/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 31 The weak force may change quark ... [FREE SOLUTION] | 91Ó°ÊÓ

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The weak force may change quark flavor in an interaction. Explain how \(\boldsymbol{\beta}^{+}\) decay changes quark flavor. If a proton undergoes \(\boldsymbol{\beta}^{+}\) decay, determine the decay reaction.

Short Answer

Expert verified
During \(\beta^+\) decay, an up quark is transformed into a down quark, changing a proton into a neutron.

Step by step solution

01

Understand the Context of the Problem

Beta plus decay (\(\beta^+\) decay) is a type of radioactive decay wherein a proton in a nucleus is transformed into a neutron, releasing a positron and a neutrino in the process. This occurs via the weak force, and during this decay, one of the up quarks in a proton needs to change into a down quark.
02

Explore Quark Flavor Change

The weak force changes quark flavors, specifically changing an up quark (\(u\)) to a down quark (\(d\)) in the process of \(\beta^+\) decay. This flavor change is mediated by the emission of a \(W^+\) boson, which subsequently decays into a positron and a neutrino.
03

Set Up the Initial and Final State of the Decay

Initially, the proton, which comprises two up quarks (\(u\)) and one down quark (\(d\)), undergoes \(\beta^+\) decay. The transformation happens when one of the up quarks is converted into a down quark, effectively turning the proton into a neutron.
04

Write the Standard Model Process

The initial reaction for \(\beta^+\) decay of a proton can be written as:\[ p \rightarrow n + \beta^+ + u_e \]Where \(p\) is the proton, \(n\) is the neutron, \(\beta^+\) is the emitted positron, and \(u_e\) is the emitted neutrino.

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Key Concepts

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

Quark Flavor Change
Quark flavor change is a fascinating aspect of particle physics. Quarks come in different "flavors," such as up and down, which are two of the most fundamental types. When a quark changes flavor, it essentially transforms from one type to another. In beta plus (\(\beta^+\)) decay, this phenomenon occurs when an up quark in a proton changes into a down quark. This change is crucial because it leads to the conversion of a proton into a neutron, thus altering the nucleus's properties.
The flavor change process is facilitated by a special kind of particle interaction called the weak force. This force allows the quarks to switch types via the exchange of a force-carrying particle known as the \(W^+\) boson. The production of this boson is what allows the conversion of a quark's flavor, making quark flavor change possible and resulting in various nuclear processes.
Weak Force
The weak force is one of the four fundamental forces in nature, alongside gravity, electromagnetism, and the strong force. It's responsible for processes that involve changes at the subatomic level. Unlike the strong force, which holds the atomic nucleus together, the weak force is involved in the transformation of particles, like quark flavor change.
This interaction is essential in radioactive decay processes, such as beta plus decay, where the weak force changes an up quark into a down quark. During this event, a \(W^+\) boson is emitted and carries away the energy needed to accomplish the transformation. The weak force is unique because it can change the "identity" or "flavor" of subatomic particles while doing so, highlighting its pivotal role in nuclear reactions and the life cycle of stars.
Elementary Particles
Elementary particles are the building blocks of our universe, forming the foundation of everything we see around us. Quarks and leptons are two major families of these particles. Quarks come together to build protons and neutrons, which are the constituents of the atomic nucleus.
In beta plus decay, elementary particles like quarks and leptons come into play. When a proton undergoes \(\beta^+\) decay, an up quark in the proton changes into a down quark, resulting in the transformation of that proton into a neutron.
Meanwhile, the decay process releases a lepton, a positron, along with an almost massless neutrino. These particles emerge due to the weak force interaction and are essential for conserving energy, momentum, and other properties during the decay process.
Radioactive Decay
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This could be particles, electromagnetic waves, or a combination of both. Beta decay, including beta plus decay, is a specific type of radioactive decay where particles like electrons or positrons are emitted from an atomic nucleus.
In beta plus decay, a proton within the nucleus is converted into a neutron. During this conversion, a positron (the beta plus particle) and a neutrino are emitted. Such emissions take place because nuclei seek more stable configurations, often by rebalancing the proportion of protons to neutrons. This process reduces the nuclear mass energy level, leading to more stable isotopic forms. Understanding radioactive decay is vital as it has significant implications across various fields, including medicine, archaeology, and energy.

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Most popular questions from this chapter

Pair Annihilation. 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 eqnal, but slow, 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 galaxy in the constellation Pisces is 5210 Mly from the earth. (a) Use the Hubble law to calculate the speed at which this galaxy is receding from earth. (b) What redshifted ratio \(\lambda_{0} / \lambda_{s}\) is expected for light from this galaxy?

Proton Decay. Proton decay is a feature of some grand unification theories. One possible decay could be \(\mathbf{p}^{+} \rightarrow \mathbf{e}^{+}+\pi^{0}\) , which violates both baryon and lepton number conservation, so the proton lifetime is expected to be very long. Suppose the proton half-life were \(1.0 \times 10^{18} \mathrm{y}\) . (a) Calculate the energy deposited per kilogram of body tissue (in rad) due to the decay of the protons in your body in one year. Model your body as consisting entirely of water. Only the two protons in the hydrogen atoms in each \(\mathrm{H}_{2} \mathrm{O}\) molecule would decay in the manner shown; do you see why? Assume that the \(\pi^{0}\) decays to two \(\gamma\) rays, that the positron annihilates with an electron, and that all the energy produced in the primary decay and these secondary decays remains in your body. (b) Calculate the equivalent dose (in rem) assuming a RBE of 1.0 for all the radiation products, and compare with the 0.1 rem due to the natural background and the 5.0 -rem guideline for industrial workers. Based on your calculation, can the proton lifetime be as short as \(1.0 \times 10^{18} \mathrm{y} ?\)

The magnetic field in a cyclotron that accelerates protons is 1.30 T. (a) How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.) (b) The maximum radius of the cyclotron is 0.250 \(\mathrm{m}\) . What is the maximum speed of the proton? (c) Through what potential difference would the proton have to be accelerated from rest to give it the same speed as calculated in part (b)?

The quark content of the neurron is udd. (a) What is the quark content of the antineutron? Explain your reasoning. (b) Is the neutron its own antiparticle? Why or why not? (c) The quark \(k\) content of the \(\psi\) is \(c\) . Is the \(\psi\) its own antiparticle? Explain your reasoning.

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