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Chapter 11: Problem 40

Based on the quark composition of a neutron, show that is charge is 0 .

Short Answer

Expert verified
The neutron consists of one up quark with charge \(+\frac{2}{3}\) and two down quarks each with charge \(-\frac{1}{3}\). The overall charge of a neutron is calculated by summing the charges of its constituent quarks: \(+\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) = \(\frac{2 - 1 - 1}{3}\) = \(\frac{0}{3}\). Thus, the charge of a neutron is 0, confirming its neutrality.

Step by step solution

01

1. Determine the charge of quarks present in neutron

The neutron has one up quark and two down quarks. The up quark has a charge of \(+\frac{2}{3}\), and each down quark has a charge of \(-\frac{1}{3}\).
02

2. Calculate the overall charge of the neutron

Now, we need to find the overall charge of the neutron by summing the charges of its constituent quarks: Neutron Charge = (Charge of up quark) + (Charge of 1st down quark) + (Charge of 2nd down quark)
03

3. Substitute the charges of quarks and evaluate the sum

Replace the charges of the quarks in the equation: Neutron Charge = \(+\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) Now, perform the calculation: Neutron Charge = \(\frac{2}{3} -\frac{1}{3} -\frac{1}{3}\) = \(\frac{2 - 1 - 1}{3}\) = \(\frac{0}{3}\)
04

4. Conclude the result

The overall charge of the neutron is 0, as shown by the quark composition and the calculation. This demonstrates that a neutron is a neutral particle in terms of its electric charge.

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Key Concepts

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

Neutron Structure
The neutron is one of the fundamental particles found in the nucleus of an atom. It plays a crucial role in the stability of the nucleus and its overall composition.
Unlike protons, neutrons do not carry a net electric charge. This neutrality is due to its quark composition.
Neutrons are made up of three quarks. Specifically, a neutron consists of:
  • 1 up quark
  • 2 down quarks
These quarks are bound together by the strong nuclear force, which is one of the four fundamental forces in nature. Understanding how these quarks interact helps us comprehend why the neutron is neutral.
Quark Charge
Quarks are the elementary particles that form protons and neutrons. They come in different types, known as "flavors," each with specific characteristics.
Importantly, quarks have fractional electric charges, unlike the full positive or negative charges found in more familiar particles. In a neutron:
  • The up quark has a charge of \(+\frac{2}{3}\).
  • Each down quark possesses a charge of \(-\frac{1}{3}\).
Though these charges are fractional, they are fundamental to our understanding of particle physics and the makeup of matter in the universe.
Particle Physics
Particle physics is the branch of science that studies the smallest known building blocks of the universe and the forces that govern them.
It seeks to understand particles such as quarks, the fundamental constituents of protons and neutrons.
This field utilizes particle accelerators, sophisticated theoretical models, and advanced technology to probe deeper into the structure of matter.
By studying the interactions and properties of particles, physicists aim to uncover the nature of the universe at its most fundamental level. Particle physics helps us answer essential questions about the makeup of matter, the forces at play, and the origins of the universe.
Electric Charge Calculation
The electric charge of a neutron is calculated by summing the charges of its constituent quarks. To determine that a neutron is indeed neutral, follow these steps:
Start by considering the combination of quarks:
  • 1 up quark with a charge of \(+\frac{2}{3}\)
  • 2 down quarks, each with a charge of \(-\frac{1}{3}\)
Combine these charges:\[\text{Neutron Charge} = \left( +\frac{2}{3} \right) + \left( -\frac{1}{3} \right) + \left( -\frac{1}{3} \right) = \frac{0}{3} = 0\]
This calculation confirms that the neutron has an overall electric charge of zero. Understanding how these quark charges cancel out is essential in particle physics, illustrating the elegance of how nature balances charge even at the subatomic level.

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Most popular questions from this chapter

What is the general quark composition of a baryon? Of a meson?

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) \(\pi^{-}+\mathrm{n} \rightarrow \mathrm{K}^{-}+\Lambda^{0}\)

In general, how do we determine if a particle reaction or decay occurs?

Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \(500 \mathrm{MeV} .\) (a) What would the relativistic quantity \(\gamma=\frac{1}{\sqrt{1-v^{2} / c^{2}}}\) be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?

How much energy is released when an electron and a positron at rest annihilate each other? (For particle masses, see Table 11.1.)
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