/*! 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 50 The rest energy of an electron i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 50

The rest energy of an electron is \(0.511 \mathrm{MeV} .\) What momentum (in MeV/c) must an electron have in order that its total energy be 3.00 times its rest energy?

Short Answer

Expert verified
Answer: The momentum of the electron is approximately 1.44 MeV/c.

Step by step solution

01

Write down the relativistic energy-momentum relationship

The relativistic energy-momentum relationship is given by: E虏 = (mc虏)虏 + (pc)虏 where E is the total energy, m is the mass, c is the speed of light, and p is the momentum.
02

Express the total energy in terms of rest energy

We are given that the total energy is 3 times the rest energy, so we can write: E = 3mc虏
03

Substitute the total energy expression into the energy-momentum relationship

Now, substitute the total energy expression into the energy-momentum relationship: (3mc虏)虏 = (mc虏)虏 + (pc)虏
04

Solve the equation for momentum (p)

To find the momentum, we can rearrange the equation and solve for p: (3mc虏)虏 - (mc虏)虏 = (pc)虏 (8m虏c鈦�) = (pc)虏 p = \sqrt{8m虏c虏}
05

Substitute the values and calculate the momentum

Now we can substitute the given rest energy value and the speed of light to find the momentum in MeV/c: Rest energy (E鈧�) = 0.511 MeV c = 1 (when working in units of MeV/c) E鈧� = mc虏 m = \frac{E鈧�}{c虏} = \frac{0.511}{(1)虏} = 0.511 Now, substitute these values into the momentum equation: p = \sqrt{8(0.511)虏} p 鈮� 1.44 \, MeV/c The momentum of the electron when its total energy is 3 times its rest energy is approximately 1.44 MeV/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!

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

The Tevatron is a particle accelerator at Fermilab that accelerates protons and antiprotons to high energies in an underground ring. Scientists observe the results of collisions between the particles. The protons are accelerated until they have speeds only \(100 \mathrm{m} / \mathrm{s}\) slower than the speed of light. The circumference of the ring is \(6.3 \mathrm{km} .\) What is the circumference according to an observer moving with the protons? [Hint: Let \(v=c-u\) where $v \text { is the proton speed and } u=100 \mathrm{m} / \mathrm{s} .$]
A neutron, with rest energy 939.6 MeV, has momentum 935 MeV/c downward. What is its total energy?
Starting with the energy-momentum relation \(E^{2}=E_{0}^{2}+\) \((p c)^{2}\) and the definition of total energy, show that $(p c)^{2}=K^{2}+2 K E_{0}[\mathrm{Eq} .(26-11)]$.
A spaceship is moving away from Earth with a constant velocity of \(0.80 c\) with respect to Earth. The spaceship and an Earth station synchronize their clocks, setting both to zero, at an instant when the ship is near Earth. By prearrangement, when the clock on Earth reaches a reading of $1.0 \times 10^{4} \mathrm{s}$, the Earth station sends out a light signal to the spaceship. (a) In the frame of reference of the Earth station, how far must the signal travel to reach the spaceship? (b) According to an Earth observer, what is the reading of the clock on Earth when the signal is received?

A body has a mass of \(12.6 \mathrm{kg}\) and a speed of \(0.87 c .\) (a) What is the magnitude of its momentum? (b) If a constant force of \(424.6 \mathrm{N}\) acts in the direction opposite to the body's motion, how long must the force act to bring the body to rest?
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Nuclear Physics

Read Explanation

Mechanics and Materials

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Engineering Physics

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.