/*! 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 29 Physicists have proposed a parti... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 29

Physicists have proposed a particle called the Higgs particle, which would explain why other particles have the masses they do. If the Higgs' rest energy is \(150 \mathrm{GeV},\) what's the range of the force it mediates?

Short Answer

Expert verified
The range of the force mediated by the Higgs particle is approximately \(1.316 \times 10^{-18}\text{ m}\.\)

Step by step solution

01

Identifying What's Given

We are given the rest energy of the Higgs particle, which is \( E = 150 \text{ GeV} \). We need to find the range of the force it mediates.
02

Understanding the Relationship Between Energy and Force Range

The range \( R \) of a force mediated by a particle is determined by its rest energy \( E \) using the following principle: \( R = \frac{\hbar c}{E} \), where \( \hbar \) is the reduced Planck's constant \( 1.0545718 \times 10^{-34} \text{ Js} \), and \( c \) is the speed of light \( 3 \times 10^8 \text{ m/s} \). It's also important to convert energies from GeV to Joules (1 GeV = 1.60218 脳 10^{-10} Joules).
03

Converting Energy from GeV to Joules

Convert the Higgs particle's rest energy to joules: \[150 \text{ GeV} = 150 \times 1.60218 \times 10^{-10} \text{ J} = 2.40327 \times 10^{-8} \text{ J}.\]
04

Calculating the Range of the Force

Using the formula for force range, calculate it:\[R = \frac{\hbar c}{E} = \frac{1.0545718 \times 10^{-34} \times 3 \times 10^8}{2.40327 \times 10^{-8}}\]Simplify the calculation:\[R \approx \frac{3.1637154 \times 10^{-26}}{2.40327 \times 10^{-8}} = 1.316 \times 10^{-18}\text{ m}.\]
05

Understanding the Result

The calculated range represents the effective range of the force mediated by the Higgs particle. This range is extremely small, consistent with the short-range interactions of massive force carriers like the Higgs boson.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Force Range and Its Calculation
When we talk about the range of a force mediated by a particle like the Higgs boson, we mean how far the influence of that particle's force can extend. The range is primarily determined by its rest energy, which makes sense as more energetic particles can influence regions further away鈥�.

To calculate the range, we use the formula:
  • \[ R = \frac{\hbar c}{E} \]
where:
  • \( R \) is the force range,
  • \( \hbar \) is the reduced Planck's constant, \( 1.0545718 \times 10^{-34} \text{ Js} \),
  • \( c \) is the speed of light, \( 3 \times 10^8 \text{ m/s} \),
  • \( E \) is the rest energy of the particle, here given in GeV but often required to be converted into Joules for this calculation.
The range is typically very small for massive particles like the Higgs, suggesting that these particles influence only very short distances. Understanding force range is crucial as it describes the interaction scale in the universe.
Rest Energy and Higgs Particle
The concept of rest energy is a fundamental aspect of modern physics and relates to the energy a particle possesses even when not in motion. For the Higgs boson, the rest energy is given as 150 GeV.鈥�

To understand its significance:
  • Rest energy demonstrates why particles have mass.
  • This energy is a result of the relation prescribed by Einstein's famous equation, \( E=mc^2 \), showing how mass and energy are interchangeable.
  • A higher rest energy implies a more massive particle, which in turn implies shorter force range due to the inverse relationship in the formula for force range.
The Higgs boson, by introducing rest energy, gives mass to other particles, explaining how they acquire it. This understanding is central to the standard model of particle physics.
Understanding Planck's Constant
Planck's constant is a well-known fundamental constant in quantum mechanics, representing the quantization of physical properties, such as energy. It is intimately connected to many fundamental processes, including the definition of the force range.鈥�

The reduced form of Planck鈥檚 constant, represented as \( \hbar \), is used in many physics equations, including:
  • \( \hbar = \frac{h}{2\pi} \)
  • It is used to calculate the range of forces mediated by particles, showing how quantum mechanics governs these processes.
  • The value of \( \hbar \) is \( 1.0545718 \times 10^{-34} \text{ Js} \), a tiny number that nonetheless has huge implications in the micro-world.
Understanding and using Planck's constant helps physicists connect the behavior of particles, like the Higgs, with their apparent energy and mass properties.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To use high-energy particles as probes of other subatomic particles, the probe particles' de Broglie wavelength must be comparable to the distance being probed. Suppose you want to probe an elementary particle on a distance scale of about \(1.0 \times 10^{-18} \mathrm{~m} .\) Find the kinetic energy of \((\mathrm{a})\) a proton and \((\mathrm{b})\) an electron used to probe this distance scale.

In \(\beta^{-}\) decay, the particles produced are an electron and (a) a neutrino; (b) an antineutrino; (c) a photon; (d) a proton.

The predominant constituent of the universe is (a) ordinary matter, (b) dark matter, (c) dark energy.

Explain the origin of the cosmic microwave background.

Which one of the following reactions is allowed? (a) \(\mu^{-}+\) \(p \rightarrow n+\bar{\nu}_{\mu} ;\) (b) \(\mu^{-}+p \rightarrow n+\nu_{\mu}\) (c) \(e^{-}+p \rightarrow n+\bar{\nu}_{e}\) (d) \(\mu^{-} \rightarrow n+e^{-}+\bar{\nu}_{\mu}+\nu_{e}\).
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Thermodynamics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electrostatics

Read Explanation

Electricity and Magnetism

Read Explanation

Famous Physicists

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.