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Chapter 33: Q33PE (page 1187)

(a) Three quarks form a baryon. How many combinations of the six known quarks are there if all combinations are possible?

(b) This number is less than the number of known baryons. Explain why.

Short Answer

Expert verified

(a) The number of all possible combinations is\(216\).

(b) The number of combinations is less than the number of known baryons because the count of anti-quarks is not considered.

Step by step solution

01

Concept Introduction

A baryon is a form of composite subatomic particle in particle physics that has an odd number of valence quarks.

A quark is a basic ingredient of matter and a sort of elementary particle.

Antiquarks are the antiparticles that correspond to each flavour of quark.

02

Combination of six quarks

(a)

Find out number of all the possible combination for baryon which are made of three quarks. Since, six quarks are there and they are different, and all the combinations are possible. Therefore, it is obtained that –

\({\rm{uuu, ddd, ccc, sss, ttt, bbb,}}....\)and many other combinations of these.

The final number is simply given by–

\({{\rm{6}}^3} = 216\)

Therefore, the number of combinations is \(216\).

03

Number of combinations less than number of baryons

(b)

There are baryons more than\(216\)as it is calculated in previous part. During the calculations it is not considered that there are also\(6\)anti-quarks which could be in the compositions of the baryons.

Therefore, this number is less than the number of known baryons.

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Most popular questions from this chapter

The primary decay mode for the negative pion \({\pi ^{\rm{ - }}} \to {{\rm{\mu }}^{\rm{ - }}}{\rm{ + }}{{\rm{\bar \upsilon }}_{\rm{\mu }}}\).

(a) What is the energy release in \({\rm{MeV}}\) in this decay?

(b) Using conservation of momentum, how much energy does each of the decay products receive, given the \({\pi ^{\rm{ - }}}\) is at rest when it decays? You may assume the muon antineutrino is massless and has momentum \(p = \frac{{{E_\nu }}}{c}\), just like a photon.

In supernovas, neutrinos are produced in huge amounts. They were detected from the \({\rm{1987 A}}\) supernova in the Magellanic Cloud, which is about \({\rm{120,000}}\) light years away from the Earth (relatively close to our Milky Way galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, they can get close.

(a) Suppose a neutrino with a \({\rm{7 - eV/}}{{\rm{c}}^{\rm{2}}}\) mass has a kinetic energy of \({\rm{700 KeV}}\). Find the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/ {\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) for it.

(b) If the neutrino leaves the \({\rm{1987 A}}\) supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find \({\rm{v}}\) for the neutrino, since it \(\gamma \) is so large.)

The reaction \({{\rm{\pi }}^{\rm{ + }}}{\rm{ + p}} \to {{\rm{\Delta }}^{{\rm{ + + }}}}\) (described in the preceding problem) takes place via the strong force.

(a) What is the baryon number of the \({{\rm{\Delta }}^{{\rm{ + + }}}}\)particle?

(b) Draw a Feynman diagram of the reaction showing the individual quarks involved.

What are the advantages of colliding-beam accelerators? What are the disadvantages?

Plans for an accelerator that produces a secondary beam of \({\rm{K}}\)-mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \({\rm{500 MeV}}\).

(a) What would the relativistic quantity \(\gamma {\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}{{{{\rm{\nu }}^{\rm{2}}}} \mathord{\left/{\vphantom {{{{\rm{\nu }}^{\rm{2}}}} {{{\rm{c}}^{\rm{2}}}}}} \right. \\} {{{\rm{c}}^{\rm{2}}}}}} }}\) be for these particles?

(b) How long would their average lifetime be in the laboratory?

(c) How far could they travel in this time?
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