/*! 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 83 The proton collision that create... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 27: Problem 83

The proton collision that creates the pion also creates a gamma-ray photon traveling in the same direction as the pion. The photon will get to the medical bay first because it is moving faster. What is the speed of the photon in the pion鈥檚 reference frame? A. 0.00005c B. 0.5c C. 0.99995c D. c

Short Answer

Expert verified
The speed of the photon in the pion鈥檚 reference frame is 'c'.

Step by step solution

01

Understanding the Theory of Relativity and the Speed of Light

According to the theory of relativity, the speed of light, denoted by the letter 'c', is a cosmic speed limit 鈥� it can't be exceeded, and it's the same for all observers, regardless of their state of motion. This means that from any reference frame 鈥� whether that's someone standing still on Earth or a pion speeding along in a collision event 鈥� the speed of light is always 'c'.
02

Applying the Theory of Relativity to the Given Scenario

In this specific scenario, the speed of the photon is being measured from the pion's reference frame. As established above, the theory of relativity tells us that even if the pion were moving at nearly the speed of light itself, it would still observe the photon's speed as 'c', the same speed any other observer would measure.
03

Identifying the Correct Answer

By understanding and applying the theory of relativity, the speed of the photon in the pion's reference frame is still 'c'. Hence, the correct answer is D: 'c'.

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.

Speed of Light
The speed of light in a vacuum is a fundamental constant of nature, represented by the symbol 'c'. It measures approximately 299,792,458 meters per second.
This speed is crucial in physics because it sets the upper limit for how fast information and matter can travel in the universe.
The importance of 'c' can't be overstated, as it forms the basis of Einstein's theory of relativity. A key feature of light speed is that it's the same in all inertial frames of reference, no matter the motion of the source or observer.
  • This means that whether you are moving toward a light source or away from it, you will measure the light's speed as 'c'.
  • Its constancy underlines many relativistic effects, such as time dilation and length contraction.
Reference Frame
A reference frame is like a viewpoint from which the motion and location of objects are observed and measured. It involves a coordinate system that helps define where things are.
Understanding reference frames is essential in physics, especially in relativity, because different observers may see events happening at different speeds or in different orders, depending on their state of motion.
When we talk about reference frames in the context of relativity, it's useful to remember two principles:
  • Inertial frames of reference involve observers who are not experiencing acceleration. They move at constant velocity relative to each other.
  • Non-inertial frames involve accelerating observers.
In special relativity, the key takeaway is that the laws of physics, including the speed of light, are the same in all inertial frames.
Photon
Photons are the fundamental particles of light. They are massless, which allows them to travel at the ultimate speed limit 鈥� the speed of light, 'c'.
Photons are unique in that they do not experience time or distance as objects with mass do.
Their properties make them essential in understanding not just optical phenomena, but also the forces that hold atoms together.
  • Photons have no electric charge.
  • They can possess different energies, which we perceive as different colors of light.
  • Despite being mathematical constructs, they are very real, influencing everything from photosynthesis to quantum mechanics.
Cosmic Speed Limit
The term "cosmic speed limit" is often used to describe the upper speed boundary set by the speed of light in a vacuum. This limit is one of the most intriguing aspects of Einstein's theory of relativity.
No object with mass can reach or exceed this speed, as it would require infinite energy.
This cosmic speed limit has profound implications for our understanding of the universe, constraining how quickly signals can travel and thereby influencing causality.
  • The speed of light acts as the ultimate speed that anything in our universe can achieve.
  • This limit helps ensure that cause precedes effect in observable events.
  • It highlights the connection between time and space, as described by the spacetime continuum.

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

Jose is looking to the east. Lightning bolt 1 strikes a tree 300 m from him. Lightning bolt 2 strikes a barn 900 m from him in the same direction. Jose sees the tree strike 1.0 ms before he sees the barn strike. According to Jose, were the lightning strikes simultaneous? If not, which occurred first and what was the time difference between the two?

A quarter-pound hamburger with all the fixings has a mass of 200 g. The food energy of the hamburger (480 food calories) is 2 MJ. a. What is the energy equivalent of the mass of the hamburger? b. By what factor does the energy equivalent exceed the food energy?

Subatomic particles called pions are created when protons, acceler ated to speeds very near \(c\) in a particle accelerator, smash into th nucleus of a target atom. Charged pions are unstable particles the decay into muons with a half-life of \(1.8 \times 10^{-8}\) s. Pions have bee imvestigated for use in cancer treatment because they pass throug tissue doing minimal damage until they decay, releasing significar energy at that point. The speed of the pions can be adjusted so the the most likely place for the decay is in a tumor. Suppose pions are created in an accelerator, then directed int a medical bay \(30 \mathrm{m}\) away. The pions travel at the very high spee of \(0.99995 c .\) Without time dilation, half of the pions would hav decayed after traveling only \(5.4 \mathrm{m},\) not far enough to make it \(\mathrm{t}\) the medical bay. Time dilation allows them to survive long enoug to reach the medical bay, enter tissue, slow down, and then deca where they are needed, in a tumor. 81\. I What is the half-life of a pion in the reference frame of th patient undergoing pion therapy? A. \(1.8 \times 10^{-10} \mathrm{s}\) B. \(1.8 \times 10^{-8} \mathrm{s}\) C. \(1.8 \times 10^{-7} \mathrm{s}\) D. \(1.8 \times 10^{-6} \mathrm{s}\)

Your 1000-m-long starship has warning lights at each end that, to you, flash simultaneously every minute. You are moving directly away from the planet Zerkon at 0.70c. To a Zerkonian, do the lights flash simultaneously? If not, which flashes first the light at the front of your ship or the trailing one?

You are on a spacecraft traveling away from the earth at 0.50c. A beacon on earth flashes exactly once per second. a. From the point of view of a person on earth, what is the time between one flash reaching your ship and the next? b. From your point of view, what is the time between one flash reaching your ship and the next?
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Modern Physics

Read Explanation

Magnetism

Read Explanation

Thermodynamics

Read Explanation

Electromagnetism

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.