Summer Research Program for Science Teachers

Partners in Science

Steven H. Schwartz
New Dorp High School

Staten Island, NY

August 2004

How do protons stick together in a nucleus?

Standard Model of the Atom - Baryons

# Objectives

·        Understand that the Standard Model of the atom includes particles beyond protons, neutrons, and electrons.

·        Describe the nucleus as a conglomeration of quarks that manifest themselves as protons and neutrons.

·        Identify the antiparticle for each elementary particle.

·        Contrast charge quantization on the atomic level (integer multiples of the elementary charge) and the subnuclear level (fractional multiples of the elementary charge).

·        Determine whether an assembly of quarks constitutes a valid baryon.

[Content standard B: Fundamental Physical Understandings]

# Background Knowledge

·        The Bohr and Schrödinger (wave-mechanical) atomic models.

·        Protons are positively charged; neutrons are neutral.

·        All matter carries an integer multiple of the fundamental charge (possibly zero).

# Materials

[Teaching Standard D – Provide students with the time, space, and resources for learning science]

·        A deck of “quark cards” for each group of 3–4 students.  Each deck includes three cards for each flavor of quark and three cards for each anti-quark: three up cards, three anti-up cards, three down cards, etc.

·        The “Classification of Matter” chart in the New York State Physics Reference Tables.

# Plan

[Teaching Standard A: Inquiry-Based Science]

[Teaching Standard B: Guide and Facilitate Learning]

[Teaching Standard E: Nurture Learning Communities]

[Assessment Standard B: Assess what is learnt]

[Assessment Standard C: Authentic Assessment]

[Content Standard A: Ability to Perform Scientific Inquiry]

[Program Standard D: Sufficient Time for Learning]

Students are placed into groups of three or four.

Students are given the following problem.  Protons are positive and should repel one another.  Neutrons are neutral and should not attract protons or other neutrons.  How then do protons and neutrons bind in an atomic nucleus?  Students discuss possible answers in their groups for several minutes, and then discuss their hypotheses as a class.

The teacher presents the following as direct instruction using the Reference Tables.  Alternately, the teacher can distribute group-based reading materials.

·        Review: In the Bohr and Schrödinger models, matter is fundamentally composed of protons, neutrons, and electrons.

·        The Standard Model divides all matter into hadrons (heavier particles composed of quarks) and leptons (lighter particles).

·        Hadrons, including protons and neutrons, are composed of smaller fundamental particles called quarks.

·        Baryons are as composed of three quarks.  Each quark has a charge as shown; each quark has an anti-quark with the same mass and opposite charge.  A proton is uud; a neutron is udd.

·        All quarks attract one another (strong nuclear force) regardless of electric charge.  Hence, quarks cohere to form nucleons (protons and neutrons), and the nucleons attract one another because of interactions among the underlying quarks.

Can any three quarks form a baryon?

·        Each group is given a deck of quark cards.  The teacher demonstrates assembling a “baryon” by selecting three cards, e.g. uud.  Remind the students that charge conservation requires that the net charge on the baryon is the sum of the individual quarks’ charges.  The net charge on uud is +1e.  Remind the students that the charge is not “+1”, but is a multiple of “e”.

Challenge the groups to assemble an “illegal” baryon, one whose net charge is not an integer multiple of “e”.  Have the groups share their solutions.  They are to model the baryon using the quark cards.  An example: cc(anti-c).

Which groupings of quarks result in a legal (or illegal) baryon?

·        Student groups design and carry out an experiment in which they assemble various combinations of three quark cards, then determine the net charge on the combination.

·        There are 123 = 1728 possible quark combinations, so analyzing all possible combinations is not an option.  Students must identify an independent variable and choose a representative sample set.  (The net charge is the dependent variable.)  The correct independent variable is whether each quark is a particle or antiparticle.

·        Groups assemble the baryons in their sample sets, determine the net charge in each case, and generalize their results.

·        The correct conclusion is that any three quarks, or three anti-quarks, produce a legal baryon.  A one/two split (one quark + two anti-quarks, or the converse) is illegal.

# Summary

After this exercise, each group conducts a metacognitive reflection in which each student volunteers at least one thing the group did well and one thing that could be improved next time.  Students also discuss, perhaps as a class, how learning about this additional “bottom layer” on the atomic model changes their perception of the permanence of scientific knowledge.  [Teaching Standard C: Ongoing Assessment]

The class summarizes with an oral review of the portion of the Standard Model presented.  The strong interaction between quarks is emphasized to answer the Aim question.

The next lesson discusses mesons and leptons.  A legal meson comprises one quark and one anti-quark.  Since this information is explicitly in the Reference Tables, it is not worth doing as a full inquiry-based activity, but can be used to unite the two lessons.

[Content Standard G: Historical Perspective; Nature of Scientific Knowledge]