Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks

Exams
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology

EXAM TYPES

GCSE

IGCSE

AS

A Level

International A Level

University Admissions Tests

GCSE SUBJECTS

GCSE 1

GCSE 2

GCSE 3

GCSE 4

GCSE 5

SOME-TEXT

IGCSE SUBJECTS

IGCSE 1

AS SUBJECTS

AS 1

A Level SUBJECTS

A Level 1

International A Level SUBJECTS

International A Level 1

University Admissions Tests SUBJECTS

University Admissions Tests 1
Features
Features

Discover all of these amazing features with a free account.

Flashcards

Vaia AI

Notes

Study Plans

Study Sets
What’s new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
Resources
Discover

All the hacks around your studies and career - in one place.

Find a job

Find a degree

Student Deals

Magazine

Mobile App
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

Job Board
The largest student job board with the most exciting opportunities.

Vaia Deals
Verified student deals from top brands.

Our App
Discover our mobile app to take your studies anywhere.

Go to App

Learning Materials

Features

Discover

Chapter 36: Q. 38 (page 1060)

At what speed, as a fraction of $c$ , must an electron move so that its total energy is $10 %$ more than its rest mass energy?

Short Answer

Expert verified

$v = 1.24 \times 10^{8} m / s$

Step by step solution

01

Given Information

We have given that, $c = 3 \times 10^{8} m / s$

Total energy is $10 %$ more.

02

Simplify

Given values are: $c = 3 \times 10^{8} m / s$ and total energy is $10 %$ more.

To find the speed $v$ , we use the below given formula.

role="math" localid="1649826808978" $\frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = m c^{2} + 10 % of m c^{2}$

Now, put the given values in the above formula to find the speed.

$\frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = m c^{2} + 0.1 \times m c^{2} \frac{m c^{2}}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = 1.1 m c^{2} \frac{1}{\sqrt{(1 - \frac{v^{2}}{c^{2}})}} = 1.1 \sqrt{(1 - \frac{v^{2}}{c^{2}})} = \frac{1}{1.1} 1 - \frac{v^{2}}{c^{2}} = \frac{1}{1.21} \frac{v^{2}}{c^{2}} = \frac{0.21}{1.21} v^{2} = c^{2} \cdot \frac{21}{121} v = c \cdot \sqrt{\frac{21}{121}} v = 1.24 \times 10^{8} m / s$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Particle A has half the mass and twice the speed of particle B. Is the momentum $p_{A}$ less than, greater than, or equal to $p_{B}$ ? Explain.

At what speed, as a fraction of $c$ , is a particle’s total energy twice its rest energy?

A ball of mass m traveling at a speed of $0.80 c$ has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass $2 m$ departs the collision with a speed of $0.40 c$ . Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.

a. What is $γ_{p}$ , written as a fraction like a/b?

b. What is the initial total momentum? Give your answer as a fraction times $m c$ .

c. What is the initial total energy? Give your answer as a fraction times $m c^{2}$ . Don’t forget that there are two balls.

d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is $2 m$ . Instead, let the final state of the system be an unknown mass $M$ traveling at an unknown speed $u_{f}$ . You have two conservation laws. Find $M$ and $u_{f}$ .

The half-life of a muon at rest is $1.5 μ s$ . Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of $7.5 μ s$ .

a. What is the speed, as a fraction of $c$ , of the muons in the storage ring?

b. What is the total energy of a muon in the storage ring? The mass of a muon is $207$ times the mass of an electron.

An out-of-control alien spacecraft is diving into a star at a speed of $1.0 \times 10^{8} m / s$ . At what speed, relative to the spacecraft, is the starlight approaching?

See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Wave Optics

Read Explanation

Measurements

Read Explanation

Astrophysics

Read Explanation

Particle Model of Matter

Read Explanation

Energy 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.

Sign-up for free