The Quark Puzzle A 3D printable model and/or paper printable puzzle that allows students to learn the laws of colour charge through inquiry.

Size: px

Start display at page:

Download "The Quark Puzzle A 3D printable model and/or paper printable puzzle that allows students to learn the laws of colour charge through inquiry."

Arleen Conley
5 years ago
Views:

1 The Quark Puzzle A 3D pritable model ad/or paper pritable puzzle that allows studets to lear the laws of colour charge through iquiry. It is available at this lik: LEARNING OBJECTIVES As a result of this activity, studets will kow ad be able to: Idetify the fudametal particles i the Stadard Model chart. Describe properties of quarks, icludig flavour, colour charge ad electric charge. Describe the role of quarks i formig baryos ad mesos. State the rules for combiig quarks to make mesos ad baryos. Describe the symmetry betwee particles ad ati-particles Use the claims-evidece-reasoig to evaluate scietific claims. PRIOR KNOWLEDGE Studets should be itroduced to the otatio for particles, ati-particles, colour charge ad aticolour charge. Studets also eed to kow how to add positive ad egative fractios. BACKGROUND MATERIAL Studets attempt to discover the possible combiatios of the puzzles pieces. These pieces are desiged to follow the laws of colour charge for baryos ad mesos. Specifically, these boud states must be colour charge eutral: -- (or ati-, ati- ad ati-) for baryos ad either with ati-, with ati-, or with ati- for Mesos. The quark puzzle pieces follow these rules, formig closed, solid figures for allowed boud states, while refusig to fit together for forbidde combiatios. Give a set of quark pieces ad some time, studets should be able to fid certai restrictios o what is allowed. Some rules that studets could discover : Atiquarks always possess a ati-colour charge. All baryos cosist of three quarks or three atiquarks. The colour charges must be, ad together, or the three ati-colours together. All mesos cosist of two quarks: oe quark ad a atiquark. They must possess a colour charge ad its correspodig ati-colour charge. All hadros possess a total electric charge of -2, -1, 0, +1 or +2. All mesos possess a total electric charge of -1, 0 or +1. Some limitatios of the quark puzzle pieces: Quarks are ot shaped like the puzzle pieces ad do ot possess actual colour. The pieces physically touch while real quarks are boud by virtual gluos ad quarks. The quark pieces caot describe particles that are i superpositio states such as π 0.

Scaffolded Quark Puzzle Activity - Aswers Each piece is a model that represets a tiy particle that is too small to see, called a quark. Every quark has a flavour, a electric charge ad a colour charge.

Examples of colour charge are ad ati- ( ). Makig Groups of Quarks Quarks form groups. There are two groups with special ames, they are baryos ad mesos.

2 Scaffolded Quark Puzzle Activity - Aswers Each piece is a model that represets a tiy particle that is too small to see, called a quark. Every quark has a flavour, a electric charge ad a colour charge. You ca fid these properties prited o the side of the quark. Flavours iclude up (u), dow (d), ati-up ( u ) or ati dow ( d ). +2/3 is a example of electric charge. Examples of colour charge are ad ati- ( ). Makig Groups of Quarks Quarks form groups. There are two groups with special ames, they are baryos ad mesos. I this model baryos ad mesos have special shapes. Meso Three quarks that form a cube are called baryos. Two quarks that form a double pyramid are called Mesos. Some combiatios fit together icely, others oes do ot. See diagrams below. Good Joit Bad Joit Here the pieces fit together icely. Here the pieces do ot fit together icely. Usig groups that fit together icely complete the tasks o the followig pages. Hit: If it is difficult to build a group, try dividig sort the quarks by colour charge first ad try oe from each pile.

3 Activity 1 Buildig a Proto A proto is a baryo made of two up (u) quarks ad oe dow (d) quark. There are may possible colour charge combiatios. Put the pieces together to fid what combiatios are possible. Record the colour combiatios ad electrical charges i the table below. Oe row has bee filled out as a example for you. Oce you put the pieces together, you ca fid the electric charge by addig the electric charge of each quark piece together. Table of Colour Combiatios for Protos Particle or Up Quark Name ad Meso? Colour Charge symbol Up Quark Colour Charge Dow Quark Charge Colour Electric Charge Proto (p) 2/3 + 2/3-1/3 = +1 Proto (p) 2/3 + 2/3-1/3 = +1 Proto (p) 2/3 + 2/3-1/3 = +1 Proto (p) Questios: 1.) How may differet colour charge combiatios of the proto did you fid? 3 2.) Challege Questio: Is it possible there are other colour charge combiatios that you have ot foud? How ca you be sure? I order to build a proto with the provided pieces all the quarks have to be of differet colours. Therefore the colour of the dow quark defies the whole proto. Sice there are oly 3 colours for the dow quark, there ca oly be 3 combiatios

4 Activity 2 Buildig Ati-Protos A ati-proto is a baryo made of two u quarks ad oe d quark. Put the ati-quark pieces together to fid what combiatios are possible. Record the colour charge combiatios ad electrical charges i the table below. Table of Colour Combiatios for Ati-Protos Particle Name ad symbol or Meso? Ati-Up Quark Colour Ati-Up Quark Colour Ati-Dow Quark Colour Electric Charge Ati-Proto ( p ) ati- ati- ati- -2/3-2/3+ 1/3 = -1 Ati-Proto ( p ) ati- ati- ati- -2/3-2/3+ 1/3 = -1 Ati-Proto ( p ) ati- ati- ati- -2/3-2/3+ 1/3 = -1 3.) How may differet colour charge combiatios of the ati-proto did you fid? 3 4.) How does this compare to the colour charge combiatios for protos from activity 1? The colour combiatios are the same with the correspodig ati-colour charge rather tha the colour charge.

5 Activity 3 Buildig Neutros ad Ati-Neutros A eutro () is a baryo made of oe u quark ad two d quarks. A ati-eutro ( ) is a baryo that cotais oe u quark ad two d quarks. Put the quark ad ati-quark pieces together to build eutros ad ati-eutros. Record the colour combiatios ad electrical charges i the table below. Particle Name ad symbol or Meso? Up/Ati-Up Quark Colour Dow/Ati- Dow Quark Colour Dow/Ati- Dow Quark Colour Electric Charge 2/3-1/3-1/3 = 0 2/3-1/3-1/3 = 0 2/3-1/3-1/3 = 0 ati- ati- ati- -2/3 +1/3+ 1/3 = 0 ati- ati- ati- -2/3 +1/3+ 1/3 = 0 ati- ati- ati- -2/3 +1/3+ 1/3 = 0 5.) How may differet colour charge combiatios of the ati-eutro did you fid? 6 6.) How does this compare to the colour charge combiatios for protos ad ati-protos from activity 1 ad 2? The colour charge combiatios for eutros ad ati-eutros are idetical to those for the protos ad ati-protos. 7.) What electric charges are possible? Is this the same as for protos ad ati-protos? For a eutro ad ati-eutro oly a electric charge of 0 is possible. For protos the electric charge must be +1, but ati-protos the charge must be -1.

6 Activity 4 Buildig Pios A pio is a meso made of u, d, u ad d quarks. For pios there are may differet flavours, values for the colour charge ad electric charge. Build pios out of the pieces ad fill i the combiatios you fid i the table below: Table of Colour Combiatios for Pios Particle Name or Meso? Flavour Combiatio Colour Charge Combiatios Electric Charge Pio (π) Meso u d r r, b b, g g +1 Pio (π) Meso d d r r, b b, g g 0 Pio (π) Meso u u r r, b b, g g 0 Pio (π) Meso d u r r, b b, g g -1 4.) What are the differet possible values of electric charge for pios? -1, 0 ad 1 5.) (Challege) Are there ay other possible values for electric charge for pios? How ca you be sure? Sice the oly flavour provided are u, d, u ad d ad a quark must always be pai with a atiquark, there are oly 4 possible combiatios. Therefore the electric charge values are restricted to those foud i the table.

7 Activity 5 - Claims, Evidece ad Reasoig Usig the combiatios you have foud i the tables (or usig the pieces to explore other combiatios if ecessary) state whether the followig claims are supported or ot. After this, write dow the evidece ad reasoig that led you to this coclusio. The first claim is completed for you as a example. Claim 1: Neutros ca have a electric charge of +1. True or False False Evidece ad Reasoig: _A eutro is made of two dow quarks ad oe up quark. The provided_ dow quarks always have a electric charge of -1/3 ad the up quarks have charge +2/3. Therefore whe these are combied the et charge is always 0. Therefore it is ot possible to have a eutro with charge +1. Claim 2: Protos ca have a electric charge of +1. True or False True Evidece ad Reasoig: All combiatios of two up quarks ad oe dow quark have a charge of +1. Therefore +1 is a possible charge. Claim 3: Mesos must have oe ad oe ati- quark. True or False False Evidece ad Reasoig: It is also possible to build a meso with colour charges pairs of ad ati- or ad ati-. Claim 4: It is possible for a baryo to have a overall electric charge of -2. True or False True Evidece ad Reasoig: Combiig 3 ati-up quarks creates a baryo with a charge of -2. Note this is called the Δ ++ ati-baryo.

8 Claim 5 (Challege): It is possible for a meso to have a overall electric charge of +1/3. True or False False Evidece ad Reasoig: A meso must always cosist of a baryo ad a ati-baryo. The oly electric charges for a baryo are -1/3 ad +2/3. The optios for a ati-baryo are -2/3 ad +1/3. Tryig all combiatios gives: -1/3 + -2/3 = -1, -1/3 + 1/3 = 0, +2/3 + -2/3 = 0 ad +1/3 + 1/3 = 1. Claim 6 (Challege): All particle systems (mesos or baryos) ca oly have whole umber electric charge. True or False True Evidece ad Reasoig: Claim 7 showed that mesos ca oly have whole umber charge. If baryos must have iteger charge the ati-baryos must as well sice they have opposite electric charge. For baryos must be made of real quarks for which there are oly two possible charges -1/3 or +2/3. Therefore the possible combiatios are: -1/3 + -1/3 + -1/3 = -1, 2/3 + -1/3 +-1/3 = 0, 2/3 + 2/3 + -1/3 = 1 ad 2/3 + 2/3 + 2/3 = 2.Therefore baryos, ati-baryos ad mesos must have whole umber charge.

9 Activity 6 Comparig the Puzzle to Real Particles (Research Task) The puzzle provided is oly a model ad it does ot show what real quarks look like. Do some research ad i the table below write dow the differeces ad similarities betwee the puzzle ad real quarks. Oe row has bee completed for you a example: Category Quark Puzzle Real Particles Shape ad size Empty Space I this puzzle, a proto has a cube shape. Pios have a double pyramid shape. The particles are big ad you ca touch them. I the puzzle, quarks are very close together (they actually touch) ad there is almost o empty space betwee them. Real protos ad pios have o welldefied shape that humas ca see or eve imagie. Real baryos ad mesos are so small you caot see them. I real protos, the space aroud the quarks is much larger tha the quarks themselves. The quarks are spread out. Real quarks do ot touch each other; istead gluos hold them together. Colour Charge The quark pieces are colou ad have colour labels, this represets a colour charge. Real quarks do t have a colour that we ca see. However they have a colour charge, this is the charge of the strog uclear iteractio. Ati-particles (Challege) Ati-particles look the same as the correspodig particle. They have opposite charges ad a bar is placed above the particle symbol ad colour. Ati-particles are idetical to their correspodig particles but they cotai opposite electric charge. Whe a real particle ad atiparticle meet they aihilate, both particles trasform ito eergy. Differece betwee up ad dow quark (Challege) I the quark puzzle up ad dow quarks differ oly by the symbols o the side of the quark. Up ad dow quarks have very similar mass i particle physics, but differ i electric charge. The strog uclear force (colour force) iteracts idetically with up ad dow quarks.

10 Ope Iquiry with the Quark Puzzle Guide to Quark Puzzle Pieces Each piece is a model that represets a quark. Every quark has a flavour, a electric charge ad a colour charge. You ca fid these properties prited o the side of the quark. Flavours iclude up (u), dow (d), ati-up ( u ) or ati-dow ( d ). +2/3 is a example of electric charge. Examples of colour charge are ad ati- ( ). Some combiatios fit together icely, others oes do ot. See diagrams below. Good Joit Bad Joit Here the pieces fit together icely. Here the pieces do ot fit together icely. Usig groups that fit together icely to discover the laws ad complete the missio. Hit: If it is difficult to build a group, try dividig sort the quarks by colour charge first ad try oe from each pile.

11 Missio Briefig: Fugitive Particles Purpose: To discover patters of various kids to fid a set of rules that gover the mysterious ad elusive quarks. Discussio: It has bee trusted to you to discover the rules that the quarks obey. Ufortuately eve though the particles make up everythig all aroud you, they are so small there is o way that you are able to see them idividually. Luckily, we have obtaied a model of puzzle pieces, which obey the same rules as actual quarks. Your missio should you choose to accept is to use these puzzle pieces to discover the laws that dictate how these particles form groups. You must preset your fidigs as a series of rules that someoe else could use to determie possible ad impossible combiatios of quarks. For a hit to get started, see guidelies o the back of this sheet.

6.3 Testing Series With Positive Terms

6.3 Testing Series With Positive Terms 6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial