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A Conceptual Introduction To Wave Properties and Quantum Physics

Kevin Warren

Chris Yohn

OU RET Program 2016

OU Department of Physics and Astronomy

University of Oklahoma

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Table of Contents:

Part 1: Waves

1. Activity 1: Exploring Waves: Hands-on activity for students making waves with slinky springs

2. Activity 2: Wave Characteristics: Guided inquiry activity introducing wavelength and frequency

3. Activity 3: Wave Interactions: Hands-on activity for students to combine waves with a long spring

4. Activity 4: Wave Interference: Guided inquiry activity introducing constructive and destructive interference

5. Extension Activity 5*: PhET Simulation: Fourier: Making Waves: Computer simulation of combining two or more waves to make a new wave. Play the ‘Wave Game”. Designed for use in computer lab.

6. Extension Activity 6*: Fabric of Space: Build two demonstration tables, roll marbles around and have some fun with your students while discussing the idea of space-time fabric, planetary orbits and the formation of the solar system.

7. Extension Activity 7*: The Interferometer and How It Works: Watch some videos and discuss how the LIGO interferometer was able to measure gravity waves for the first time! Remind students we haven’t done everything yet.

Part 2: Introduction to Quantum Physics

8. Activity 8: Introduction to Quantization: Hands-on activity where students make weight measurements of objects, graph the data to find patterns and, through discussion, get introduced to the idea of quantized amounts.

9. Activity 9: Mathematical Relationships in Electromagnetic Waves: Guided inquiry activity that introduces students to the mathematical relationships between the energy, wavelength and frequency of waves.

10. Demonstration: The Photoelectric Effect: Use an ultraviolet light to discharge an electroscope in front of your class. This experiment demonstrates the particle properties of electromagnetic radiation, the first part of the dual nature of matter.

11. Activity 10: PhET Simulation: Photoelectric Effect: This guided inquiry activity uses a computer simulation allow students to observe what is going on at the atomic level during the photoelectric effect. Students will use graphs to find the equation for photon energy which includes kinetic energy, work function and Planck’s constant. The ‘Big’ idea taken away from this activity is that photons of light behave as particles as they deliver energy in quantized packets during the photoelectric effect.

12. Activity 11: PhET Simulation: Diffraction of Waves: This guided inquiry activity uses computer simulations that allow students to observe diffraction of water and light waves through and around barriers. Students will observe diffractions patterns while performing the ‘double-slit’ experiment. Instructor will shine a laser through a double slit slide and project an interference pattern on the wall. The ‘Big’ idea taken away from this activity is that small particles produce the same interference pattern as photons of light, the second part of the idea of the dual nature or matter.

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13. Extension Activity 12*: Palm Pipes: Hands-on activity in which students will create different tones with pipes of different lengths. The activity is followed by an introduction to the standing sound waves inside of the pipes and their relationship to the length of the pipes. Only specific wavelengths can produce sound in the pipes. This idea will be related to quantized energy in electrons.

14. Extension Demonstrations*:

Singing Rods: Rub your fingers along various metal rods to produce impressive sounds. Demonstrate that certain places on the rods are not moving as the rod vibrates. This activity demonstrates standing waves, wavelength and nodes.

Standing Wave Generator: A motor is used to move a string that will produce standing waves. This demonstration provides a visual of standing waves, wavelengths and nodes

Whirly Sound Tubes: Whirl a tube to produce a low pitch. As you whirl the tube faster, two more higher pitches will be heard. This demonstrates that only specific wavelengths of sound can fit in the tube. This idea will be related to quantized energy in electrons.

12. Activity 13: Particle In A Box: This guided inquiry activity pulls together concepts learned in the previous seven activities as students are challenged to think about electrons as standing waves. The ideas of wave functions and probability densities are introduced and connected to the idea of quantized energies.

13. Activity 13 Reading: Students apply what they learned about probability densities in the previous activity to atomic orbitals in hydrogen atoms.

14. Extension Activity 14*: Light Emitted By Hydrogen Atoms: Another attention grabbing, hands-on activity during which students will observe different types of light through C-spectra paper which separates the light into its component colors. This activity provides more evidence of quantized energy in electrons.

15. Extension Activity 15*: Electron Energy In Hydrogen Atoms: A guided inquiry activity which uses data and mathematical relationships learned in previous activities to explain the observations of light spectral lines in the previous activity.

*Extension Activities are optional topics that can enhance and broaden the unit.

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Activities that focus on classical waves only:

1. Activity 1: Exploring Waves: Hands-on activity for students making waves with slinky springs

2. Activity 2: Wave Characteristics: Guided inquiry activity introducing wavelength and frequency

3. Activity 3: Wave Interactions: Hands-on activity for students to combine waves with a long spring

4. Activity 4: Wave Interference: Guided inquiry activity introducing constructive and destructive

13. Extension Activity 12*: Palm Pipes: Hands-on activity in which students will create different tones with pipes of different lengths. The activity is followed by an introduction to the standing sound waves inside of the pipes and their relationship to the length of the pipes. Only specific wavelengths can produce sound in the pipes. This idea will be related to quantized energy in electrons.






Activities that focus on quantum waves only:

8. Activity 8: Introduction to Quantization: Hands-on activity where students make weight measurements of objects, graph the data to find patterns and, through discussion, get introduced to the idea of quantized amounts.

9. Activity 9: Mathematical Relationships in Electromagnetic Waves: Guided inquiry activity that introduces students to the mathematical relationships between the energy, wavelength and frequency of waves.

10. Demonstration: The Photoelectric Effect: Use an ultraviolet light to discharge an electroscope in front of your class. This experiment demonstrates the particle properties of electromagnetic radiation, the first part of the dual nature of matter.

11. Activity 10: PhET Simulation: Photoelectric Effect: This guided inquiry activity uses a computer simulation allow students to observe what is going on at the atomic level during the photoelectric effect. Students will use graphs to find the equation for photon energy which includes kinetic energy, work function and Planck’s constant. The ‘Big’ idea taken away from this activity is that photons of light behave as particles as they deliver energy in quantized packets during the photoelectric effect.

12. Activity 11: PhET Simulation: Diffraction of Waves: This guided inquiry activity uses computer simulations that allow students to observe diffraction of water and light waves through and around

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barriers. Students will observe diffractions patterns while performing the ‘double-slit’ experiment. Instructor will shine a laser through a double slit slide and project an interference pattern on the wall. The ‘Big’ idea taken away from this activity is that small particles produce the same interference pattern as photons of light, the second part of the idea of the dual nature or matter.





12. Activity 13: Particle In A Box: This guided inquiry activity pulls together concepts learned in the previous seven activities as students are challenged to think about electrons as standing waves. The ideas of wave functions and probability densities are introduced and connected to the idea of quantized energies.

13. Activity 13 Reading: Students apply what they learned about probability densities in the previous activity to atomic orbitals in hydrogen atoms.

14. Extension Activity 14*: Light Emitted By Hydrogen Atoms: Another attention grabbing, hands-on activity during which students will observe different types of light through C-spectra paper which separates the light into its component colors. This activity provides more evidence of quantized energy in electrons.

15. Extension Activity 15*: Electron Energy In Hydrogen Atoms: A guided inquiry activity which uses data and mathematical relationships learned in previous activities to explain the observations of light spectral lines in the previous activity.


Activities that focus on gravity waves:

6. Extension Activity 6*: Fabric of Space: Build two demonstration tables, roll marbles around and have some fun with your students while discussing the idea of space-time fabric, planetary orbits and the formation of the solar system.

7. Extension Activity 7*: The Interferometer and How It Works: Watch some videos and discuss how the LIGO interferometer was able to measure gravity waves for the first time! Remind students we haven’t done everything yet.

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Box Materials List by Unit:

Activity 1: 10 slinkiesActivity 3: 10 Long Springs, meter sticks, masking tapeActivity 5: Computer LabActivity 6: Fabric Table, 2-1kg discs, marblesActivity 8: Fundamental Units: Set of 30 EnvelopesPhotoelectric Effect Demonstration: Computer Lab, Electroscope, balloon, laser pointer, UV lightActivity 11: laser pointer, double slit slide, diffraction grating slideActivity 12: Palm Pipes: 4 Sets of red pipes and one set of multi-colored pipesSinging Rods Demonstration: Singing Rods KitStanding Waves Demonstration: Standing Wave GeneratorWhirly Sound Tubes SetActivity 14: Gas Light Tube Socket, Hydrogen Gas Tube, Helium Gas Tube, C-Spectra Paper, Spectroscopes

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Activity 1: Exploring Waves Name: .

Introduction: When you hear the word ‘wave’ you may picture an ocean shore or think of sounds moving through the air. We are going to explore a much smaller world where tiny things like light and particles possess wave characteristics. To get warmed up, we are going to make some waves with a spring and observe some of the important characteristics of waves.

Materials: Slinky or other spring

Procedure:1) Get a partner and a slinky.

2) Find a place where you can stretch out the slinky on a table top or on a tile floor. Slinky must be on floor!

3) Hold one end of the slinky and have your partner hold the other end and stretch the slinky 4-6 meters.

4) Use the time you are given to investigate waves with the slinky. Investigate as many things as possible in the time allowed. As you investigate, record your observations and any data that you may collect. At the conclusion of this activity, you will be reporting your findings to the class.

Here are some suggestions. How many different ways can you make waves move through the slinky? How many waves can you make in the slinky at one time? How big can you make waves? How is the size of a wave related to the number of waves you make at the same time? How are waves related to energy? (Does it take more energy to make more waves?) How does the tension in the slinky affect the waves? (You can increase the tension by gathering some

of the slinky at one end and holding it while you make waves) Do waves have displacement, velocity and acceleration?

Questions:1) You may already know some things about waves. Write down any terms that you associate with waves. Can you define these terms?

2) If you were describing the waves that you made to another person, what are some characteristics of the waves you would use?

3) Draw a picture of one wave.

4) Draw a picture of multiple waves with one line.

Present your finding to the class

Activity 1 Teacher’s Guide:8

The purpose of this activity is to provide students with an opportunity to explore some wave properties on their own without detailed instructions. Various ideas about waves will result from this activity. There is no need to go into depth of any concepts at this point.

Investigations: Students can make transverse and longitudinal waves Students can make more waves by moving the slinky faster Students can affect the amplitude by the distance they move the slinky When smaller waves are generated, the wavelength is shorter Moving your arm faster (more energy) makes more waves Waves travel faster as the tension is increased The waves do not have these properties, but a given point on the spring does

Questions:1) You may already know some things about waves. Write down any terms that you associate with waves. Can you define these terms?

Answers vary

2) If you were describing the waves that you made to another person, what are some characteristics of the waves you would use?

Answers vary

3) Draw a picture of one wave.

4) Draw a picture of multiple waves with one line.

Note: Make sure students keep the slinky on a surface while making waves. When slinky is jerked around vertically in the air it will get kinked and tangled and stretched too far and ruined.

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Activity 2: Wave Characteristics Name: .

Shown above are two waves that are moving from left to right passing the same point P in one second.

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Concept Questions: Refer to Model 1 while answering the following questions about wave characteristics.

1) a) Use a ruler to measure distance ‘a’ in millimeters for both waves.

1b) Compare characteristic length ‘a’ for wave A and B.

2) Measure and compare characteristic length ‘b’ for wave A and B.

3) Define wavelength (a).

4) Define amplitude (b).

5) Identify the number of complete wavelengths shown in the model for both waves.

6) Determine the frequency of each wave by dividing your answer to question 5 by 1 second.

7) Compare the frequencies of wave A and wave B.

8) Write a sentence describing the relationship between the wavelength and the frequency of a wave.

9) In Activity 1 you learned that it took more energy to make more waves, write a statement describing the relationship between frequency and energy.

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Activity 2 Teacher’s Guide

The purpose of this activity is for student’s to define wavelength, wave amplitude and wave frequency.

1) a) Use a ruler to measure distance ‘a’ in millimeters for both waves.

a) 2.5 cm b) 1.3 cm

1b) Compare characteristic length ‘a’ for wave A and B.

Distance ‘a’ is longer in wave A and shorter in wave ‘b’

2) Measure and compare characteristic length ‘b’ for wave A and B.

Distance ‘b’ is shorter in wave A (1.3 cm) and longer in wave B (2.5 cm)

3) Define wavelength (a).

Wavelength is the distance that represents 1 cycle of a wave. The distance between 2 peaks or 2 troughs.

4) Define amplitude (b).

Amplitude is the distance that represents the maximum displacement from the x-axis of the plotted wave.

5) Identify the number of complete wavelengths shown in the model for both waves.

Wave A has 7 cycles, Wave B has 14 cycles

6) Determine the frequency of each wave by dividing your answer to question 5 by 1 second.

Frequency of A: 7 cycles/second or Hertz, B: 14 cycles/second or Hertz

7) Compare the frequencies of wave A and wave B.

The frequency of A is one-half the frequency of B.

8) Write a sentence describing the relationship between the wavelength and the frequency of a wave.

The relationship between frequency and wavelength is inverse. The shorter wavelength has a larger frequency.

9) In Activity 1 you learned that it took more energy to make more waves, write a statement describing the relationship between frequency and energy.

The relationship is direct. The more energy a wave possesses the larger its frequency.

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Activity 3: Wave Interactions Name: .

Purpose: You have recently learned about wave properties. In this activity you will observe the changes in the amplitude of two waves that meet in the middle of a long spring.

Part 1: Making waves

1) Place a 1 meter piece of masking tape on the floor. Measure a distance of 3m away from the center of the first piece of tape and place an identical piece of tape on the floor. Place a third identical piece of tape at 6m from the first piece of tape. Mark the center of each piece of tape. 2) Hold the end of the spring at the center of the 0m tape mark. Have your partner hold the other end of the spring and stretch it to the 6m tape mark and hold it at the center. The third person should sit at the 3m mark and observe the displacement of the spring from the center mark during the activity.

3) Your partner should hold the spring at the center mark at 6m. Using a quick snap movement, move the end of the spring from the center of the tape mark to end of the tape mark and back to the center. This should create a wave that travels down to your partner and back to you. We will call this a transverse wave. Have your partner create a wave in the same way while you hold your end at the center mark. Take some time to practice making transverse waves with the spring until you and your partner can make consistent waves. Record your observations of the displacement along the 3m tape mark. How does the displacement compare to the displacement at the 0m tape mark?

Draw 3 pictures of the wave as it travels down and back.

Part 2: Wave Interaction

4) You and your partner will snap the slinky from the center to the end and back to the center of the tape at the same time and in the same direction. Practice your timing so that the two waves meet in the middle of the spring. The third person will observe the displacement along the 3m tape. Record your observations of the displacement along the 3m tape mark. How does the displacement compare to the displacement at the 0m tape mark?

Draw a picture of the wave before, during and after they meet in the middle.

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Activity 3 Teacher’s Guide:

The purpose of this activity is to observe waves combine in different ways. The next activity will introduce the terms constructive and destructive interference.

3) The student should observe that the displacement/amplitude of the wave is the same at both marks. Friction may cause a slight decrease.

4) The amplitude of the wave should approximately double at the center mark when the two waves combine.

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5) You and your partner will snap the spring from the center to the end and back to the center of the tape at the same time but in the opposite direction. Practice your timing so that the two waves meet in the middle of the spring. The third person will observe the displacement along the 3m tape.

Record your observations of the displacement along the 3m tape mark. How does the displacement compare to the displacement at the 0m tape mark?

Draw a picture of the wave before, during and after they meet in the middle.

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Teacher’s Guide Continued:5) The amplitude should cancel out and be close to zero at the center mark.

Watch it: https://www.youtube.com/watch?v=ypcX1LdmMPM

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https://www.youtube.com/watch?v=ypcX1LdmMPM

Activity 4: Wave Interference Name: .

Sketch Result: Sketch Result:

The model above shows two different ways that waves can interfere with each other.

Concept Questions: 1) Predict how the waves in Set A combine and sketch the result above.

2) Predict how the waves in Set B combine and sketch the result above.

3) Set A represents constructive wave interference. In your own words, define constructive wave interference.

4) Set B represents destructive wave interference. In your own words, define destructive wave interference.

For the following, assume the two waves have the same frequency and velocity.5) On the right, sketch a wave that will destructively interfere with the wave on the left.

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Activity 4: Teacher’s Guide

1) Predict how the waves in Set A combine and sketch the result above.

The waves will combine to form a wave with twice the magnitude.

2) Predict how the waves in Set B combine and sketch the result above

The waves will combine and cancel out.

3) Set A represents constructive wave interference. In your own words, define constructive wave interference.

Constructive interference describes when waves combine that have amplitude in the same direction so that the result is a wave with a larger amplitude than the original waves.

4) Set B represents destructive wave interference. In your own words, define destructive wave interference.

Destructive interference describes when waves combine that have amplitudes opposite directions so that the result is a wave with a smaller amplitude than the original waves.

5) On the right, sketch a wave that will destructively interfere with the wave on the left.

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6) Sketch two waves that are different from the previous drawings that will destructively interfere.

7) Sketch two waves that will only partially experience destructive interference.

8) Sketch a wave that will constructively interfere with the following wave:

9) Two pulse waves are sent through a spring in opposite directions as shown below. Sketch the result of the pulse waves at the instant they combine. Is this constructive or destructive interference?

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Teacher’s Guide

6) Sketch two waves that are different from the previous drawings that will destructively interfere.

Drawings vary

7) Sketch two waves that will only partially experience destructive interference.

Drawings vary8) Sketch a wave that will constructively interfere with the following wave:

9) Two pulse waves are sent through a spring in opposite directions as shown below. Sketch the result of the pulse waves at the instant they combine. Is this constructive or destructive interference?

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10) Two pulse waves are sent through a spring in opposite directions as shown below. Sketch the result of the pulse waves at the instant they combine. Is this constructive or destructive interference.

11) Sketch an original pulse wave pattern and show the result of the combined pulse waves.

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Teacher’s Guide

10) Two pulse waves are sent through a spring in opposite directions as shown below. Sketch the result of the pulse waves at the instant they combine. Is this constructive or destructive interference.

11) Sketch an original pulse wave pattern and show the result of the combined pulse waves.

Drawings vary

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Activity 5: Phet Simulation: Fourier: Making Waves Purpose: In this activity you will use a simulation to learn more about how waves combine through constructive and destructive interference by playing a game.

Play the ‘Wave Game’

1) Open the URL: https://phet.colorado.edu/en/simulations/category/physics/quantum-phenomena2) Open the simulation named: Fourier: Making Waves3) Select the ‘Wave Game’ tab.4) Click and drag the amplitude bar until you match the given wave pattern. 5) When you feel you have mastered level 1, change the level setting to level 2.6) Continue moving up the levels. As you level up you will begin to combine waves. As you do this, think about how the waves are combining through constructive and destructive interference. 7) Continue moving up the levels until you reach the highest level or you run out of time.

Teachers: There are many activities you can do with this simulation. Click the ‘teacher’ link on the page that you used to download the simulator.

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https://phet.colorado.edu/en/simulations/category/physics/quantum-phenomena

Activity 6: Fabric of Space DemonstrationPurpose: As an application of wave interference, we are going to introduce the recent measurement of gravity waves using interferometers. A reasonable question to ask at this point is ‘How can waves move through space?’. To help understand the answer to this question, we are going to observe a model of what is known as the fabric of space. We can think about a cross-section of space as a piece of fabric. When an object is placed into that fabric is creates a distortion we can think of as a depression. The more massive the object is, the deeper the depression will be in the fabric.

The image below shows the sun, a more massive neutron star and an even more massive black hole and their effect on the fabric of space.

When other objects or even light moves through space, they are moving along the contour of this fabric and their paths will follow the contours created by these massive objects.

For example, a planet orbiting the sun would be moving around the curvature in the fabric of space created by the sun.

In our next activity, we will learn how gravity waves are produced, how they move through the space fabric, how they distort Earth and how we detect them using wave interference.

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Teacher’s Guide for the Fabric of Space Activity

1) Set up the tables before class (see instructions below). Practice the demonstrations until you can perform them successfully.

2) Place a 1kg disc in the center of the table fabric.

3) Pick up one marble and hold your hand toward the mass. Roll the marble to your left or right toward the edge of the table so that is slowly spirals toward the mass. Relate this to a less massive object orbiting a more massive object.

4) Take a handful of marble in each of your hands. Roll the marbles in opposite directions away from you. You want the marbles to collide on the other side of the table. At the point when only a few marbles are still moving, all of the marbles can be moving in the same direction. This will not happen each time, so plan on repeating it several times. Discuss how all the matter in a solar systems could have been moving around in all directions at one point in time but eventually settled in one direction.

5) Pick two marbles that are slightly different in mass in one hand. Separate them with your fingers. Release the marbles in an ‘orbit’ with one hand. As the marbles orbit the 1kg mass they may also begin orbiting each other. You may have to repeat this several times. Discuss a planet and its moon orbiting each other as they orbit the sun.

6) Move the 1kg disc off-center and place a second disc about 1-2 feet away from the first disc. Roll one marble at an angle between the discs. Try and get the marble to figure-eight the two discs. This is not easy and takes some practice. Discuss free-return trajectories used by early spacecraft in the Apollo programs.

7) Allow students some time to experiment on their own with the table.

Watch this video to see the live demonstration with an example of a teacher discussion: https://www.youtube.com/watch?v=MTY1Kje0yLg

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https://www.youtube.com/watch?v=MTY1Kje0yLg

Instructions for building fabric table:1) Screw white PVC adaptor onto the grey T-connector(picture a). There are eight of these.

a) b) c) d) 2) Push a PVC with green paint into each of the eight white adaptors. (pic b)3) Push the PVC T-connector onto the other side of each PVC pipe with green paint. (pic c)4) Connect a red pipe to one side of each grey connector. The red pipes are in the tube that came outside the box(pic d)5) Connect four of the red pipes together by laying them out on the floor. Repeat for second table. (pic e)

e) f) g) 6) Connect the free ends together by slowly bending the red pipes and stand the table up (pic f). This is much easier with 2-4 people helping.7) Connect four PVC pipes painted with red ends to four-way PVC connector and lay on floor in middle of table (pic g)8) Connect T-connector on bottom of each leg to the X shaped base piece (pic h)9) Drape fabric several inches over red pipe and secure with J-hook (pic i)10) Pull fabric across the table to opposite side so that the material is tight and not sagging down and secure with another J-hook (pic j).

h) i) j) 28

11) Attach fabric to other 2 sides of table with 2 more J-hooks so that the fabric is not sagging down in the center.Add additional J-hooks until there are 3 hooks per section of red pipe. (pic K)

k) l) 12) Place a weighted disc in the center of the fabric to create the curvature. If you need additional weight for the second table, you can use a medium sized water filled balloon.

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Activity 7: What is an interferometer and how it works The same beam of light is split into two coherent beams that each travel an equal path to a different mirror and back before coming back to combine and form a constructive interference fringe at the screen. In an interferometer one of the mirrors is able to be adjusted forward or backwards, which cause a difference in path length of the two beams of light. In order to change constructive interference to destructive interference the overall path length of must change by 2/ג since the light will take this path there and back to make an overall phase shift between the beams of 2/ג (2ΔL = ג/

2).

In general the total distance one of the mirrors is shifted can be measured as a multiple of the number of times that the interferometer interference pattern shifts from constructive to destructive interference or vice-versa (2ΔL = m 2/ג ).

https://www.youtube.com/watch?v=RzZgFKoIfQIThe video shows the actual LIGO interferometer with a good demonstration of its components and how they work.

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https://www.youtube.com/watch?v=RzZgFKoIfQI

https://www.youtube.com/watch?v=4GbWfNHtHRg

Explains idea of gravitational waves and the need to measure light with interferometer to show the stretching and compressing of space by the gravitational wave since any measurement tool would also be stretched and compressed by the gravitational wave.

https://www.youtube.com/watch?v=j-u3IEgcTiQ

This video shows how changing the length of one of the two arms on an interferometer causes the interference of recombining the split laser beam to change. The length of the two paths goes from constructive interference when the difference in the lengths of the path is a whole number multiple of the wavelength of the laser light to destructive interference when the difference in the length of the path is a half integer multiple of the wavelength. The demonstration is done by turning a screw that changes the length of one of the path by micrometers, but in the LIGO experiment the two perpendicular paths are identical length until the compression in one dimension and stretching in the other dimension changes the interference pattern.

https://www.sciencenews.org/article/gravitational-waves-explained

This video shows the signature signal recorded showing evidence of the creation of a gravitation wave created as two black holes closely orbited each other before coming together. It also emphasizes that all accelerating objects create gravitational waves, but that it takes a very, very massive event to produce waves that are big enough to be measured above the background noise of other vibrations that shake the detector.

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https://www.sciencenews.org/article/gravitational-waves-explained


https://www.youtube.com/watch?v=4GbWfNHtHRg


Activity 8: Determining Fundamental Units Name:

Materials:Electronic balance (not provided)Sealed envelopes numbered 1-30Computer with Microsoft Excel or other spreadsheet software(if computers are not available, students can create graphs on paper or one graph can be sketched on board)

Procedures: Evenly distribute the 30 envelopes out to different groups to weigh. Create a data table and graph in Excel or write data on the white board.

Analysis: 1.) What patterns do you notice about the class data? Do you have any suggestions to better organize the data?

2.) Obtain one of the envelopes labeled with an asterisk (*). Measure the mass of the envelope and use your data to determine where it fits in with the other data..

3.) Determine the increase in mass between the similar groups of envelopes. In the space below, explain how you arrived at your answer.

4.) What is your best estimate for the mass of the envelope? In the space below, explain how you arrived at your answer.

5.) Based on your data, do you think that an identical envelope could have a mass value of 12.0 grams? Justify your answer.

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Activity 8 Teacher’s GuideAnalysis: 1.) What patterns do you notice about the class data? Do you have any suggestions to better organize the data?

At first glance there is no obvious patterns in the data. Guide the students to group all of the envelopes with the same weight. There are several specific increases in the weights. Each increase in the weight is about the same. Ideally, it would be exactly the same but humidity in the air changes the weights of the envelopes.

2.) Obtain one of the envelopes labeled with an asterisk (*). Measure the mass of the envelope and use your data to determine where it fits in with the other data. Record your data and calculations below. Then check with your teacher to see if you were correct. See above3.) Determine the increase in mass between the similar groups of envelopes. In the space below, explain how you arrived at your answer.

4.) What is your best estimate for the mass of the envelope? In the space below, explain how you arrived at your answer.Answers vary but the envelope weighs around 3.28g5.) Based on your data, do you think that an identical envelope could have a mass value of 12.0 grams? Justify your answer.

No, only certain weights are allowed because the weight increases in multiples of 3.5 grams. There is no way to make 12 grams with these fundamental units.

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6.) The mass values in this lab were “quantized” because the additional mass in the envelopes was limited to using only whole numbers increments of the amount you determine in step 3. Based on the results of this lab, how would you define “quantized”.

7.) Is mass in “real life” quantized? Explain your answer.

Extension:

Show Video: Millikan Oil Drop Experiment

https://www.youtube.com/watch?v=XMfYHag7Liw

8.) In 1909, Robert Millikan performed a famous experiment with charged oil drops to measure the charge of an electron. Each oil drop contained at least one extra electron to cause unbalanced charge. Although Millikan did not know how many extra electrons were on each drop, he measured the unbalanced charge on many drops and used this data to determine the charge of a single electron. Suppose that the measurements listed below represent the charges of some of the oil drops used by Millikan. Based on this data, what is the charge on an electron?

1.6 x 10-19 C

3.2 x 10-19 C

4.8 x 10-19 C

6.4 x 10-19 C

9.) According to your results from Question #8, what would a charge of .8 x 10 -19 C represent? Do you think it is possible for a particle to exist with this amount of charge?

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Teacher’s Guide Continued:

6.) The mass values in this lab were “quantized” because the additional mass in the envelopes was limited to using only whole numbers increments of the amount you determine in step 3. Based on the results of this lab, how would you define “quantized”.

Quantized mass means that the weight can only increase and decrease in fixed quantities. Masses in between these fixed values are not allowed or possible.

7.) Is mass in “real life” quantized? Explain your answer.

Yes. Matter is made of fundamental particles that have quantized masses.

Extension:

Millikan Oil Drop Experiment


8.) In 1909, Robert Millikan performed a famous experiment with charged oil drops to measure the charge of an electron. Each oil drop contained at least one extra electron to cause unbalanced charge. Although Millikan did not know how many extra electrons were on each drop, he measured the unbalanced charge on many drops and used this data to determine the charge of a single electron. Suppose that the measurements listed below represent the charges of some of the oil drops used by Millikan. Based on this data, what is the charge on an electron?

1.6 x 10-19 C3.2 x 10-19 C4.8 x 10-19 C6.4 x 10-19 C

1.6 x 10-19 C, the charge of an electron is quantized, therefore, each charge value is a multiple of the fundamentally smallest value.

9.) According to your results from Question #8, what would a charge of .8 x 10 -19 C represent? Do you think it is possible for a particle to exist with this amount of charge?

This would represent half of the fundamental unit (charge of electron) and is not possible because energy is quantized and must be integer multiples of the fundamental unit.

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Activity 9: Mathematical Relationships in Electromagnetic Waves: Name:

1) Based on your observations in Activity 2, complete the following statement:

As the wavelength of a wave decreases, the frequency of the wave _________________________________.

Is the relationship between wavelength and frequency directly proportional or inversely proportional?

Table 1: Show below are sample data from electromagnetic waves in a vacuum tube.

Wavelength (m) Frequency (s-1) Speed (m/s)1.0 3.0x108

6.0x10-3 5.0x1010

5.0x10-7 6.0x1014

2.0x10-12 1.5x1020

2) For each row in the table 1, combine the wavelength and frequency values in a way that will give the speed of the waves. Think about the units.

3) Based on the data table 1, what is the value of the speed of the waves?

4) Using the symbols λ (wavelength), v (frequency), and c (speed), write an equation that is consistent with the data in the table above.


As the frequency of a wave increases, the energy of the wave _________________________________.

Is the relationship between the frequency and the energy of the wave directly proportional or inversely proportional?

Show below are sample data from electromagnetic waves in a vacuum tube.

Frequency (s-1) Energy (J) Constant (J·s)3.0x108 1.98x10-25

5.0x1010 3.3x10-23

6.0x1014 3.96x10-19

1.5x1020 9.9x10-14

6) For each row in the table above, combine the frequency and energy values in a way that will give a constant value with the unit J·s.

7) Based on the data in the table, what is the value of the constant?

8) Using the symbols f (frequency), E (energy) and h (Planck’s constant), write an equation that is consistent with the data in the table above.

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Mathematical Relationships in Electromagnetic Waves: Teachers Guide


As the wavelength of a wave decreases, the frequency of the wave increases.

Is the relationship between wavelength and frequency directly proportional or inversely proportional?

Inversely proportional

2) For each row in the table 1, combine the wavelength and frequency values in a way that will give the speed of the waves.

All values are 3.0x108m/s

3) Based on the data table 1, what is the value of the speed of the waves?

3.0x108m/s

4) Using the symbols λ (wavelength), f (frequency), and c (speed), write an equation that is consistent with the data in the table above.

λ·f = c


As the frequency of a wave increases, the energy of the wave increases.

Is the relationship between the frequency and the energy of the wave directly proportional or inversely proportional?

Directly proportional

6) For each row in the table above, combine the frequency and energy values in a way that will give a constant value with the unit J·s.

All values are 6.6x10-34J·s

7) Based on the data in the table, what is the value of the constant?6.6x10-34J·s

8) Using the symbols f (frequency), E (energy) and h (Planck’s constant), write an equation that is consistent with the data in the table above.

E=hf

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9) A wave of red light has a wavelength of 6.5x10-7m. Calculate the frequency and energy of the red light using the equations you wrote in questions 4 and 8.

10) A wave of green light has a wave length of 5.1x10-7m. Calculate the frequency and energy of the green light.

11) A wave in the ultraviolet spectrum has a wave length of 2.5x10 -7m. Calculate the frequency and energy of the ultraviolet wave.

12) A cell phone uses a wave with a frequency of 8.0x108 s-1 or 800 MHz (Megahertz). Calculate the energy of this wave.

13) Use your answers to 9, 10 and 11 to compare the energy of red, green and UV light.

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9) A wave of red light has a wavelength of 6.5x10-7m. Calculate the frequency and energy of the red light using the equations you wrote in questions 4 and 8. 4.6x1014s-1 and 3.0x10-19J

10) A wave of green light has a wave length of 4.5x10-7m. Calculate the frequency and energy of the green wave.

5.9x1014s-1 and 3.9x10-19 J

11) A wave in the ultraviolet spectrum has a wave length of 2.5x10 -7m. Calculate the frequency and energy of the ultraviolet wave. 1.2x1015 s-1 and 8.0x10-19 J

12) A cell phone uses a wave with a frequency of 8.0x108 s-1 or 800 MHz (Megahertz). Calculate the energy of this wave.

5.3x10-25 J

13) Compare the energy of red, green, and UV light. Green light is more energetic than red and UV is more energetic than green light.

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Demonstration 1: Discharge an electroscope using UV light source

Purpose: This demonstration with help students understand that electrons can absorb energy from radiation. Electrons can be ionized from metal, if the radiation is sufficiently energetic.

Materials:Electroscope Balloon UV source Red/Green laser pointer

Procedure:1) Touch the discharged balloon to the electroscope to show that the electroscope parts are not moving.2) Charge the balloon by rubbing it on your arm hair or head.Ask the students what is happening during this process. Through discussion, establish that the balloon is being charged during this process. Ask students how a net charge could be created on the balloon. Establish the idea that the balloon is made of atoms which are made up of subatomic particles and that electrons are particles that more easily removed and transferred between atoms. Students will have to accept that electrons are moving onto the balloon from the hair. Adding negative electrons to the balloon creates a net negative charge on the balloon. 3) Charge the balloon and touch the charged balloon to the electroscope zinc plate so that the rod inside the electroscope is displaced from its neutral (vertical) position.Ask the students what causes the electroscope . The rod is displaced because it now has a negative charge.Ask the students how the electroscope rod became charged. Electrons moved from the balloon onto the electroscope. Electrons spread out over the electroscope giving all of its parts a negative charge.4) Ask the students to predict the result of shining a red laser pointer on the zinc plate of the electroscope.With the electroscope charged, shine a red laser pointer on the zinc plate. (Nothing happens)Caution: Do not shine the lasers at eyes and do not look at light directly reflected from surfaces the laser is projected onto. Only the instructor should use the laser pointer. Do not leave the laser out in room where student may find and use the laser.5) Ask the students to predict the result of shining UV light on the zinc plate. With the electroscope charged, shine a UV light on the zinc plate.(The electroscope discharges. This works best with shorter UV radiation. If the electroscope is not discharging, gently scuff the round zinc plate on top with some coarse sand paper.)Do not look at the UV light source or reflective surfaces being exposed to the UV source. Only the instructor should use the UV source. Do not leave UV source out in room where student may find and use the UV source.Ask the students what would cause the electroscope to move back to the uncharged position. Establish that adding electrons charged the electroscope so removing electrons would discharge it. Ask students why the red light did not cause the electroscope to discharge and the UV did cause a discharge.(The UV light is more energetic than the red light. The red light did not provide enough energy to remove the electrons from the electroscope)

In the next activity we will use a simulation to investigate these observations in more detail.

If you need help, watch this video: https://www.youtube.com/watch?v=z-3XaXCvjZw

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https://www.youtube.com/watch?v=z-3XaXCvjZw

Activity 10: Photoelectric Effect Simulation Name: .

1) Open: https://phet.colorado.edu/en/simulation/legacy/photoelectric2) Start simulator. Open the three graphs on the right side of the simulator.3) Use the pull down menu to change the metal to zinc which is the metal used in our electroscope.4) Set the wavelength of light to about 650 nm which is visible red light like the light produced by our laser pointer.5) Set the intensity to 50%. You should now see red light coming from the source and directed at a zinc plate. The zinc plate is located inside a vacuum tube with another metal plate on the opposite side of the tube. The plates are connected in a circuit with an ammeter and a battery. What do you observe happening?

6) Slowly shorten the wavelength until you observe something happening. Record your observation.

At which wavelength are electrons ejected from the zinc metal?

Is this consistent with what you observed with the electroscope?

Based on your observations, what causes the electrons particles to become ejected from the zinc?

7) Set the wavelength of the UV at 240nm. Investigate the effect of changing the intensity. Observe the current value and the graphs. The current will increase as more electrons are ejected over time. Intensity is a measurement of the number of UV photons striking the zinc plate at a given time.Record your findings.

Observe the graph of intensity and current. Describe the relationship between the intensity of light and the current.

Observe the frequency vs kinetic energy graph. What is the effect of the light intensity on the kinetic energy of the electrons?

8) Repeat step 7 with the 650 nm red light. Record your findings.

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https://phet.colorado.edu/en/simulation/legacy/photoelectric

Activity 10 Teacher’s Guide:5) Set the intensity to 50%. You should now see red light coming from the source and directed at a zinc plate. The zinc plate is located inside a vacuum tube with another metal plate on the opposite side of the tube. The plates are connected in a circuit with an ammeter and a battery. What do you observe happening?

Nothing is happening

6) Slowly shorten the wavelength until you observe something happening. Record your observation. At which wavelength are electrons ejected from the zinc metal?Is this consistent with what you observed with the electroscope?Based on your observations, what causes the electrons particles to become ejected from the zinc?

Particles are moving from the zinc across the vacuum tube. ~250 nm Yes the radiation that causes electrons to be ejected is in the UV range Radiation of sufficient energy are giving electrons energy to be ejected

7) Set the wavelength of the UV at 240nm. Investigate the effect of changing the intensity. Observe the current value and the graphs. The current will increase as more electrons are ejected over time. Intensity is a measurement of the number of UV photons striking the zinc plate at a given time.Record your findings.Observe the graph of intensity and current. Describe the relationship between the intensity of light and the current. Observe the frequency vs kinetic energy graph. What is the effect of the light intensity on the kinetic energy of the electrons?

Increasing the intensity causes more electrons to be ejected as shown by the increase in current. The graph is linear with a positive slope so there is a direct relationship The kinetic energy is not affected by the intensity

8) Repeat step 7 with the 650 nm red light. Record your findings.

Nothing happens

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9) Set the wavelength back at 240 nm with 50% intensity. Slowly decrease the wavelength while observing the frequency(f) of wave verses kinetic energy(KE) of electrons graph. Describe the graph curve.

Write a mathematical equation for the graph curve in terms of y, m, x and b.

Identify the y and x variables in the equation.

The slope represents Planck’s constant, h. Use data from the graph to calculate the value of Planck’s constant.

Convert your slope value into Joules using the conversion 1 Joule = 6.242x1018 electron volts.

The y-intercept, b, is known as the work function, Φ. The work function is the energy required to ionize an electron on a piece of metal. In chemistry this value is the ionization potential or ionization energy of an electron.Write the mathematical equation in terms of KE, f, h and Φ.

The energy of a photon of light is given by the formula, Ephoton=hf.Write your mathematical equation with Ephoton.

Based on the equation you wrote, when will the ejected electron have no kinetic energy?

10) Change the metal from zinc to sodium. Find the maximum wavelength that causes electrons to be ejected from sodium atoms. Record your finding.

How do the energy of these photons compare to the energy of the photons of light required to eject electrons in zinc?

Does sodium have a larger or smaller work function than zinc? Explain. 11) Find the maximum wavelength that causes electrons to be ejected from the other metals on the list. Record your findings.

Rank all of the metals in increasing order of work function. You can do this by finding the point on the x-axis where the electrons first obtain energy. The closer the point is to the y-axis, the smaller the work function.

12) Predict the position of the unknown metal (?????) in the series above.

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9) Set the wavelength back at 240 nm with 50% intensity. Slowly decrease the wavelength while observing the frequency(f) of wave verses kinetic energy(KE) of electrons graph. Describe the graph curve. Write a mathematical equation for the graph curve in terms of y, m, x and b.Identify the y and x variables in the equation.The slope represents Planck’s constant, h. Use data from the graph to calculate the value of Planck’s constant. Convert your slope value into Joules using the conversion 1 Joule = 6.242x1018 electron volts.The slope represents Planck’s constant, h.The y-intercept, b, is known as the work function, Φ. The work function is the energy required to ionize an electron on a piece of metal. In chemistry this value is the ionization potential or ionization energy of an electron.Write the mathematical equation in terms of KE, f, h and Φ.The energy of a photon of light is given by the formula, Ephoton=hf.Write your mathematical equation with Ephoton.

Based on the equation you wrote, when will the ejected electron have no kinetic energy?

The graph is linear y=mx+b y-variable is kinetic energy (KE), x-variable is frequency (f) 10 eV/(3^15-0.6^15 Hz)=4.16^-15 eV·s ; 4.16^-15/6.242^18=6.68x10-34J·s KE=hf – Φ, the work function value is negative KE=Ephoton- Φ When the photon energy is equal to the work function

10) Change the metal from zinc to sodium. Find the maximum wavelength that causes electrons to be ejected from sodium atoms. Record your finding.How do the energy of these photons compare to the energy of the photons of light required to eject electrons in zinc?Does sodium have a larger or smaller work function than zinc? Explain.

Electrons are ejected around 500nm and current is shown around 450nm These photons have longer wavelengths and are less energetic The work function must be a smaller quantity because less energetic photons cause ejection

11) Find the maximum wavelength that causes electrons to be ejected from the other metals on the list. Record your findings. Rank all of the metals in increasing order of work function. You can do this by finding the point on the x-axis where the electrons first obtain energy. The closer the point is to the y-axis, the smaller the work function.

Smallest: Na→Ca→Zn→Cu→Pt

12) Predict the position of the unknown metal (?????) in the series above.

The unknown falls between Ca and Zn

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Teacher Discussion Notes after students have completed the Photoelectric Effect Simulation:

What this experiment demonstrates about light?Wave theory incorrectly predicted that the kinetic energy of the ejected electrons would increase as the intensity of the light increased.

The experiment shows that, at a given frequency, the kinetic energy of the electrons is constant as the intensity changes.

Wave theory predicted that electrons would gradually gain energy from light until it had enough energy to ionize. This means that lower energy radiation over time would eventually cause ejection. This is not what we observed. Low energy light is incapable of ejecting electrons even at high intensity and long periods of time.

The experiment shows that electrons are ejected instantaneously when light of sufficient wavelength is used. This supports the idea that energy is delivered in an instant by the light to the electrons in fixed amounts or quantities. This quantity of energy would need to be delivered by a particle of light or a photon.

Light is behaving as particles. Each particle of light has a quantity of energy. Each particle of light that collides with an electron delivers its energy to that electron. This energy is described by the equation, Ephoton=KE+Φ=hf.

Electrons will be ejected if the photon energy is larger than the work function (a negative value).

If the energy of the photon is larger than the work function, the additional energy will become the electrons kinetic energy.

If all of the photons are delivering the same amount of energy, all of the electrons ejected will have the same kinetic energy.

Increasing the intensity of the photons causes more electrons to collide with photons resulting in more electrons being ejected with the same kinetic energy.

Energy can only be delivered in multiples of the quantity, hf. Energy is known to be quantized. A quanta of energy is equal to hf.

When the wavelength of light is changed, the frequency and the energy of the photon are also changed. Shorter wavelengths have higher frequencies and energies. Higher energy photons will give the ejected electrons greater kinetic energy. Energy is quantized, so the energy of the electrons will increase in fixed amounts. E = hf or 2hf or 3hf …… nhf where n is a positive integer.

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Optional: Ripple Tank Wave DemonstrationPurpose: Students are most familiar with water waves. It is helpful to show students the diffraction properties of water waves before we demonstrate the wave properties of light. This can be done with a ripple tank or by showing a few videos:

Ripple Tank Wave Interference: https://www.youtube.com/watch?v=-8a61G8Hvi0

Series of 5 videos: https://www.youtube.com/watch?v=y53z2zVipAs&list=PLFE829A78F461BD20

Video 1 reviews wavelength and amplitude

Video 2 reviews frequency

Video 3 demonstrates wave diffraction. We suggest you show the first 35 seconds of this video before you begin Activity 9 to help students understand wave diffraction. Stop the video and allow students to investigate the factors that affect the diffraction of waves using the PhET simulations. After students complete the simulations, you can finish the video for reinforcement.

Video 4 and 5: Diffraction Patterns of Light. Show your live demonstrations before you view this video. Show this video if you have problems with your demonstration or for reinforcement.

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https://www.youtube.com/watch?v=y53z2zVipAs&list=PLFE829A78F461BD20

https://www.youtube.com/watch?v=-8a61G8Hvi0

Activity 11: Diffraction of Waves Name _________ __ When a rock is thrown into a pond it causes ripples in the water. These are transverse waves which means that the water oscillates up and down, but the water molecules are not carried outward with the wave. The waves carry the energy of the disturbance radially outward.

The Huygen-Fresnel Principle states that every point on an outward moving circular ripple (wavefront) can be treated like a point source creating its own wavelet. The individual wavelets move outward, and tangent to all of these wavelets a new wave front is created like in the diagram to the left.

Generating a plane wavefront like in the image below that is straight rather than curved requires a large number of point sources in a line that are all oscillating in phase with one another. This could be accomplished in water by moving a board up and down to produce a straight wavefront moving away parallel to the board. Each point on the new wavefront then acts like a point source to produces its own wavelets. Tangent to the wavelets a new wavefront is then formed.

This treatment of wavefronts as being composed of an infinite number of point sources helps explain how wavefronts diffract when they go around a barrier or through an opening in a barrier.

If light traveled through a slit in the barrier with no diffraction, light would only be observed directly behind the slit (a). If light diffraction occurs, the light will spread out will be observed outside of the area directly behind the slit. The light will be most intense directly behind the slit but can also be observed moving outward from that point. Diagram (c) includes the wavelets created by the point sources on each wavefront to show how each successive wavefront diffracts farther into the shadow zone of the wall.

(a)(b)

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(c)

Open the PhET Wave Interference Simulation: https://phet.colorado.edu/en/simulation/wave-interference

Instruction for simulation:-Click on the “Light” tab. -Click ‘Show Screen’-Click ‘Show Intensity’-Click on “One Slit” on the toolbar on the right. Move the ‘Barrier Location’ slide bar to the second mark to the

right of the zero.-Observe the intensity graph

a.) Is the intensity graph consistent with diagram (a) or (b) shown above? What does this indicate about light diffraction?

b.) Change the red light (lower frequency) to blue (higher frequency). Did the diffraction increase or decrease? (The greater the diffraction, the lower the intensity directly behind the slit)

Write a statement that relates the frequency of the light to the amount of diffraction.

c.) Use the Huygen-Fresnel Principle that any point on a wavefront can be viewed as a new point source to justify the diffraction pattern as the frequency increases?

c.) Why can you hear your friend yelling from around the corner even though you cannot see him? Both light and sound are waves that diffract, and so why is there a difference?

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https://phet.colorado.edu/en/simulation/wave-interference

Diffraction of Waves – Teacher’s Guide

a.) Is the intensity graph consistent with diagram (a) or (b) shown above? What does this indicate about light diffraction?(b) The intensity of the light is dispersed and not only observed in one area directly behind the slit

b.) Change the red light (lower frequency) to blue (higher frequency). Did the diffraction increase or decrease? (The greater the diffraction, the lower the intensity directly behind the slit)

The intensity directly behind the slit increased indicating there is less diffraction in the blue light.

Write a statement that relates the frequency of the light to the amount of diffraction. As the frequency increases (shorter wavelength), the amount of diffraction decreases

c.) Use the Huygen-Fresnel Principle that any point on a wavefront can be viewed as a new point source to justify the diffraction pattern as the frequency increases?

At higher frequencies there are fewer point sources and wavelets which decreases the diffraction of the light

c.) Why can you hear your friend yelling from around the corner even though you cannot see him? Both light and sound are waves that diffract, and so why is there a difference?

Low frequency waves with large wavelengths, like sound, diffract much more than high frequency waves with short wavelengths, like light. Higher frequency waves more directional than low frequency waves.

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Additional Teacher Resources for Wave Diffraction:

The following short video does a good job of summarizing the factors that affect the amount of diffraction, and it could be used to review or clarify the concept the following day.

1.) Diffraction increases as the slit width decreases (as long as the slit is big enough for the wave to move through the opening).2.) Diffraction decreases and the frequency of the wave increases.

Apertures and Wave Diffraction (2:39)https://www.youtube.com/watch?v=BH0NfVUTWG4&t=38s

Another good summary video of both slits to pass through and barriers to move around. It also mentions briefly why we can hear someone talking around a corner even if we cannot see them.Bozeman Science – Wave Diffraction (4:19)https://www.youtube.com/watch?v=1bHipDSHVG4

This video is longer, but there are a few short clips within it which show animations of breaking the wavefronts into point sources that produce wavelets, which recombine into new wavefronts that will diffract as they pass through a slit or around a barrier.Mindset Learn – Huygen’s Principle (14:41)https://www.youtube.com/watch?v=zGpoi-Y65JM

This is a diagram taken from Hyperphysics that could be used to ask a follow up question about why an observer is able hear low frequency sounds sooner than high frequency sounds when they are approaching from around the corner.http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html

Follow up question

http://www.princeton.edu/~rvdb/images/Questar/PoissonSpot.html

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http://www.princeton.edu/~rvdb/images/Questar/PoissonSpot.html

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html

https://www.youtube.com/watch?v=zGpoi-Y65JM

https://www.youtube.com/watch?v=1bHipDSHVG4

https://www.youtube.com/watch?v=BH0NfVUTWG4&t=38s

Activity 11 Part 2: Double Slit Interference of Waves Name :


1.) Set up Instructions for simulation:-Click on “Light” on the top left tab.-Click on “Reset All,” and click “Yes” on the pop up screen to reset all of the settings.-Slide the “Wavelength” bar on the left to the dark blue color.-Slide the “Amplitude” bar on the left all of the way to the right to produce maximum amplitude.-Click on “Double Slit” on the right toolbar.-Slide the “Slit Width” bar to one mark to the right of 0nm.-Slide the “Barrier Location” bar to two marks to the right of 2590nm.-Slide the “Slit Separation” bar to one mark to the right of 1750nm.-Click on “Show Screen.”-Click on “Intensity Graph” when it pops up after clicked “Show Screen.”

a.) Draw what appears on the screen and the position vs. intensity graph on the diagram.

b.) Explain why this pattern appeared on the screen.

2.) Slide the “Barrier Location” bar to one mark to the left of 2590nm, and give the simulation a few seconds to produce the new pattern.

a.) Draw what appears on the screen and the position vs. intensity gap on the diagram.

b.) What is different about this pattern compared to the pattern in problem number one?

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Activity 11 Part 2: Double Slit Interference of Waves – Teacher’s Guide


1.) Set up Instructions for simulation:

a.) Draw what appears on the screen and the position vs. intensity graph on the diagram.

b.) Explain why this pattern appeared on the screen.

The wavefronts reached the double slit barrier. All of the wavefront was blocked except for the parts in front of the openings. The unblocked portions went through the barrier and hit the screen directly across from the openings creating two bright spots.

Question #1 Result

2.) Slide the “Barrier Location” bar to one mark to the left of 2590nm, and give the simulation a few seconds to produce the new pattern.

a.) Draw what appears on the screen and the position vs. intensity gap on the diagram.

b.) What is different about this pattern compared to the pattern in problem number one?

The new pattern has seven smaller bright spots instead of two larger bright spots.

Question #2 Result

c.) What is weird about this pattern?

The fact that there are more bright spots than holes in the barrier means that light is not simply passing through the barrier and striking the screen across from the opening. Diffraction could explain the widening of the bright spots, which is how the light bright spots are across the screen, but diffraction does not explain why there are dark spots within the pattern. Why does light appear to skip over some parts of the screen?

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c.) What is weird about this pattern?3.) Change the wavelength of light to determine how it changes the separation of the bright and dark fringes. Use the “Wavelength” slide bar on the left.

4.) Change the distance between the slits (see diagram to left) and record how it changes the separation of the bright and dark fringes. Use the “Slit Width” slide bar on the right toolbar. Be aware that if d is too big the interference pattern will disappear when the waves no longer overlap.

5.) Change the distance between the double slit barrier and the screen (L) and record how it changes the separation of the bright and dark fringes. Use the “Barrier Location” slide bar on the right toolbar. Be aware that if L is too small the interference pattern will disappear when the waves no longer overlap.

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Teacher’s Guide Continued: 3.) Change the wavelength of light to determine how it changes the separation of the bright and dark fringes. Use the “Wavelength” slide bar on the left.

Increasing wavelength increases the space between the dark and bright fringes.

4.) Change the distance between the slits and record how it changes the separation of the bright and dark fringes. Use the “Slit Width” slide bar on the right toolbar. Be aware that if d is too big the interference pattern will disappear when the waves no longer overlap.

Increasing the distance between the slits decreases the space between the dark and bright fringes.

5.) Change the distance between the double slit barrier and the screen and record how it changes the separation of the bright and dark fringes. Use the “Barrier Location” slide bar on the right toolbar. Be aware that if L is too small the interference pattern will disappear when the waves no longer overlap.

Increasing the distance between the slits and the screen increases the space between the dark and bright fringes.

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Notes: Explanations of light interference in the double slit experiment:

Whether it is water, sound, or light when scientists see an alternating pattern of bright and dark spots with more bright spots than holes in the barrier they think of wave interference, and they call it an interference pattern. In problem number one there was no interference pattern because the waves did not

diffract enough for the waves to overlap and interfere with one another, like in the image below. When the waves from the two slits overlap and interfere with one another you will see a checkered pattern, like in the middle of the image to the right.

To understand how wave interference causes the bright and dark spots on the screen we need to go back to the concept of wave addition that we used with the interferometer. The addition of the waves can produce a bright spot from

constructive interference when the waves are completely in phase, and the addition of the waves can produce a dark spot from destructive interference when waves are 180o out of phase with each other.

The waves are in phase with one another when they pass through the double slit barrier. Each wave travels the same distance to the middle of the screen, and so the waves are still in phase to give constructive interference at the center. However, the waves travel different distance to different parts of the screen, which causes them to arrive out of phase. The waves are still arriving at the screen at the dark spots, but they are 180o out of phase, which cancels the disturbance of each wave to create no net disturbance. Locations between the middle of the bright and dark spots are not completely in or out of phase. This means that there will be a smaller amount of constructive or destructive interference to produce a different level of disturbance at the screen.

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Teacher’s Guide Explanations of Simulation Results in Activity 11 Part 2

increasing L increases space between bright and dark spots yincreasing wavelength increases space between bright and dark spots yincreasing slit separation d decreases space between bright and dark spots ydsinƟ = path difference = r2 – r1 = mג sinƟ = y/Ly = mגL/d

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Activity 11 Part 3: Reviewing Classical Wave Addition Name:

Open the Quantum Wave Interference Simulation: https://phet.colorado.edu/en/simulation/quantum-wave-interference

1.) Click on the “2 Lasers” tab at the top left of the simulation.a.) Turn on the laser on the left, and record what happens on the screen

then turn the laser off.

b.) Turn on the laser on the right, and record what happens on the screen then turn the laser off.

c.) Predict if there will be an interference pattern if you turn on both lasers at the same time.

d.) Turn on both lasers, and record what happens.

e.) What do you need to change to change the result of part d?

f.) Change that variable, and record the results of doing the experiment.

Part A

Part B

Part D

Part F

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https://phet.colorado.edu/en/simulation/quantum-wave-interference

Activity 11 Part 3: Reviewing Classical Wave Addition – Teacher’s Guide 1.) Click on the “2 Lasers” tab at the top left of the simulation.

a.) Turn on the laser on the left, and record what happens on the screen then turn the laser off. There is a bright spot across the screen with the highest intensity directly in front of the source to the left.

Part A:

b.) Turn on the laser on the right, and record what happens on the screen then turn the laser off. There is a bright spot across the screen with the highest intensity directly in front of the source to the right.

Part B:

c.) Predict if there will be an interference pattern if you turn on both lasers at the same time.Students may predict yes or no. The waves will diffract enough to overlap since the sources are close enough, and so

students may lean towards believing that there will be an interference pattern.

d.) Turn on both lasers, andrecord what happens. There is not an interference pattern created by the two sources.

Part D:

e.) What do you need to change to change the result of part d?The waves must have the same wavelength to create an interference pattern. In other words the light must be

monochromatic (the same color) for the waves to create destructive interference.

f.) Change that variable, and record the results of doing the experiment.

Be careful to slide the “Gun Controls,” which selects the wavelength of the laser, to the same location for each gun. If the wavelengths are slightly off, the waves will not interfere with one another. Once the waves are the same wavelength they will create an interference pattern on the screen that has regions of destructive interference which creates dark spots.

Part F:

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2.) Click on the “High Intensity” tab at the top left of the simulation.a.) Turn on the laser. Record the pattern on the screen, and explain why

it is there.

b.) Click on “Potential Barriers” on the toolbar on the right, and then click “Add Barrier.” Slide the barrier directly above the laser and near to the screen at the top. Record the pattern on the screen, and explain why it is there.

c.) Slide the barrier directly above the laser and near to the laser at the bottom. Record the pattern on the screen, and explain why it is there.

Part A

Part B

Part C

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Teacher’s Guide Continued:2.) Click on the “High Intensity” tab at the top left of the simulation.

a.) Turn on the laser. Record the pattern on the screen, and explain why it is there. The light spreads out across the screen with the highest intensity directly in front of laser. The light diffracts because it is a wave, which means that every point on the wavefront can be thought of as a point source that form new wavelets that sum together to form a new wider wavefront in front of the source further down as the wave propagates. The brightest area is directly in front of the source since it is the shortest distance away and intensity decreases as the wave spreads out.

Part A:

b.) Click on “Potential Barriers” on the toolbar on the right, and then click “Add Barrier.” Slide the barrier directly above the laser and near to the screen

The light spreads out again, but the barrier blocks the wavefront in the middle, which creates a bright spot on each side of the barrier. The barrier is too close to the screen for the divided wavefront to overlap after the barrier, which means that there is no diffraction pattern.

Part B:

c.) Slide the barrier directly above the laser and near to the laser at the bottom. Record the pattern on the screen, and explain why it is there.

The light spreads out again, but the barrier blocks the wavefront in the middle. A diffraction pattern which includes a bright spot directly in front of the barrier is formed on the screen because the divided parts of the wavefront overlap before getting to the screen.

Part C:

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3.) Instructions to set up simulation: -Click on the “X” on the barrier to remove it. -Click on “Double Slits” on the right toolbar. -Slide the “Slit Width” bar to the middle. -Slide the “Slit Separation” bar all the way to the right to push the slits apart.

a.) Slide the “Vertical Position” bar all the way to the left to raise the slits. Record the pattern on the screen, and explain why it is there.

b.) Slide the “Vertical Position” bar all the way to the right to lower the slits. Record the pattern on the screen, and explain why it is there.

Part A:

Part B:

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3.) Instructions to set up simulation:

a.) Slide the “Vertical Position” bar all the way to the left to raise the slits. Record the pattern on the screen, and explain why it is there.

The light spreads out again, but the barrier blocks the wavefront except through the slits. A bright spot forms in front of each slit, but there is no diffraction because the barrier is too close to the screen for the divided wavefront to overlap after the slits.

Part A:

b.) Slide the “Vertical Position” bar all the way to the right to lower the slits. Record the pattern on the screen, and explain why it is there. The light spreads out again, but the barrier blocks the wavefront except through the slits. A diffraction pattern which includes a bright spot directly in front of the barrier is formed on the screen because the divided parts of the wavefront overlap after the slits before getting to the screen.

Part B:

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Teacher Demonstration: Double Slit Laser Light Interference PatternPurpose:

The purpose of this demonstration is to show students a light diffraction pattern similar to the ones they observed in the previous computer simulation.

Materials: Laser pointer pen Double Slit Slide

Procedure:

Shine the red laser through the double slit and project the image onto the wall. You can mount the laser and the slide on some ring stands with transparent tape.The pattern will show up better with the lights off.Note: There are three other single slits on the slide. The larger single slit will not produce the interference pattern. The two larger single slits will produce an interference pattern.

Note: After the next simulation students may want to know what the significance of the double slit verses a single slit since both slits produce the pattern. You can tell them that only the double slit will produce an interference pattern when single electrons are passed through the barriers.

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Notes: And Then . . . It Got Weird – The Quantum World What is the big deal? Waves spread out (diffract) as they move because the Huygen-Fresnel Principle which

states that each point of the wavefront can be viewed as a point source creating its own expanding wavelet.

A wave can interfere with another wave with the same wavelength if the waves overlap, or a wave can interfere with itself when barriers block part of its wavefront and the divided parts of the wavefront later overlap each other. When the overlapping waves hit a screen there will be a series of bright and dark spots (an interference pattern) that corresponds to constructive and destructive interference between the waves. How many more simulations are you going to make us do? We get it.

Scientists are thorough, and it is important to test theories in extreme cases to see if the theory is supported by the new data or if a new theory is needed. For example, Newton’s 2nd Law (ΣF = ma) matches experimental data very well at day to day speeds, but as you approach the speed of light it changes from a linear relationship between force and acceleration to an asymptote that requires an infinite amount of force to have any change in speed.

Testing the boundaries of the double slit experiment includes firing one photon at a time at the slit rather than multiple photons at the same time, which would obviously prevent the photons from interfering with each other. Each individual photon that was not blocked by the barrier would either pass through one slit or the other.

DeBroglie’s Idea:

As a result of the photoelectric effect, photons were found to have properties of particles. Photons behaved as particles colliding and delivering quantized amounts of energy to electrons. An important property of objects colliding is their momentum. Momentum is the product of an objects mass and velocity. At the time a mathematical relationship for the momentum of a photon had been formulated: p=h/λ.

A scientist by the name of Louis De Broglie had proposed an important question. If photons have particle-like properties, do particles also have wave-like properties? He rearranged the equation above in the following ways:

or λ is wavelength in metersh is Planck’s constant: 6.63x10-34J·sm is mass in kilogramsν is velocity in meters per second

Derivation: For photons moving near the speed of light: E2=m2c4+ p2c2

m=0 for photons of light: E2=p2c2 or E=pc=mc2

E=hc/ λ =pc → h/ λ =p → h/p = λ

De Broglie suggested that if this relationship works for photons, it could also work for things like subatomic particles. How can we test this idea? Scientist would need to do a double slit experiment with particles.

Predict what pattern should show up on the screen when one electron at a time is fired.

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Activity 11 Part 4: Particles passing through the double slit https://phet.colorado.edu/en/simulation/quantum-wave-interference

1.) Instructions to set up simulation:-Click on the “Single Particles” tab at the top left of the simulation.-Click on “Double Slits” on the right toolbar.-Slide the “Slit Width” bar to the left to decrease the slit size.-Slide the “Slit Separation” bar all the way to the right to push the slits apart.-Slide the “Vertical Position” bar all the way to the right to lower the slits.

a.) Click “Fire” on the laser. Record observations of what happens.

b.) Click “Auto Repeat” in the Gun Controls box, and record observations after a few photons.

c.) Click “Rapid” next to the stop button at the bottom of the simulation, and record observations after a minute of observation.

d.) Does the data support your prediction? Be specific about what was expected or unexpected.Firing photons through one at a time came up with a really weird result, which did not match the classical view

of the world. Scientists wanted more information, and so they decided to put detectors at the slits so that they could know which slit each photon was passing through on its way to the screen.

2.) Instructions to set up simulation:-Click on the “High Intensity” tab at the top left of the simulation.-Click on “Double Slits” on the right toolbar.-Slide the “Slit Width” bar to the left to decrease the slit size.-Slide the “Slit Separation” bar all the way to the right to push the slits apart.-Slide the “Vertical Position” bar to the middle.

a.) Turn the gun on. Record observations of what happens.

b.) Click on both the detector on the left slit and the detector on the right slit on the right toolbar, and record observations of what happens.

c.) What is strange about the result to part b?

Part A:

Part B:

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Activity 11 Part 4 Teacher’s Guide:Predict what pattern should show up on the screen when one electron at a time is fired.

Since there were no other photons to interfere with after passing through the slit the result of sending through many photons one at a time should be two bright spots directly across from the slits. Scientists would have additional support for the theory that individual photons had a distinct path that went through one single slit and hit the screen at on one specific location on the screen. The diffraction pattern only emerged from photons interacting with each other.

Now it is time to test the prediction. Open the Quantum Wave Interference Simulation: https://phet.colorado.edu/en/simulation/quantum-wave-interference

1.) Instructions to set up simulation:

a.) Click “Fire” on the laser. Record observations of what happens.A hazy plume goes up through both slits, but only one single dot appears somewhere random on the screen.

b.) Click “Auto Repeat” in the Gun Controls box, and record observations after a few photons.A new dot shows up on the screen at different random locations each time a photon is fired.

c.) Click “Rapid” next to the stop button at the bottom of the simulation, and record observations after a minute of observation.

Each individual photon shows up at a random place, but the randomness seems to be broken up by regions where few to no hits are made on the screen.

d.) Does the data support your prediction? Be specific about what was expected or unexpected.The interference pattern that contains regions without hits is surprising because there were no other photons to interfere with since only one photon was fired at a time.

Firing photons through one at a time came up with a really weird result, which did not match the classical view of the world. Scientists wanted more information, and so they decided to put detectors at the slits so that they could know which slit each photon was passing through on its way to the screen.

2.) Instructions to set up simulation:-Click on the “High Intensity” tab at the top left of the simulation.-Click on “Double Slits” on the right toolbar.-Slide the “Slit Width” bar to the left to decrease the slit size.-Slide the “Slit Separation” bar all the way to the right to push the slits apart.-Slide the “Vertical Position” bar to the middle.

a.) Turn the gun on. Record observations of what happens.An interference pattern forms on the screen containing bright and dark spots.

b.) Click on both the detector on the left slit and the detector on the right slit on the right toolbar, and record observations of what happens.

The interference pattern goes away, and an unbroken band of intensity is shown on the screen.

c.) What is strange about the result to part b?Nothing about the experiment was changed except that there were observations made about which slit each photon passed through. The result was influenced by observation.

Part A:

Part B:

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You can get the same result if you do this experiment is the “Single Particle” part of the simulation, but the result is a little more difficult to see since the single particle simulation only shows number of hits rather than average intensity on the screen.

Since the world was already showing signs of being very different from what we observe in every day life Louis De Broglie thought that there might be symmetry between waves and particles. He proposed that since light was able to exhibit particle and wavelike properties a particle like an electron might exhibit wavelike properties.

3.) Begin with the same settings as you ended with in problem 2.

a.) To shoot electrons click on the drop down menu above the gun controls panel and click “Electrons.” Record observations of what happens.

b.) Turn off the detectors by clicking “Detector on Left Slit” and “Detector on Right Slit.” Record observation of what happens.

You can get the same results in the simulation with neutrons and helium atoms which are much more massive than electrons.

Part A:

Part B:

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3.) Begin with the same settings as you ended with in problem 2.

a.) To shoot electrons click on the drop down menu above the gun controls panel and click “Electrons.” Record observations of what happens. There is a continuous spot across the screen.

b.) Turn off the detectors by clicking “Detector on Left Slit” and “Detector on Right Slit.” Record observation of what happens. An interference pattern is created.

You can get the same results in the simulation with neutrons and helium atoms which are much more massive than electrons.

Part A:

Part B:

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Activity 12: Palm Pipes Name:If you bang the open end of a piece of PVC pipe against the palm of your hand, you’ll make a musical sound. Play with the pipes. What property of the pipes determines the pitch?

Explain the relationship:

Note

Length (cm) Frequency (Hz)

CDEFGA

15.814.012.511.810.59.4

523587659698784880

Mary Had a Little Lamb (C, D, E, G)E D C D E E E D D E E G GE D C D E E E E D D E D C

Twinkle, Twinkle, Little Star (C, D, E, F, G, A)C C G G A A G F F E E D D CG G F F E E DG G F F E E DC C G G A A G F F E E D D C

Oh Susanna (C, D, E, F, G, A)C D E G G A G E C D E E D C DC D E G G A G E C D E E D D CF F A A A G G E C DC D E G G A G E C D E E D D C

Farmer in the Dell (C, D, E, G, A)G C C C C CD E E E E EG G A G E CD E E D D C

London Bridge (C, D, E, F, G, A)G A G F E F GD E F E F GG A G F E F GD G E C

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Teacher’s Guide: Activity 12: Palm PipesIf you bang the open end of a piece of PVC pipe against the palm of your hand, you’ll make a musical sound. Play with the pipes. What property of the pipes determines the pitch?

The length of the pipe.

Explain the relationship:

The longer the length, the lower the pitch.

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Teacher’s Guide: Activity 12: Palm PipesWhat’s Going On?

When you hit the open end of the pipe against your hand, air molecules in the bottom of the tube are squeezed together. This starts a process that takes four trips up and down the tube.

The molecules that have been squeezed together, in turn, squeeze the molecules next to them, and so on. In a sort of domino effect, the pulse of compression (high-pressure air) travels up the tube. When the pulse of compression reaches the top of the tube, it expands outward into the air around the tube. In the process, some air molecules overshoot the end of the tube, producing a region of expansion (low-pressure air) in the top of the tube.

Air molecules just below the area of expansion rush upward to fill it, creating a pulse of expansion that travels back down the tube. When this pulse reaches the bottom, it reflects off your palm and travels back up the tube as another pulse of expansion.

When it reaches the top, some air from outside the tube rushes into the low-pressure area, creating an area of compression, which travels as another pulse back down the tube. When this pulse of compression reaches the palm of your hand, it reflects, and at this point the whole process repeats itself.

A pulse that starts at your palm as a compression makes four complete transits of the tube (up as a compression, down as an expansion, up as an expansion, and down as a compression) before one whole cycle is completed. This four part cycle corresponds to one wavelength of a sound, or one single vibration. A series of these repeated cycles is the source of the sound you hear when you “play” one of the pipes.

The length of the tube affects the note that the tube produces. Because the speed of sound waves is the same in all the tubes, the length of the tube has a direct effect on the time it takes

for a compression-expansion pulse to make its four transits of the tube. The longer it takes for a pulse to complete its cycle and start over again, the fewer the cycles, or vibrations, per second. The fewer the vibrations per second, the lower the frequency of the sound, and the lower the musical note. Thus long tubes produce lower notes, and short tubes produce higher notes.

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Fundamental Frequency and Overtones

Speed is defined as the distance traveled per unit time. If a wave travels a distance equal to one wavelength, the time elapsed is equal to the period (T) of the wave. Period (T) is actually the time for one complete vibration of a wave.

Thus, for a wave, the speed is equal to the wavelength (ג) divided by the period (T). v = ג / T

But period (T) is the reciprocal of frequency (f). Frequency tells us how many waves/vibrations there are per

unit time. So, substituting the period in the equation by T = 1/f, we get v = ג f. Sound waves are longitudinal or compressional waves, which means that the wave form consists of compressions are rarefactions as shown below.

In a palm pipe, the air molecules in the bottom of the tube are squeezed together as you hit the pipe against your palm. The compression pulse travels up, reflects from the open end as an expansion, the expansion reflects from your hand, then if reflects from the open end as a compression, and the process repeats.

The repetition of this process results to standing sound waves. Since the pipe is closed on one end and open on the other end, the wave profile will look like the figure below where there is maximum displacement at the open end. At the fundamental frequency (first harmonic), the length of the pipe is ¼ of the wavelength.

Since L = 4 / ג

Solving for ג would give us 4 = ג L

1.) If you substitute 4 = ג L into v = ג f, what would be the formula for the wave speed (v)?

2.) Choose one of the palm pipes and calculate the wave speed, which is the speed of sound.

3.) Using the value of the speed of sound calculated in #2, what would be the frequency of sound produced in a 30.0cm palm pipe?

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Teacher’s Guide: Fundamental Frequency and Overtones:

Since L = 4 / ג

Solving for ג would give us 4 = ג L

1.) If you substitute 4 = ג L into v = ג f, what would be the formula for the wave speed (v)? v = 4L f

2.) Choose one of the palm pipes and calculate the wave speed, which is the speed of sound.

v = 4L f so v = 4 (23.6cm) (349cycles/s) = 32,945.6cm/s or roughly 329.5m/s.

3.) Using the value of the speed of sound calculated in #2, what would be the frequency of sound produced in a 30.0cm palm pipe?

v = 4L f so let’s round off 32,945 as 33,000cm/s then 33,000cm/s = 4 (30cm) f or 33,000cm/s = 120cm f divide both sides by 120cm. Then 275cycles/s = f or f = 275 hertz.

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Since L = 3 4 / ג

Solving for ג would give us 4 = ג L / 3

4.) If you substitute 4 = ג L / 3 into v = ג f, what would be the formula for the wave speed (v)?

5.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 1 st overtone?

Since L = 5 4 / ג


6.) If you substitute 4 = ג L / 5 into v = ג f, what would be the formula for the wave speed (v)?

7.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 2 nd overtone?

Since L = 7 4 / ג


8.) Draw the wave inside the tube for the 3rd overtone.

9.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 3rd overtone?

Since L = 9 4 / ג


10.) Draw the wave inside the tube for the 4th overtone.

11.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 4 th overtone?

12.) Spend a minute and write down a general relationship for determining the frequency of any general overtone.

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Since L = 3 4 / ג


4.) If you substitute 4 = ג L / 3 into v = ג f, what would be the formula for the wave speed (v)? v = 4L f / 3

5.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 1 st overtone?v = 4L f / 3 so f = 3v / 4L = 3(33,000cm/s) / 4(30cm) = 825 cycles/s or 825 hertz

Since L = 5 4 / גSolving for ג would give us 4 = ג L / 5

6.) If you substitute 4 = ג L / 5 into v = ג f, what would be the formula for the wave speed (v)? v = 4L f / 57.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 2 nd overtone?v = 4L f / 5 so f = 5v / 4L = 5(33,000cm/s) / 4(30cm) = 1,375 cycles/s or 1,375 hertz

Since L = 7 4 / גSolving for ג would give us 4 = ג L / 7

8.) Draw the wave inside the tube for the 3rd

overtone.

9.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 3rd overtone?v = 4L f / 7 so f = 7v / 4L = 7(33,000cm/s) / 4(30cm) = 1,925 cycles/s or 1,925 hertz

Since L = 9 4 / ג


10.) Draw the wave inside the tube for the 4th overtone.

11.) Using the same 30cm palm pipe with the same speed of sound found in #2, calculate the frequency of the 4 th overtone?

v = 4L f / 9 so f = 9v / 4L = 9(33,000cm/s) / 4(30cm) = 2,475 cycles/s or 2,475 hertz

12.) Spend a minute and write down a general relationship for determining the frequency of any general overtone.f1 = v / 4L, f3 = 3v / 4L = 3f1, f5 = 5v / 4L = 5f1, f7 = 7v / 4L = 7f1 General Equation = nv / 4L where n = 1,3, 5, odd integers

Taken from Exploratorium: http://www.exo.net/~donr/activities/Palm_Pipes_Plus_Tunes.pdf

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http://www.exo.net/~donr/activities/Palm_Pipes_Plus_Tunes.pdf

Demonstrations: Standing Waves and HarmonicsPerform the ‘Singing Rod’ Demonstration.

The purpose of this demonstration is to show students that certain points along the rod have no displacement. We will call these points ‘nodes’.

Use the instruction included. You need to practice this beforehand.

Watch it: https://www.youtube.com/watch?v=EYhwKve0MZU

Video of a rod that is not included but interesting and related: https://www.youtube.com/watch?v=sIw0Fh-fXIM

Perform the ‘Standing Wave’ Demonstration

The purpose of this demonstration is to show the students standing waves.

Assemble the machine and connect the battery. A standing wave can now be observed. Change the length of the string to produce a standing wave with a different number of nodes. You need to practice with this machine beforehand. If you have an adjustable strobe light, you can light up the string with the strobe light so that it appears to be static. Refer back to the ‘Singing Rods’ and how there were standing waves and nodes along those rods.

Watch it: https://www.youtube.com/watch?v=Y4zTHbxwpFMStrobing the string: https://www.youtube.com/watch?v=a2qSL_JIeOc

Perform the ‘Sound/Whirly Tube’ Demonstration.

The purpose of the demonstration is to show students that only certain ‘allowed’ wavelengths are able to generate sounds inside the tube. Wavelengths in between the ‘allowed’ cannot exist and do not make sounds.Only specific wavelengths can exist inside the tube.

Hold the sound tube at one end.Whirl the free end of the sound to in a circle. Slowly increase the speed of the whirling so that all of the tones are heard.

Watch it: https://www.youtube.com/watch?v=CuGnsW0ysrA

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https://www.youtube.com/watch?v=CuGnsW0ysrA

https://www.youtube.com/watch?v=a2qSL_JIeOc

https://www.youtube.com/watch?v=Y4zTHbxwpFM

https://www.youtube.com/watch?v=sIw0Fh-fXIM

https://www.youtube.com/watch?v=sIw0Fh-fXIM

https://www.youtube.com/watch?v=EYhwKve0MZU

Activity 10: Particle in a 1-D Box Name:

a) b)

a) A one-dimensional box that contains an electron. The sides of the box are separated by the distance L. The depth of the well is defined by the potential energy of the particle which has a range of 0→∞. The electron cannot escape the box. The potential energies, U1, U2, and U3 are shown on three different axis that are separated vertically for clarity. The separations are not shown to scale. This box will show the wave functions of the electron. A wave function, Ψ, is a mathematical description of the shape of the wave. The principle quantum number, n, represents the energy of the electron.

b) A one-dimensional box containing electrons that will show the probability densities of the electron (square of the wave functions) with three different energies.

Concept Questions: As you answer the following questions, imagine the electron exists as a standing wave with nodes at the sides of the box.1) On the dashed line, Ψ1 U1, sketch the simplest wave function for an electron that shows the wave contained in the box. 2) Write an expression for the wavelength of this wave in terms of L: ______________3) Write a statement that describes the relationship between the energy and the wavelength of a wave.

4) On the dashed line, Ψ2 U2, sketch the next wave function that shows the wave contained in the box. This will represent the electrons at a different energy.5) Write an expression for the wavelength of this wave in terms of L: ______________

6) Compare the wavelengths and the energies of the first two wave functions for the electron.

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Activity 10 Teacher’s Guide:

Concept Questions:1) On the dashed line, U1, sketch the simplest wave function for an electron that shows the wave contained in the box.

2) Write an expression for the wavelength of this wave in terms of L:

λ=2L

3) Write a statement that describes the relationship between the energy and the wavelength of a wave.

Shorter wavelengths are more energetic

4) On the dashed line, U2, sketch the next wave function that shows the wave contained in the box. This will represent the electrons at a different energy.

See picture above

5) Write an expression for the wavelength of this wave in terms of L: ______________

λ=L

6) Compare the wavelengths and the energies of the first two wave functions for the electron.

The second wavelength is shorter and more energetic

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7) On the dashed line, Ψ3 U3, sketch the next wave function that shows the wave contained in the box.

8) Write an expression for the wavelength of this wave in terms of L: ______________

9) Compare the wavelengths and energies of the electron with this energy to the electron with the second energy described.

10) Predict three different wavelengths that will show the wave contained in the box. _________________ ___________________ ____________________

11) Sketch the square of the wave functions you drew in box (a) in box (b). Use a different axis for each sketch.

12) The square of the first wave function is shown below (label the y-axis Ψ2).

Use your pencil to shade the area representing the probability density of the electron.Label the following:The most probable location for the electron.The place(s) where the electrons cannot be found (nodes).

13) The square of the second wave function is shown below (label the y-axis Ψ2).:

Use your pencil to shade the area representing the probability/probabilities density of the electron.Label the following:The most probable location(s) for the electron.The place(s) where the electrons cannot be found.

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7) On the dashed line, U3, sketch the next wave function that shows the wave contained in the box.See picture above

8) Write an expression for the wavelength of this wave in terms of L: ______________λ=2L/3

9) Compare the wavelengths and energies of the electron with this energy to the electron with the second energy described.

The third wavelength is shorter and more energetic10) Predict three different wavelengths that will show the wave contained in the box.

Some possible answers: λ=L/2, L/3, L/411) Sketch the square of the wave functions you drew in box (a) in box (b). Use a different axis for each sketch.

12) The square of the first wave function is shown below:

Use your pencil to shade the area representing the probability density of the electron.Label the following:The most probable location for the electron.The place(s) where the electrons cannot be found.13) The square of the second wave function is shown below:


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14)The square of the third wave function is shown below (label the y-axis Ψ2).:


15) In the box below, sketch a wave that cannot fit in the box (label the y-axis Ψ2)..

16) Estimate the principle quantum number for the wave you sketched. 17) Do you agree with the following statement? Explain.

An electron in a 1-D box can have any amount of energy.

18) How does the particle in a box support the idea of quantized energy?

Reinforcement: Open the Phet simulation ‘Quantum Bound States’: https://phet.colorado.edu/en/simulation/legacy/bound-states1) Reduce the width of the box to 0.5 nm.2) Click on each of the three energy level lines and observe the probability densities for each.3) Select the wave function button to the right and click the play button. Click each of the energy level lines to observe each wave function.

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https://phet.colorado.edu/en/simulation/legacy/bound-states

14)The square of the third wave function is shown below:


15) In the box below, sketch a wave that cannot fit in the box.

One Possible Answer:

16) Estimate the principle quantum number for the wave you sketched.

n=1.75

17) Do you agree with the following statement? Explain.

An electron in a 1-D box can have any amount of energy.

Electrons can only have integer value of n for their energies (n=1,2,3,4….)

18) How does the particle in a box support the idea of quantized energy?

Quantized energy occurs in fixed amounts. Only standing waves that have nodes at the boundaries of the box fit in the box. The position of these nodes depends on the wavelength and therefore the energy of the particles. Therefore, particles can only have certain allowed amounts of energy.

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Activity 10 Extension: Notes: Probabilities of Electrons in Hydrogen Atoms:

As you learned in the previous activity, squaring the wave function of an electron in a box gives a probability density which helps you understand where an electron can and cannot exist and where it is most likely to exist. Electrons in atoms have wave functions or mathematical descriptions of the shapes of the wave. For example:

http://electron6.phys.utk.edu/phys250/modules/module%203/hydrogen_atom.htmSquaring these wave functions produces probability densities in the space around the nucleus of the hydrogen atom. These probability densities in atoms are known as orbitals. In this activity we will examine some of the basic orbitals in hydrogen atoms.

We have established that electrons in atoms have different energy values and those energies are quantized. The energy of electrons is defined by the principle quantum number. You have already learned about the principle quantum number, n, which can have positive integer values (n=1,2,3,4…). The second quantum number is known as the angular momentum number, . The angular momentum number can have values from 0 to n-1. We will look at the first four values of which are 0, 1, 2 and 3. Together the principle and angular momentum quantum numbers produce a probability density known as an orbital. We will examine four types of orbitals known as s, p, d and f. These letters are abbreviations of the mathematical terms spin, principle, diffuse and fundamental. The mathematics (see paragraph 1) are beyond the scope of this discussion so we will use some graphs and images to understand the shapes of these orbitals.

The following are probability densities of electrons in hydrogen atoms. Neutral hydrogen atoms have only 1 electron which allows us to ignore the effects of electron-electron interactions within atoms. The lowest energy state for an electron in the hydrogen atom is known as the 1s orbital (n=1, =0). There is one s-type orbital for each value of the principle quantum number (1s, 2s, 3s ….). The probability density is shown below (left) with a two dimensional rendering (right) where the axis intersect is the nucleus and the blue points are probable positions of electrons around the nucleus:

The diagrams indicates that the probability begins at zero at zero angstroms from the nucleus, reaches a maximum at a distance of about 0.5 angstroms and reaches zero again around 3 angstroms. In three dimensions, this would produce a spherically-shaped orbital. (1 angstrom = 10-10m)

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http://electron6.phys.utk.edu/phys250/modules/module%203/hydrogen_atom.htm

The next orbital is the 2s orbital (n=2, =0). The probability density is shown below (left) with a two dimensional rendering (right):

The diagrams indicates that the probability begins at zero at zero angstroms from the nucleus, increases around 0.5 angstroms, reaches zero at around one angstrom, reaches a maximum at a distance of about 3 angstroms and reaches zero again around 8 angstroms. In three dimensions, this would produce a spherically-shaped orbital with a node in the middle.

The next orbital is the 2p orbital (n=2, =1). The probability density is shown below (left) with a two dimensional rendering (right):

p-type orbitals have two lobes on either side of the nucleus with nodes at the nucleus and around 8 angstroms from the nucleus. There are three p-type orbitals for each principle quantum number beginning with n=2 (2p, 3p, 4p….). One of each pair of the three lobes is oriented along the x-axis, y-axis and z-axis. The following may help you visualize the three p-type orbitals.

The next type of orbital is the d-type orbital ((n=3, =2). There are five d orbitals for each n value beginning with n=3 (3d, 4d, 5d, 6d….). The shapes of the five d-type orbitals are shown below.

There are other types of orbitals in hydrogen atoms. A different type of orbital exist with each increasing value of the angular momentum quantum number. The numbers and shapes of these orbitals quickly become more complex and will not be shown. See more about orbitals: https://en.wikipedia.org/wiki/Atomic_orbital

Watch a video: https://www.youtube.com/watch?v=K-jNgq16jEY

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https://www.youtube.com/watch?v=K-jNgq16jEY

https://en.wikipedia.org/wiki/Atomic_orbital

Demonstration Activity 11: Light emitted by Hydrogen atoms

Purpose: Students will observe the line spectra produced by hydrogen atoms. Students will relate their observations to the idea of quantized energy in the atoms.

Materials: Gas Tube Light Socket Hydrogen gas lamp Spectrascopes C-Spectra Squares

Procedure:1) Pass out C-Spectra squares. Have students look at room lights through the squares.Give each student a spectra scope and explain how to use it. Have students observe the ceiling lights in your room. They should observe a continuous spectrum.2) Turn the room lights off and the hydrogen lamp on. Have the students observe the line spectra of hydrogen. The C-spectra squares are easier for students to use. The spectroscopes have a scale inside that will give a rough estimate of the wavelength of light. 3) Turn the lights back on.

You can repeat this with the helium gas tube to show that each element has a unique line spectrum.

Concept questions for discussion:1) What did you see when you looked at the light coming from the hydrogen atoms?2) The lamp socket provided electricity to the hydrogen lamp. What could the electricity be doing to the hydrogen atoms?3) Based on your previous activities, what could happen to an electron in an atom if it gained energy?4) Do we know if electrons are ionized by the lamp?

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Teacher’s Guide Activity 11: Light emitted by Hydrogen atoms

Concept questions for discussion:1) What did you see when you looked at the light coming from the hydrogen atoms?

2) The lamp socket provided electricity to the hydrogen lamp. What could the electricity be doing to the hydrogen atoms?

Electricity could be increasing the energy of the particles in the hydrogen gas

3) Based on your previous activities, what could happen to an electron in an atom if it gained energy?

Electrons can ionize from the atoms

4) Do we know if electrons are ionized when the lamp is on?

Not enough evidence

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Activity 12: Electron Energy in Hydrogen Atoms Name: .

After observing the line spectra of hydrogen, the scientist Niels Bohr proposed that the electron in hydrogen atoms can have different energies and that the energies are quantized. Bohr used the principal quantum number, n, to describe the energy of the electron in hydrogen. The principal quantum number has positive integer values (n=1,2,3….∞). The potential value on the right is obtained by using the formula: E=(-13.6 eV)/n2

If a charge is moving in the direction that it would normally move, its electric potential energy is decreasing. The electron would move toward the nucleus because opposite charges attract. Negative electrons are attracted to the positive nucleus.The ground state describes the lowest energy state of the electron and the ionization potential is the energy state of an electron that has separated from the nucleus.

Concept Questions:1) What is the lowest potential energy value an electron can possess in a hydrogen atom?

2) What is the highest potential energy value an electron can possess in a hydrogen atom?

3) When an electron is in a state higher than its ground state it is described as being in an excited state. Which principal quantum numbers in the picture represent excited states in a hydrogen atom?

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Teacher’s Guide: Activity 12 Electron Energy in Hydrogen Atoms

Concept Questions:1) What is the lowest potential energy value an electron can possess in a hydrogen atom?

n=1, -13.6V

2) What is the highest potential energy value an electron can possess in a hydrogen atom?

n=∞, 0V

3) When an electron is a state higher than its ground state it is described as being in an excited state. What principal quantum numbers in the picture represent excited states in a hydrogen atom?

n=2,3,4,5,6

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4) If an electron in the ground state gained energy, what could happen to the electron other than ionization?

5) If an electron in an excited state returned to the ground state, what would happen to the energy?

6) Where would the lost energy go and how would that energy be transported? Think about what you learned in the ‘Photoelectric Effect’ activity.

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4) If an electron in the ground state gained energy, what could happen to the electron?

It could exist in an excited state

5) If an electron in an excited state returned to the ground state, what would happen to the energy?

The energy the electron gained to become excited would be lost.

6) Where would the lost energy go and how would that energy be transported? Think about what you learned in the ‘Photoelectric Effect’ activity.

The energy lost could be delivered out of the atom in the form of a photon particle in the same way that

it is delivered to the electron in the photoelectric effect.

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Activity 12: Electron Energy in Hydrogen Atoms Name: .

Type of Radiation UV Visible InfraredWavelength Range (nm) 100-400 400-700 700-1800

The Lyman series shows the wavelength of photons emitted from electrons in hydrogen atoms as they lose energy transitioning between excited states (n=2,3,4,5,6) and the ground state (n=1).The Balmer series shows the wavelength of photons emitted from electrons in hydrogen atoms as they lose energy transitioning between excited states (n=3,4,5,6) and the ground state (n=2).The Paschen series shows the wavelength of photons emitted from electrons in hydrogen atoms as they lose energy transitioning between excited states (n=4,5,6) and the ground state (n=3).Wavelength is related to the difference in electron energy by the following formula: λ=hc/∆E

Concept Questions:7) Write a statement that describes the relationship between wavelength and energy.

8) Which type of radiation is made up of photons possessing the largest energies?

9) Which energy transition is the most energetic? (n=1 to n=2 or n=2 to n=3 …)

10) Which energy transition is the least energetic?

11) If you were looking at electrons transitioning from n=3 to n=2, what would you observe? (yellow light, UV …)

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7) Write a statement that describes the relationship between wavelength and energy.

As the wavelength decreases, the energy increases

8) Which type of radiation is made up of photons possessing the largest energies?

Ultraviolet

9) Which energy transition is the most energetic?

n=6→n=1; 94 nm is the shortest wavelength 10) Which energy transition is the least energetic?

n=4→n=3; 1875nm is the longest wavelength

11) If you were looking at electrons transitioning from n=3 to n=2, what would you observe?

Red light

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12) Can you observe the Lyman series with your eyes? Explain.

13) Do hydrogen lamps emit photons from the Paschen series? Explain.

14) Which series would you be able to observe with your eyes?

15) When you observed the line spectra, why did you see a line(s) of violet color?

16) Why don’t you see a yellow line in hydrogen’s spectrum?

17) Based on the model shown above, explain the spectral lines you observed when you looked at the hydrogen lamp.

18) Explain how your observations in this activity support the idea that electron energies are quantized.

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12) Can you observe the Lyman series with your eyes? Explain.

No, these photons are in the ultraviolet range

13) Do hydrogen lamp emit photons from the Paschen series? Explain.

Possibly, the radiation will be in the infrared range. We would need an IR detector

14) Which series can you observe with your eyes?

Balmer series, the wavelengths are in the visible range

15) When you observed the line spectra, why did you see a line(s) of violet color?

One of the emissions, 410nm, is in the violet color range

16) Why don’t you see a yellow line in hydrogen’s spectrum?

None of the energy transitions produce a photon with the energy and wavelength in the range of yellow

17) Based on the model shown above, explain the spectral lines you observed when you looked at the hydrogen lamp.

Four of the energy transitions produce photons with energy and wavelength values in the visible spectrum. These photons produce the visible light we see in the hydrogen spectrum.

18) Explain how your observations in this activity support the idea that electron energies are quantized.

Electrons in hydrogen atoms only have certain allowed energies. When electrons lose energy they emit photons possessing the energy difference between the energy levels. Because energy levels are quantized, only certain wavelengths are emitted producing the line spectrum. If electrons could have any energy, photons emitted would also have all energies and the spectrum would be continuous.

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