Chapter 20: Problem 15
Protons and neutrons are made from combinations of the two most common quarks, the \(u\) quark (charge \(+\frac{2}{3} e\) ) and the \(d\) quark (charge \(-\frac{1}{3} e\) ). How could three of these quarks combine to make (a) a proton and (b) a neutron?
Short Answer
Expert verified
The combination of quarks for a proton is two 'u' quarks and one 'd' quark. For a neutron, it is one 'u' quark and two 'd' quarks.
Step by step solution
01
Recognize the charge of a proton
A proton has a positive charge equivalent to \(+e\). This means that the combination of three quarks (either 'u' or 'd') should sum up to \(+e\) for a proton.
02
Find the quark combination for a proton
Knowing that \(+e\) is equivalent to \(+1e\), and considering that each 'u' quark contributes \(+\frac{2}{3}e\) and each 'd' quark contributes \(-\frac{1}{3}e\), we find that the combination of two 'u' quarks and one 'd' quark will give the total charge of a proton: \(2(+\frac{2}{3}e) + (-\frac{1}{3}e) = +1e\). Hence, a proton is made up of two 'u' quarks and one 'd' quark.
03
Recognize the charge of a neutron
A neutron has no net charge, which is equivalent to \(0\). This means the combination of three quarks (either 'u' or 'd') should sum up to \(0\) for a neutron.
04
Find the quark combination for a neutron
Given that each 'u' quark contributes \(+\frac{2}{3}e\) and each 'd' quark contributes \(-\frac{1}{3}e\), the combination of one 'u' quark and two 'd' quarks will give the total charge of a neutron: \(+\frac{2}{3}e + 2(-\frac{1}{3}e) = 0\). Hence, a neutron is made up of one 'u' quark and two 'd' quarks.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Proton Charge
The charge of a proton is one of the fundamental aspects of particle physics and is crucial in understanding the structure of atoms. A proton carries a positive charge, designated as \(+e\) or equivalently, \(+1\) in atomic units. This positive charge is balanced by electrons in an atom to preserve overall electrical neutrality.
To understand how a proton obtains its charge, it's helpful to look at its subatomic components, known as quarks. Specifically, a proton is composed of two 'u' (up) quarks, each with a charge of \(+\frac{2}{3}e\), and one 'd' (down) quark, with a charge of \(-\frac{1}{3}e\). When you add up the charges of these three quarks, the result is \(2(\frac{2}{3}e) + (\frac{-1}{3}e) = +1e\), which matches the charge of a proton.
To understand how a proton obtains its charge, it's helpful to look at its subatomic components, known as quarks. Specifically, a proton is composed of two 'u' (up) quarks, each with a charge of \(+\frac{2}{3}e\), and one 'd' (down) quark, with a charge of \(-\frac{1}{3}e\). When you add up the charges of these three quarks, the result is \(2(\frac{2}{3}e) + (\frac{-1}{3}e) = +1e\), which matches the charge of a proton.
Significance of the Proton Charge
The proton's charge is significant because it determines the electromagnetic interactions with other charged particles, particularly electrons. This interaction is fundamental for the formation of atoms and thus, is essential for the chemistry that underlies all materials and life processes.Neutron Charge
Unlike a proton, a neutron is electrically neutral, meaning it does not carry a net charge. The neutrality of a neutron plays a vital role in the stability of atomic nuclei, as neutrons act as a buffer between the positively charged protons, reducing the electrostatic repulsion that would otherwise push the nucleus apart.
The internal structure of a neutron consists of quarks. Specifically, one 'u' quark and two 'd' quarks. The 'u' quark has a charge of \(+\frac{2}{3}e\), and the 'd' quarks each have a charge of \(-\frac{1}{3}e\). Combining these charges results in \(\frac{2}{3}e + 2(\frac{-1}{3}e) = 0\), confirming the neutron's neutral charge.
The internal structure of a neutron consists of quarks. Specifically, one 'u' quark and two 'd' quarks. The 'u' quark has a charge of \(+\frac{2}{3}e\), and the 'd' quarks each have a charge of \(-\frac{1}{3}e\). Combining these charges results in \(\frac{2}{3}e + 2(\frac{-1}{3}e) = 0\), confirming the neutron's neutral charge.
Neutron's Role in the Nucleus
Neutrons are critical for the structure of atomic nuclei, as their lack of charge allows them to effectively bind with protons to form more massive nuclei, contributing to the variety of elements found in the universe.Quark Combinations
Quarks are elementary particles that combine in specific ways to form protons and neutrons, the building blocks of atomic nuclei. The most common quarks that make up protons and neutrons are the 'u' (up) and 'd' (down) quarks. In combinations of three, they form distinct particles, each with different properties due to their quark composition.
The proton is formed by two 'u' quarks and one 'd' quark, summing up to its positive charge, while the neutron consists of one 'u' quark and two 'd' quarks, resulting in its neutral charge. These configurations are held together by the strong force, mediated by particles called gluons.
The proton is formed by two 'u' quarks and one 'd' quark, summing up to its positive charge, while the neutron consists of one 'u' quark and two 'd' quarks, resulting in its neutral charge. These configurations are held together by the strong force, mediated by particles called gluons.
Stability and Interactions
Quark combinations in protons and neutrons are not only essential for defining their charges but also for their stability and how they interact with other particles. The different combinations of quarks contribute to the diversity of matter and the complexity of forces within an atom's nucleus.Elementary Particles
Elementary particles are the fundamental building blocks of the universe, indivisible and not composed of any smaller constituents. They include quarks, electrons, neutrinos, and many others, each with unique properties such as mass, charge, and spin. Quarks themselves are a type of elementary particle, and their combinations form composite particles, like protons and neutrons, known as hadrons.
The study of elementary particles falls under the field of particle physics, which aims to understand the nature of these particles and the forces that govern their interactions. This field has led to significant discoveries, including the unification of weak and electromagnetic interactions, the establishment of the Standard Model of particle physics, and the confirmation of the Higgs boson.
The study of elementary particles falls under the field of particle physics, which aims to understand the nature of these particles and the forces that govern their interactions. This field has led to significant discoveries, including the unification of weak and electromagnetic interactions, the establishment of the Standard Model of particle physics, and the confirmation of the Higgs boson.