e- A e- e-

44 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.

45 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.

46 Voltage versus current for different intensities of light. Number of electrons (current) increases with brightness, but energy of electrons doesn t! I I 3 I 2 I 1 V s Stopping Potential 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. V

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

48 Photoelectric effect simulation laboratory Day 4

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

50 Photoelectric simulations Link for simulated photoelectric effect experiment p28/photoeffect/photo.htm

51 Lab 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, preferably 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 the week we return from break. They may be ed to me, or printed and brought to class.

52 Nuclear Decay Day 5

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

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

55 Uranium isotopes U U 92 92

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

57 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.

58 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 dioactivity/radioactivity.html

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

Beta (b - ) Decay 14 14 0 6 7 1 C N e A beta particle (negative electron) is released.

60 Beta (b - ) Decay C N e 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.

61 Positron (b + ) Decay He H e 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.

62 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.

63 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. Gamma Radiation, g

64 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.

65 Complete the reaction, identify the type of decay, and calculate the energy. Sample Problem 232 Th 228 Ra? 90 88

66 Complete the reaction, identify the type of decay, and calculate the energy. Sample Problem 234 0? Pa e? 91 1

67 Nuclear Fusion and Fission Day 6

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.

68 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. tml

69 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.

70 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?

creating greenhouse gases. A disadvantage is the production of highly radioactive waste.

71 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

Weapons based on nuclear fission involve slamming together enough material to

72 Nuclear Weapons Nagasaki, Japan 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. Little Boy was dropped on Hiroshima and contained U-235 produced in Oak Ridge, TN.

73 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 n Pu Sb Tc n

74 Complete the following reaction and determine the energy released. Sample problem ? n U Sr n

75 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. 1 1 H H He 2

76 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!

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

78 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.

79 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? Sample problem

80 Wave-Particle Duality Day 7

81 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).

82 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

83 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/l Check out the units! They are those of momentum.

What if matter behaves the same way as light does?

84 What s the matter with Matter? Light travels in waves, but also bounces off of things like particles would. What if matter behaves the same way as light does? - Louis de Broglie Well wha do ya know, it DOES! Matter is thought of as different sized particles. The wavelike behavior of these particles is aptly named matter waves.

Wavy Matter A particle s mass has a lot to do with the

BUT if the particle has a very small mass, like that of an

85 Wavy Matter A particle s mass has a lot to do with the wavelength it travels at. If a particle has the mass of a baseball, the wavelength will be so small that it cannot be observed. BUT if the particle has a very small mass, like that of an electron for example, then the wavelength is large enough to equal the wavelengths of light, and scientists can observe that.

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

87 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.

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

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

90 Changes made in 2002 Removed (5% of syllabus) Alpha particle scattering Rutherford scattering Bohr model (but energy levels remain) Radioactivity Half life Unchanged Wave particle dynamics Nuclear reactions Mass energy equivalence

SECTION A Quantum Physics and Atom Models

AP Physics Multiple Choice Practice Modern Physics SECTION A Quantum Physics and Atom Models 1. Light of a single frequency falls on a photoelectric material but no electrons are emitted. Electrons may