Quarks are fundamental particles in the Standard Model of particle physics. They make up the protons and neutrons that we are familiar with, but also a zoo of other more exotic particle systems like pions and kaons. Quarks have never been isolated; they always form groups of two or three. But what are the rules that govern these quarks systems?
Find out more with the quark puzzle, a set of 3D printable pieces that represent quarks. Each piece is labelled with a quark type, electric charge and colour charge, and has joints that allow it to connect to other quark pieces. Your students can use these to discover the rules of the strong interaction and colour charge, or to build your own models of particle systems. The 2D version of this puzzle was originally proposed by Gettrust, E. (2010).
Suggestions for educators
The learning objectives of the activities we propose are:
- Resulting electric charges of particle systems are always integer numbers (e.g. -1, 0, +1)
- Resulting color charges of particle systems are always color neutral
- For baryons this means, for example, that a green quark must be combined with a red quark and a blue quark, and an antigreen quark must be combined with an antired and an antiblue quark.
- For mesons this means, for example, that a green quark must be paired with an antigreen antiquark.
- Introduction to puzzle pieces and combinations of 2 or 3 pieces
- Activity 1 - building a proton: combinations of colour charges and sum of electric charges
- Activity 2 - building an anti-proton: combinations of anti-colour charge and sum of electric charges
- Activity 3 - building neutrons and anti-neutrons
- Activity 4 - building pions
- Activity 5 - claims, evidence and reasoning tasks to consolidate the learned rules
- Activity 6 - comparing the puzzle to real particles systems
For more independent students, we propose an open inquiry activity explained in our open inquiry student worksheet.
- Mission briefing: "Your mission is to use these puzzle pieces to discover the laws that dictate how these particles form groups. You must present your findings as a series of rules that someone else could use to determine possible and impossible combinations of quarks."
- Limitations of this model: comparing the puzzle to real particles systems
Information text - key concepts of (anti-)particles and particle systems
Excerpt from McGinness, Dührkoop, Jansky, & Woithe (2019)
Below, we briefly summarize all key concepts, which are a prerequisite for our proposed activity.
Structure of subatomic matter
- Protons and neutrons are particle systems made of quarks.
- Quarks are indivisible. They are called elementary particles.
- There are different types of quarks with different properties, e.g., up quarks and down quarks.
- Quarks cannot exist in isolation but quickly form bound states of particle systems.
Particle charges & interactions
- Elementary particles can be characterized by their properties such as mass and their electric charge.
- The electric charge of an elementary particle determines if and how this particle is affected by the electromagnetic interaction.
- The color charge (often called strong charge) determines if and how a particle is affected by the strong interaction.
- Each quark has an electric charge. The two possible electric charges for quarks are called +2/3 and –1/3.
- Each quark has a color charge. The three possible color charges for quarks are called green, blue, and red.
- For every quark, there exists a corresponding antiquark.
- Antiquarks have the same mass as the corresponding quark, but an opposite electric charge (–2/3 or +1/3) and an opposite color charge.
- Each antiquark has an anticolor charge. The three possible anticolor charges are called antigreen, antiblue, and antired.
There are two kinds of bound states for quarks, mesons, and baryons. Mesons are made of one quark and one antiquark. Baryons are made of three quarks or three antiquarks.
- In particle systems made of different elementary particles, the electric and color charges of the elementary particles are added up to obtain the resulting electric and color charge of the particle system.
- Electric charges can simply be added like rational numbers, e.g., for a neutron made of one up quark and two down quarks: (+2/3) + (–1/3) + (–1/3)=0
- Color charges are added as follows:
- red + green + blue = “color neutral,” i.e., white
- antired + antigreen + antiblue=“color neutral,” i.e., white
- antired + red=antigreen + green=antiblue + blue=“color neutral,” i.e., white
- These rules are inspired by additive color mixing and take the vector character of the color charge into account.
- Color charges are added as follows:
Sets of puzzle pieces and additional material
There are different sets of puzzle pieces available. The worksheets presented can use either the 3D or 2D puzzle pieces. The activities require only 12 pieces (corresponding to up and down quarks and corresponding antiquarks); however, they can be extended to more quark types.
3D puzzle pieces (require 3D printer)
We present an original set of quark puzzles pieces. These quark pieces can be joined in groups of three to build a cube (baryon), or two pieces can be put together to make a “double pyramid” (meson). The pieces only fit together if they are consistent with the color charge rules of the Standard Model of particle physics.
Download the 3D-printing files here.
2D puzzle pieces (require normal 2D colour printer or 3D printer)
We have also made available a modified version of Gettrust’s 2D puzzle pieces based on QuarkNet activity. We used stripes so students can more easily identify anticolor charges. In addition to the paper version, we also provide a 3D printable version of these 2D puzzle pieces.
Cookie cutters (require 3D printer)
A set of quark cookie cutters to make your own cookies that can be combined according to the laws of the Standard Model of particle physics (Yum!): https://www.thingiverse.com/thing:3047682
Read our paper
Read more about this activity here: McGinness, L., Dührkoop, S., Jansky, A., Woithe, J. (2019). 3D Printable Quark Puzzle: A Model to Build Your Own Particle Systems. The Physics Teacher 57(8), DOI: https://doi.org/10.1119/1.5131116