This is the teacher guide for this lesson. A student-focused guide to assist learners as they perform the activity is available.
Created by Allyson Endsley from Noun Project
Teacher Guide
Dancing matter
Mapping the quantum world with light
How can we visualize the atoms that make up all of the matter in our universe?
- Laser pointer
- Compression springs of the same or similar length(s) (at least 28, less than 1 mm width and at least 25 mm long)
- Ping-pong balls (at least 11)
- Cardboard base plate or board
- Thin black fabric
- Graph paper (at least 17 x 17 in. — okay to print out four 8.5 x 11 in. sheets and tape them together into a 17 x 22 in. rectangle). Teachers have noted that large chart paper can work as well.
- Two pieces of velcro
- Small craft mirror piece (side lengths of 1 or 2 in.)
- Hot glue and glue gun (or super glue)
- Duct tape for quick fixes
- Additional compression springs: Some springs ∼20 mm shorter than the ones used in the crystal model, some ∼20 mm longer
- Additional ping-pong balls
- Any speaker system where, when you turn the volume up, you can place your hands on it and feel it vibrating, and it can be connected to a phone/computer. This can be used for generating pure Lissajous figures (extension activity 3)
- Ringstand or equivalent to attach laser
This kit provides materials for one crystal structure and three “photons”. If your budget allows, teachers have said that having one crystal structure for every six students works best. See Figure 2 below for ideas on how to set up different crystal structures. Teachers find that hot glue works better than super glue when creating crystal structures and photons. Sanding the ping pong balls before gluing may help.
- Total time45 min
- Education levelGrades 6 - 10
- Content AreaQuantum physics
- Educational topicCrystals, atoms, light, sound
Over the past century, crystallography has been fundamental to the development of many scientific fields, and 14 Nobel prizes have been given for work in this area. It is also notable that unlike in most of the physical sciences, which women were often systematically excluded from, many of the foundational contributions to crystallography came from women (credit, however, continued to largely be given to male collaborators).
Kathleen Lonsdale and Isabel Knaggs used X-ray diffraction to study the structure of benzene. Isabella Karle and her husband pioneered a novel method for analyzing crystals, and helped revolutionize drug design. Elizabeth Wood looked at crystals with interesting electric, magnetic and superconductive properties, and worked hard to make science accessible to the public. Dorothy Hodgkin was a Nobel Prize-winning chemist who used X-ray crystallography to determine the molecular structure of penicillin, vitamin B12, and insulin. Perhaps most famously, Rosalind Franklin’s X-ray diffraction work demonstrated the double helix structure of DNA.
Crystallography
In X-ray diffraction experiments, scientists study the atomic structure of crystals, which are any materials where the atoms are arranged in orderly, repeating patterns. Beams of X-rays are shone on a crystal sample, which causes the beam to change direction and split into many smaller beams as it passes through the sample (see Figure 1). By studying the pattern the scattered beams make on a detector, scientists can work out the atomic structure of the sample.
At an atomic level, the photons that make up the X-ray beam are scattering (deflecting or bouncing) off the atoms that make up the crystal. In the ocean, water is displaced and moves up and down in a repeating pattern — an oscillation. For light, the oscillation comes from electric and magnetic fields that oscillate and propagate together through space. . These oscillations for X-rays happen faster than we can see - at 3x1019 times per second. These electromagnetic wave packets can interact with atoms!
Figure 1. Constructive and destructive interference of two identical X-ray waves in two different crystals.
When X-ray beams (which are electromagnetic waves) are scattered from two nearby atoms and overlap they may interfere constructively, which means the peaks of the two waves align (see Figure 1). When this occurs they will combine to form an even brighter/bigger wave and will create a bright spot on the detector. If the two beams combine and interfere destructively (the peaks of one wave overlap with the low points of the other) they will cancel each other out and no light will reach the detector. How the waves interfere (and thus whether a bright spot appears on the detector) is determined by the spacing between the atoms, the wavelength of the X-ray beams, and the angle between the X-ray beams and the atoms in the sample. In Figure 1, X-rays with the same wavelength are shown hitting two crystals that differ only by the spacing between the atoms. In one case the scattered waves from nearby atoms line up and you get constructive interference, while in the other case the scattered waves interfere destructively. By directing X-rays from many different angles scientists can record when bright and dark spots are seen, and thereby work out the locations of the atoms in the crystal. In this activity, students will only send one photon at a time towards the crystal, therefore their patterns won’t depend on interference as described, but diffraction. They will model how diffraction is greater when the wavelength of the photon matches with the spacing of the crystal (spring length).
Sound waves
A sound wave in a solid pushes the atoms back-and-forth, and the repulsive electric force between atoms leads each atom to push on its neighbor when it’s moved, causing the wave to propagate through the material. A crystal will have certain natural frequencies (like a musical instrument), and if a sound wave matches one of these natural frequencies then the amplitude of the atom oscillations in the crystal will grow greatly. In a 2D crystal, these sound waves will shake each atom in Lissajous patterns, which are figures with different numbers of loops like ovals, figure-eights, etc.
Atom vibrations from sound create disturbances that propagate through the crystal lattices, and we can talk about these disturbances using wave language OR particle language. These disturbances have a wavelength and amplitude (like a wave), but they also have a distinct energy and momentum (like a particle). We use the word “phonon” to describe these particle-like disturbances. One important application of phonons is quantum computers, which can be built using crystal arrays of atoms/ions like in the crystal model, and computations can be performed by shaking pairs of atoms. Quantum computers are of interest because they could one day solve problems that would be impossible to do even on the world’s most powerful supercomputer. There is an extension activity where students can learn about the quantum properties of electrons (and how this leads to superconductivity!) using the crystal model.
Teacher tips:
- Suggested STEP UP Everyday Actions to incorporate into the activity.
- Consider using whiteboards during discussions, so students have time to brainstorm and work through their ideas before saying them out loud.
- As students experiment, roam around the room to listen in on discussion and notice experiment techniques. If needed, stop the class and call over to a certain group that has hit on an important concept.
- Consider these responsive tools and strategies and/or open ended reflection questions to help push student thinking, and to help students track their thinking during the activity.
- Connect to students’ lives and create opportunities to develop STEM identity using these suggested extensions.
Allow the work of physicists to come alive by signing up for a virtual visit from a working physicist using APS’ Physicist To-Go program. You can request a quantum physicist to talk about the concepts students learned in this activity!
Key terms: Key terms (used or presented after the activities)
These are the key terms that students should know by the end of the lesson. They do not need to be front loaded. In fact, studies show that presenting key terms to students before the lesson may not be as effective as having students observe and witness the phenomenon the key terms illustrate beforehand and learn the formalized words afterward. For this reason, we recommend allowing students to grapple with the experiments without knowing these words and then exposing them to the formalized definitions afterward in the context of what they learned.
However, if these words are helpful for students on an IEP, ELL students, or anyone else who may need more support, please use at your discretion.
- Quantum: The smallest amount of a physical quantity that can exist. A quantized quantity can only exist in discrete amounts. Particles are the quantum of a substance; they cannot be divided or split into smaller quantities.
- Atom: The fundamental building block of matter, it is made up of a positively charged core called the nucleus, which is surrounded by a negatively charged cloud of electrons.
- Photon: An elementary, massless particle that is the quantum of electromagnetic radiation (e.g. light, X-rays).
- Phonon: The quantum of sound waves in a periodic arrangement of atoms.
- Crystallography: The scientific study of solids where the atoms repeat in an orderly pattern. A primary example is X-ray crystallography, where a beam of X-rays is used to determine the positions of the atoms and electrons in a material.
Objectives*
Students will be able to:
- Use a crystal model to explore how the atoms in solid matter are arranged
- Model how scientists image matter using X-rays
- Understand what sound waves look like as they move through a crystal material
*It is important to understand that student goals may be different and unique from the lesson goals. We recommend leaving room for students to set their own goals for each activity.
Before the experiment
We invite you to watch a brief video demonstration of the developer conducting the experiment you’ll be facilitating with your students.
Consider exploring Elisa Torres Durney’s scientist profile and the lesson ideas detailed on the Introduction found in your materials kits.
- Ask students to think of one or two characteristics for the other three states of matter (solid, liquid, and gas).
- Collect these ideas on a white board where the whole class can view.
Have students build or observe a common atomic structure (like glucose) using a molecule set (not included). Ask students:
- How do you think scientists figure out the atomic structure of objects, like you just created?
- Let students know that the upcoming experiments will help them understand the atomic structure of much of the matter that makes up our universe.
Consider showing students the first 1 minute and 15 seconds of this video to visualize X-ray diffraction.
Setting up
Figure 2. Crystal model setup for the X-ray crystallography activity.This step can take up to an hour and should be done in advance of the lesson. Before the students arrive, prepare one or more experimental setups (see Figure 2) using the following steps:
- Glue a spring to one of the ping-pong balls, and the other end of the spring to the base plate.
- Glue a second spring to the ball so that the spring is pointing horizontally across the base plate.
- Glue another ping-pong ball to the other end of the horizontal spring.
- Connect the second ball to the baseplate using a spring.
- Repeat the previous three steps until you like the size of your crystal (we suggest making it with at least 3x3 ping-pong balls as in Figure 2), arranged in any pattern you like from the options shown in Figure 3 below.
- Glue velcro to one of the balls and then glue a mirror piece to another piece of velcro so that the mirror can be easily added to and removed from the setup.
- Tape graph paper together to create a sheet that is at least 17 x 17 in. and center it underneath the base plate. Label different positions/angles around the crystal lattice as shown in Figure 4 below.
- Finally, cover the crystal lattice with a fabric sheet.
Figure 3. Crystal lattice puzzle pieces.To create model photons, pairs of ping-pong balls should be connected with springs. Each pair of balls is one model photon, and the length of the spring represents each photon’s wavelength. If springs with multiple lengths are available then photons with different wavelengths can be used in the experiment.
- Note: At least one photon should have the same length spring as was used in the crystal model.
During the experiment
Modeling X-ray crystallography:
Ensure that each student understands that atoms in solids tend to form periodic lattices (repeating, orderly patterns) because the system tries to minimize the energy.
Present the students with the crystal model covered by the sheet of fabric. Have students individually volunteer to gently toss photons at the covered model (Figure 3) at different angles (i.e. from different heights above the model and from different positions around the model - Figure 4).
- Note that regardless of what direction students throw the photon from, the axis that goes through both balls should be perpendicular to the direction of the throw (see video).
Figure 3. X-ray crystallography setup.Have a student observe the height above the structure and the angle from which the photon is thrown and record it in the table below (see Figure 4).
Have another student measure the distance away from the crystal model that the photon landed, and record that distance in the table.
Figure 4. X-ray diffraction experiment using the crystal model (left), and in an actual X-ray diffraction experiment adapted from Cornell (right).
The goal is for students to use the photons to try and determine what the crystal model looks like underneath the sheet, similar to how scientists use X-ray photons to determine the atomic structure of crystal samples, as they’ll learn more about in the next activity.
- Students should use the bounce distance pattern of the photon to determine where the atoms and empty spaces of the model are located. A greater bounce distance signifies that the wavelength of the photon is aligning well with the spacing of the crystal, and thus diffracting more.
- Continue for a few rounds (if available with photons of different wavelengths).
Students should be encouraged to avoid looking under the sheet. Instead, they should try to figure out what the crystal model looks like only from the data they put in the data table. In a real experiment, the information in the table is the only thing scientists have to determine what a sample’s crystal structure is.
Share with the students that when the ping-pong balls that make up a photon have the same wavelength as atoms in the crystal model, the photons will scatter farthest.
The connection between this experiment and X-ray diffraction experiments should be discussed: when the angle and wavelength of X-ray beams are correct, then constructive interference between the scattered beams will produce a bright spot on the detector, while incorrect combinations will produce a dark spot (see Figure 1 and 4). In X-ray diffraction experiments, scientists shine many different wavelengths of light at a sample at many different angles. By determining which wavelengths and orientations produce bright and dark spots, scientists can determine the atom spacing and structure of the sample. Show students images of real-life X-ray diffractions through crystals: https://quantummechanics.ucsd.edu/ph130a/130_notes/node65.html (credit: UCSD).
Group students using best practices from the STEP UP Everyday Actions Guide.
- Have them discuss the results of the experiment amongst themselves.
- Determine which combinations of angles, wavelengths, and heights lead to the largest scattering distances.
- Based on their data and observations, have student groups draw a proposed structure on their whiteboards.
- Conduct a class discussion where each group presents their proposed structure using evidence and reasoning from the activity to support their drawing.
- Reveal the crystal structure to the class. Have them rate their theories.
- Part 2: Sound waves (teacher led portion):
Figure 5. Crystal model setup for the sound waves activity.Sound waves in matter can be visualized using the crystal model and a laser pointer
- Velcro the mirror onto the crystal model, and shine the laser onto the mirror (see Figure 5) (make sure students do not look directly into the laser!).
- Secure (using a ring stand or something equivalent) the laser such that the light reflects off the mirror and hits either the ceiling or one of the walls of the room (the farther away the laser point is from the crystal model the better).
- Have students gently shake either the ping-pong balls or the base of the model.
- As the balls (and the mirror) shake back and forth, the laser dot on the wall should dance around.
- Students should have fun and see what different shapes they can create by changing the speed and manner in which they shake the balls.
These patterns the laser is tracing out are called Lissajous figures. In a real crystal, sound waves (and thermal noise) cause the atoms to jiggle and bounce around just like in the crystal model. These Lissajous patterns are one way to visualize what these sound waves look like as they bounce back and forth. In Extension Activity 3 (optional), a speaker can be used to create pure and controlled sound waves (and stable Lissajous curves) in the crystal model.
Just like light is made up of photons, these sound waves are made up of (quasi)particles called phonons, and these quasiparticles can actually be used to build quantum computers. This is a type of computer that could one day be used to solve certain problems that even the world’s fastest supercomputer would never be able to accomplish!
You can imagine that the ping-pong balls in the crystal model are the quantum bits (a bit is where the information in a computer is stored), and the sound waves are how the computer does operations on the bits to solve a problem. Students can learn more about this type of quantum computer here.
After the experiment
Give students the opportunity to discuss the key terms, and make sure each student understands them. Allow students to define the key terms in reference to the experiments and evidence they collected during this activity.
The experiment you just performed is similar to X-ray diffraction studies (see Figure 4). In these experiments, scientists shine X-ray beams, which are made up of particles called photons, on a material. By detecting how the beams scatter off of the crystal sample they can determine what the atomic structure of the object is. The wavelength of the X-rays is similar to the length of your photon’s spring. Consider the results of your experiment:
- Describe in your own words what happens when a photon hits an atom in the crystal.
- Describe in your own words what happens when a photon hits the molecule in between the atoms of the crystal. Bonus points if you use the word constructive or destructive.
- How would the experiment have turned out differently if you were using a crystal model where the springs connecting the atoms together had a different length than the photon wavelength?
- Would the same angles have produced the same scattering distances?
Explain, in your own words, what a sound wave looks like as it travels through a crystal.
Was your personal essential question answered? If so, what is the answer? If not, what additional information would you need to answer it?
- Check out our extensions activity guide!
- Real world connections
- In the student intro, many women scientists who notably made contributions to the field of X-ray crystallography are presented:
- Kathleen Lonsdale and Isabel Knaggs
- Isabella Karle
- Elizabeth Wood
- Dorothy Hodgkin
- Rosalind Franklin
- Have students choose one of these scientists to profile by answering the following questions:
- When were they born, and when did they die?
- Where did they grow up?
- What advancement did they make in science?
- How is the work of this scientist still used today?
- Sign up for Physicists To-Go to have a scientist talk to your students.
- Career and Workforce Connections: Quantum Careers lesson (1-2 class periods)
- Use Elisa Torres Durney’s scientist profile to spark conversations about who does quantum physics
- In the student intro, many women scientists who notably made contributions to the field of X-ray crystallography are presented:
- Suggestions for drawing, illustrating, and presenting content in creative ways
- Kinesthetic activity: crystal model
- The entire class can act as a big 1D crystal where everyone stands in a line and holds hands.
- Each person in the line should stand in place, but whenever one of their neighbors pushes on them they are allowed to sway in response to the push, just like the balls in the crystal model (note that each person should sway both forwards and backwards in response to the push, as though connected to their neighbors by springs).
- A transverse wave can be created having one or both people on the ends raising their arms up, and their neighbors can raise their hands up and so on down the line (this is like the waves people do at sports games!)
- You can model a longitudinal sound wave by having one or both people on the ends gently lean in and push on their neighbors, who can then push on their neighbors and so on.
- If everyone sways forwards and back fast enough and in sync with one another the class can create a (resonant) standing wave! (Meaning that everyone in the line will eventually be swaying in sync with everyone else).
- Kinesthetic activity: crystal model
- Engineering and design challenges connected to the content
**Real world situations/connections can be used as is, or changed to better fit a student’s own community and cultural context.
- MS-PS4-1Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.
- MS-PS4-2Develop and use a model to describe how waves are reflected, absorbed, or transmitted through various materials.
- HS-PS4-5Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy.
Credits
Developed by: Elisa Haber, Jessica Jenick, Adam Rubinstein, Rachel Stromswold, Amy Yangyuxin Zou - University of Rochester
Piloted by: Kimberly Becker, Ann Marie Dubick, Nataliya Fletcher, Cindy King, Nicholas Sordillo
PhysicsQuest ©️ 2025 by American Physical Society is licensed under CC BY-NC 4.0
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