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Chapter 30: Problem 50

Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations: (a) uus, (b) \(\overline{c s},(\mathrm{c}) \overline{d d u},\) and \((\mathrm{d}) \overline{c} \boldsymbol{b}\)

Short Answer

Expert verified
(a) Q=+1, B=1, S=-1, C=0; (b) Q=-1, B=0, S=-1, C=-1; (c) Q=0, B=-1/3, S=0, C=0; (d) Q=-1, B=0, S=0, C=-1.

Step by step solution

01

Understanding Quantum Numbers

To solve the problem, we need to determine quantum numbers for given quark combinations. Quarks have associated quantum numbers defined as follows: - **Electric Charge (Q):** Up (u) = +2/3, Down (d) = -1/3, Strange (s) = -1/3, Charm (c) = +2/3, Bottom (b) = -1/3; Antiparticles have the opposite charge. - **Baryon Number (B):** Each quark has B = +1/3; an anti-quark has B = -1/3. - **Strangeness (S), Charm (C):** Strange ( s ) = -1, Charm (c) = +1; Antiparticles have the opposite sign.
02

Analyze Combination (a) uus

Combining the quarks and calculating the quantum numbers for "uus":- **Charge (Q):** \(2 \cdot \frac{2}{3} + \left(-\frac{1}{3}\right) = \frac{4}{3} - \frac{1}{3} = +1\)- **Baryon Number (B):** \( rac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\)- **Strangeness (S):** The strangeness of s is -1, so S = -1.- **Charm (C):** No c present, so C = 0.
03

Analyze Combination (b) \(\overline{c}s\)

Combining the anti-quark and quark and calculating the quantum numbers for "\(\overline{c}s\)":- **Charge (Q):** \(\left(-\frac{2}{3}\right) + \left(-\frac{1}{3}\right) = -\frac{3}{3} = -1\)- **Baryon Number (B):** \(-\frac{1}{3} + \frac{1}{3} = 0\)- **Strangeness (S):** s = -1, hence S = -1.- **Charm (C):** \(\overline{c}\) has C = -1.
04

Analyze Combination (c) \(\overline{ddu}\)

Combining the anti-quarks and quark and calculating the quantum numbers for "\(\overline{ddu}\)":- **Charge (Q):** \(\left(+\frac{1}{3}\right) + \left(+\frac{1}{3}\right) + \left(-\frac{2}{3}\right) = 0\)- **Baryon Number (B):** \(-\frac{1}{3} + -\frac{1}{3} + \frac{1}{3} = -\frac{1}{3}\)- **Strangeness (S):** No s present, so S = 0.- **Charm (C):** No c present, so C = 0.
05

Analyze Combination (d) \(\overline{c}b\)

Combining the anti-quark and quark and calculating the quantum numbers for "\(\overline{c}b\)":- **Charge (Q):** \(\left(-\frac{2}{3}\right) + \left(-\frac{1}{3}\right) = -1\)- **Baryon Number (B):** \(-\frac{1}{3} + \frac{1}{3} = 0\)- **Strangeness (S):** No s present, so S = 0.- **Charm (C):** \(\overline{c}\) has C = -1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electric Charge
Electric charge is a fundamental property of particles that determines how they interact with electric and magnetic fields. In the context of quarks, each type of quark has a specific charge value associated with it. For example, the 'up' quark (u) carries a charge of \(+\frac{2}{3}\), while the 'down' (d) and 'strange' (s) quarks each carry \(-\frac{1}{3}\). On the other hand, quarks' antiparticles have charges that are opposite in sign.
  • Charm (c) quarks have a charge of \(+\frac{2}{3}\).
  • Bottom (b) quarks possess a charge of \(-\frac{1}{3}\).
  • For antiparticles, just reverse the signs.
Therefore, understanding these values is key to predicting the behavior and interactions of quark-containing particles. In particle physics, the sum of charges of individual quarks determines the overall charge of a particle.
Baryon Number
Baryon number is a quantum number that expresses the difference between the number of baryons (particles like protons and neutrons) and the number of antibaryons. Quarks, the building blocks of baryons, each have a baryon number of \(+\frac{1}{3}\), while antiquarks have a baryon number of \(-\frac{1}{3}\). In any quark combination, maintaining balance is crucial, as it ensures that total baryon numbers are conserved in interactions.
  • Baryons, such as protons, have a baryon number of 1, which is derived from the sum of the baryon numbers of their constituent quarks.
  • Antibaryons, conversely, have a baryon number of -1.
This understanding is central when calculating the baryon number in quark interactions and particle reactions.
Strangeness
Strangeness is a quantum number used to describe the presence of strange quarks within a particle. Strange quarks carry a strangeness value of -1, while antiparticles containing strange quarks would have a strangeness of +1. This quantum number helps differentiate particles like kaons and hyperons, which contain one or more strange quarks, from other types of particles.
  • A strangeness of S = -1 indicates one strange quark's presence in the particle.
  • Higher specifications or interpretations of strangeness can highlight multiple or complex quark combinations in exotic particles.
The concept of strangeness plays a vital role in understanding particle decays and interactions involving weak forces.
Charm Quantum Number
The charm quantum number is associated with the charm quark and helps categorize particles based on their quark content. A charm quark contributes a value of +1 to the charm quantum number. So, if a particle contains charm quarks, its charm quantum number will reflect this.
  • Like other quantum numbers, charm has its opposite in antiparticles: anticharm quarks have a charm value of -1.
  • This can be important in identifying particles in collider experiments and predictions related to interaction results in high-energy physics.
The presence of charm quarks, and thus their impact on the charm quantum number, is crucial for discerning particles in processes involving strong and electromagnetic forces.

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Most popular questions from this chapter

Density of the nucleus. (a) Using the empirical formula for the radius of a nucleus, show that the volume of a nucleus is directly proportional to its nucleon number \(A .\) (b) Give a reasonable argument concluding that the mass \(m\) of a nucleus of nucleon number \(A\) is approximately \(m=m_{\mathrm{p}} A,\) where \(m_{\mathrm{p}}\) is the mass of a proton. (c) Use the results of parts (a) and (b) to show that all nuclei should have about the same density. Then calculate this density in \(\mathrm{kg} / \mathrm{m}^{3},\) and compare it with the density of lead (which is 11.4 \(\mathrm{g} / \mathrm{cm}^{3} )\) and a neutron star (about \(10^{17} \mathrm{kg} / \mathrm{m}^{3} ) .\)

Radioactive tracers. Radioactive isotopes are often intro- duced into the body through the bloodstream. Their spread through the body can then be monitored by detecting the appearance of radiation in different organs. \(^{131} \mathrm{I}, \mathrm{a} \beta^{-}\) emitter with a half-life of 8.0 \(\mathrm{d}\) is one such tracer. Suppose a scientist introduces a sample with an activity of 375 \(\mathrm{Bq}\) and watches it spread to the organs. (a) Assuming that the sample all went to the thyroid gland, what will be the decay rate in that gland 24 \(\mathrm{d}\) (about 2\(\frac{1}{2}\) weeks) later? (b) If the decay rate in the thyroid 24 d later is actually measured to be 17.0 \(\mathrm{Bq}\) , what percent of the tracer went to that gland? (c) What isotope remains after the I-131 decays?

Radioactive isotopes used in cancer therapy have a "shelf- life," like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of \(^{60} \mathrm{Co}\) is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these \(^{60} \mathrm{Co}\) sources in your inventory was manufactured on October \(6,2008 .\) It is now April \(6,2011 .\) Is the source still usable? The half-life of \(^{60} \mathrm{Co}\) is 5.271 years.

Pair annilation. Consider the case where an electron \(\mathrm{e}^{-}\) and a positron \(\mathrm{e}^{+}\) annihilate each other and produce photons. Assume that these two particles collide head-on with equal, but small, speeds. (a) Show that it is not possible for only one photon to be produced. (Hint: Consider the conservation law that must be true in any collision.) (b) Show that if only two photons are produced, they must travel in opposite directions and have equal energy. (c) Calculate the wavelength of each of the photons in part (b). In what part of the electromagnetic spectrum do they lie?

A 70.0 kg person experiences a whole-body exposure to alpha radiation with energy of 1.50 MeV. A total of \(5.00 \times 10^{12}\) alpha particles is absorbed. (a) What is the absorbed dose in rad? (b) What is the equivalent dose in rem? (c) If the source is 0.0100 g of \(^{226}\) Ra (half-life 1600 years) somewhere in the body, what is the activity of the source? (d) If all the alpha particles produced are absorbed, what time is required for this dose to be delivered?
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