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Chapter 11: Problem 39

Based on quark composition of a proton, show that its charge is +1.

Short Answer

Expert verified
The proton is composed of two Up quarks (u) and one Down quark (d), represented as (u, u, d). The total charge from the Up quarks is \(+\frac{4}{3}\) and the total charge from the Down quark is \(-\frac{1}{3}\). Adding these charges, we find the proton's charge to be \(+\frac{3}{3} = +1\), as required.

Step by step solution

01

Quark Composition of a Proton

A proton is made up of three quarks: two Up quarks and one Down quark. We can represent this composition as (u, u, d).
02

Charge of Up Quarks

Each Up quark (u) has a charge of +2/3. Since a proton has two Up quarks, we need to calculate their total charge by multiplying the charge of a single Up quark by the number of Up quarks in a proton: Total charge from Up quarks = Charge of one Up quark × Number of Up quarks = \( +\frac{2}{3} × 2 \)
03

Charge of Down Quarks

A Down quark (d) has a charge of -1/3. Since a proton has only one Down quark, we don't need to multiply it with anything. So, the total charge from the Down quark in a proton is -1/3.
04

Calculating Proton Charge

Finally, we need to add the total charges from the Up quarks and the Down quark to find the charge of a proton: Proton Charge = Total charge from Up quarks + Total charge from Down quarks = \( +\frac{4}{3} + (-\frac{1}{3}) \)
05

Result

The result of the calculation is: Proton Charge = \( +\frac{3}{3} \) So, the proton carries a charge of +1, as required.

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Most popular questions from this chapter

Which of the following reactions cannot because the law of conservation of strangeness is violated? (a) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\pi^{-}\) (b) \(\mathrm{p}+\mathrm{n} \rightarrow \mathrm{p}+\mathrm{p}+\mathrm{K}^{-}\) (c) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \mathrm{K}^{-}+\sum^{+}\) (d) \(\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{+}+\sum^{-}\) (e) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\mathrm{K}^{+}+\pi^{-}\) (f) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \Xi^{0}+\pi^{-}+\pi^{-}\) (g) \(\pi^{+}+\mathrm{p} \rightarrow \Sigma^{+}+\mathrm{K}^{+}\) (h) \(\pi^{-}+\mathrm{n} \rightarrow \mathrm{K}^{-}+\Lambda^{0}\)

A proton and an antiproton collide head-on, with each having a kinetic energy of \(7.00 \mathrm{TeV}\) (such as in the \(\mathrm{LHC}\) at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

(a) The following decay is mediated by the electroweak force: \(\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{+}+v_{\mathrm{e}}\). Draw the Feynman diagram for the decay. (b) The following scattering is mediated by the electroweak force: \(v_{e}+\mathrm{e}^{-} \rightarrow v_{e}+\mathrm{e}^{-}\) Draw the Feynman diagram for the scattering.

Distinguish fermions and bosons using the concepts of indistiguishability and exchange symmetry.

(a) What is the approximate velocity relative to us of a galaxy near the edge of the known universe, some \(10 \mathrm{Gly}\) away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than \(0.9 c\).
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